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HANDBOOK FOR 
HIGHWAY ENGINEERS 



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McGraw-Hill BookCompany 

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Electrical World The Engineering andMining Journal 
Engineering Record , Engineering News 

Railway Age G aze tte American Machinist 

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HANDBOOK 

FOR 

HIGHWAY ENGINEERS 

CONTAINING INFORMATION 
ORDIN\RILY USED IN THE DESIGN AND CONSTRUC- 
TION OF ROADS WARRANTING AN EXPENDITURE 
OF $5,000 TO $30,000 PER MILE 

PART I. Principles of Design. 
PART II. Practice of Design and Construction 

BY 

WILSON G. HARGER, C.E. 

First Assistant Engineer, New York State Department of High- 
ways; Associate Member American Society of Civil Engineers 

AND 

EDMUND A. BONNEY 

Supervising Engineer, New York State Department 
of Highways 



SECOND EDITION 

Entirely Revised and Enlarged 

First Impression 



McGRAW-HILL BOOK COMPANY, Inc. 
239 WEST 39TH STREET, NEW YORK 

LONDON: HILL PUBLISHING CO., Ltd. 

6 & 8 BOUVERIE ST., E.C 

I916 



1"^! 



^ 



H^ 



«.* 



Copyright, 1912, 1916, by the McGraw-Hill Book Company, Inc. 



F/iOT EDITION 

First Impression, August, 191 2 
Second Impression, September, 191 3 



SECOND EDITION 
First Impression, June, 1916 




JUL 21 1916 



CI.A4311M2 






PREFACE TO SECOND EDITION 



Since the publication of the first edition of this book four years 
ago, considerable progress has been made in the practice of road 
design and construction. To meet this advance, this handbook has 
been revised by bringing the material on top courses up-to-date, 
and by adding considerable data on tests, designs, costs, mainte- 
nance and specifications. Not only has much of the old material 
been revised, but new material, totaling approximately ioo pages, 
has been added. The criticisms and suggestions of many who have 
used the book in the field and office have aided the authors in this 
revision. 

A more complete and systematic index has been prepared by Mr. 
Percy Waller. 

The general arrangement of the book remains untouched. 

W. G. H. 
E. A. B. 

Rochester, N.Y., May, 1916. 



PREFACE TO FIRST EDITION 

The purpose of this book is to collect, in a compact and conven- 
ient form, information ordinarily required in the field and office 
practice of road design and construction. 

The book is designed to meet the requirements of both experienced 
and inexperienced road men. The material on the relative impor- 
tance of the different parts of the design, and the possibilities of 
economy, without impairing the efficiency of the road, are primarily 
for the inexperienced engineer. The collection of cost data and the 
tables will be useful to any one engaged in road work. 

As it is difficult to avoid clerical errors and mistakes in proof- 
reading in first editions, we shall appreciate the cooperation of read- 
ers in calling our attention to any errors. 

W. G. H. 
E. A. B. 

Rochester, N.Y., April, 19 12. 



TABLE OF CONTENTS 

PART I 

PAGE 

Introductory i 

General 1-3 

Chapter I. Grades and Alignment 4-18 

Maximum Grades 

Relative importance of automobile and horse traffic in 

the selection of grades 4 

Difficulty of ascent and ease and safety of descent ... 6 

The theoretical grades that fulfil certain traffic require- 
ments and the practical considerations which govern 

the selection n 

The construction of ruling grades 12 

Minimum Grades 

On score of drainage 12 

Level grades 12 

Intermediate Grades 

Economy of earthwork 13 

Short grades 13 

Reverse vertical curves 13 

Conditions intermediate grades must fulfil 13 

Common mistakes in designing 13 

Alignment 

Minimum radius of curvature 18 

Utilization of old roadbed 18 

Sight distance 18 

Chapter II. Sections 19-32 

Conditions they must fulfil 19 

Premises of Design 

Crowns 19 

Shoulder slope 19 

Width of metaling 20 

Width of shoulder 21 

Depth of ditch 21 

Economies effected by a judicious selection 22 

Examples of sections in current use 23 

Discussion of widths 28 

Shoulder treatment 29 



viii CONTENTS 

Chapter III. Drainage 33-60 

Culverts 

Kinds used 33 

Self-cleaning velocities 33 

Determination of size 34 

From existing structures 34 

By maximum run-off formulae 34 

Discharge capacity of small culverts 38 

Side culverts 38 

Village culverts . " 39 

Small-span Bridges 

Determination of span . 39 

Scour 40 

Stream velocities 40 

Examples of small-span bridges 41 

Examples of small culverts . . . . 41 

Under Drainage 

Side and center drains 52 

Styles of construction 52 

Design of outlet 53 

Tables of weights of cast-iron pipe 54 

Mesh reinforcement 55 

Reinforcing bars 56 

Cost of small culverts 58 

Properties of I-beams 59 

Chapter IV. Foundations for Broken Stone Roads. 61-73 

The bearing power of different soils 61 

Concentrated wheel loads on improved roads .... 62 
The distributing action of foundation courses and the 

depth required for different soils 63-64 

Examples of styles of construction in use 65 

The distribution of stone in foundations 70 

Special cases 71 

Chapter V. Top Courses and their Maintenance . 74-108 

Waterbound macadam 74 

Waterbound macadam with surface treatment .... 76 

Bituminous macadam 78 

Rock asphalt 82 

Amiesite 82 

Brick pavements S3 

Asphalt block 85 

Stone block pavements 85 

Concrete pavements 87 

Small stone cube pavements 91 

McClintock cube pavements 92 

Rocmac 94 



CONTENTS ix 

Maintenance 

General Discussion 96 

Summarized costs 103 

Typical detail costs 105 

Summary of yearly costs 108 

Chapter VI. Minor Points 109-117 

Guard-rail 

Wooden . 109 

Concrete . no 

Retaining Walls • 

Plain .....in 

Reinforced in 

Toe walls 113 

Curbs 

Concrete 113 

Stone 113 

Guide signs 114 

Danger signs 114-115 

Cobble gutters • 115-116 

Brick gutters, etc 116 

Catch basins 116 

Grates 116 

Riprap 117 

Dykes 117 

Repointing old masonry 117 

Facing old abutments 117 

Chapter VII. Materials 1 18-143 

Top course, macadam stone 118 

Screenings 128 

Bottom course, macadam stone 129 

Fillers 129 

Brick 129 

Bituminous binders 130 

Concrete materials 141 

PART II 

Chapter VIII. The Survey 144-205 

Center line 144 

Levels and cross-sections 146 

Drainage 149 

Topography 150 

Traffic reports 151 

Foundation soils 151 

Location and character of materials 152 



X CONTENTS 

Right of way 154 

Stadia reduction tables 156 

Diversion lines 164 

Adjustment of instruments 164 

Curve tables and formulae 166 

Examples of curve problems 199 

Chapter IX. Office Practice 206-265 

Mapping the Preliminary Survey 

Scales 206 

Plotting center line 206 

Table of sight distances 208 

Plotting topography 208 

Bench level computations 208 

Cross-section levels, computations 209 

Plotting cross-sections 209 

Plotting profile 209 

The Design 

Preliminary report 210 

Shrinkage of earthwork 219 

Templets 220 

Economical grade line 221 

Vertical curves 223 

Formulae 223 

Sight distance 225 

Planimeter work ) . . . . 226 

Methods 226 

Accuracy 226 

Computation of earthwork 227 

Overhaul 250 

Mass diagram 253 

Macadam 255 

Concrete * 255 

Minor features 255 

Final design report 255 

Construction plans 257 

Miscellaneous Points 

Grade line over railroad grade crossings 258 

Clearances for railroad grade crossing eliminations . . 258 

Computation of right-of-way areas 262 

Parabolic crowns 262 

Summary of economical design 263 

Chapter X. Cost Data and Estimates 266-338 

Macadam Roads 266 

Earth excavation 266 

Rock excavation 266 

Unloading broken stone 268 



CONTENTS xi 

Hauling 269 

Loading fence stone 271 

Spreading crushed stone 271 

Placing boulder stone 272 

Ratio of loose to rolled depths 272 

Amounts of filler and binder 272 

Loading filler sand 273 

Spreading filler and binder 273 

Rolling 273 

Crushing 

Cost of 274 

Proportions of different sizes in output 275 

Sledging boulders for crusher 278 

Dustless screenings 280 

Stone fill, bottom course 281 

Sub-base, bottom course 281 

Applying residuum bituminous binder 281 

Kentucky rock asphalt 283 

Puddling waterbound roads . 283 

McClintock cube surfacing 284 

Amiesite 285 

Hassam concrete pavement 288 

Mixed concrete pavement 288-303 

Asphalt block 293-291 

Concrete culvert work 302-305 

Guard-rail 306 

Wooden 306 

Concrete 306 

Cobblestone gutter 307 

Vitrified pipe 307 

Speed of work 308 

Plant and pay-roll 309 

Forms of estimate 312 

Sample estimate, macadam construction 318 

Unit price, minor items 320 

Brick Pavement on Country Roads ........ 327 

Excavation 327 

Concrete base 327 

Preparing sand cushion 328 

Laying brick 329 

Grouting brick 329 

Expansion joints 329 

Edging^ . 330 

Unloading brick 330 

Hauling brick 330 

Form of estimate 331 

Sample estimate 331 

Maintenance and repair 332 

Cold oiling 333 

Calcium chloride 334 



xii CONTENTS 

Recapping 335 

Scarifying and reshaping 335 

Patrol maintenance, New York State 337 

Automobile maintenance truck 337 

Distribution of maintenance costs 338 

Chapter XL Notes on Construction 339-371 

Staking out 339 

Rough grading 341 

Fine grading 343 

Sub-base 345 

Bottom stone 346 

Top course 348 

Hassam concrete 350 

Mixed concrete 350 

Sheet asphalt, etc 351 

Brick roads 354 

Culverts • . . . 358 

Chapter XII. Specifications 372-458 

Materials 

Cement 372 

Concrete aggregate 374 

Stone gravel, etc., for pavements •. 376 

Bituminous materials 377-389 

Brick . 390 

. Stone block 396 

Cast iron pipe 398 

Reinforcements 398 

Tiles 400 

Timber . 400 

Methods of Construction 

Clearing and grubbing 401 

Excavation . 401 

Overhaul 404 

Tiles and under drains 405 

Leaching basins 405 

Catch basins 406 

Cast iron pipe 407 

Stone fill 408 

Piles 408 

Timber and lumber 409 

Riprap 409 

Concrete masonry 410 

Stone masonry 414 

Stone curbing 415 

Concrete curbing 416 

Concrete edging 417 



CONTENTS xiii 

Cobble gutters 417 

Concrete gutters 418 

Brick gutters 418 

Concrete reinforcement 418 

Guard rail 420 

Guide signs 421 

Sign posts 422 

Loose stone 423 

Sub-base 423 

Telford base 424 

Bottom courses 425 

Concrete foundation 427 

Top courses macadam 428 

Scarifying and reshaping 431 

Bituminous surface treatments . 432 

Bituminous macadams 433 

Bitulithic 439 

Amiesite 441 

Hassam concrete pavement . . • 442 

Mixed concrete pavement 443 

Glutrin 445 

Wood block 446 

Asphalt block 449 

Brick 451 

Medina sandstone block 456 

General tables and formulae 459-589 

Appendix A 

Traffic rules and regulations of the State of Ohio . . . 591 

Traffic regulations State of New York 602 



LIST OF TABLES 

PAGE 

i. Ruling grades in present use 5 

2. Tractive effort of a team of horses 6 

3. Effect of tire width on tractive resistance 7 

4. Effect of size of wheel on tractive resistance .... 8 

5. Effect of tire width on tractive resistance 9 

6. Rolling resistance on different surfaces 10 

7. Maximum loads on improved and dirt roads .... 10 

8. Amount of excavation on improved roads 14 

9. Maximum and usual widths of traveled way .... 20 

10. Maximum run-off, small watersheds 34 

n. N. Y. C. &H. R. R. culvert sizes, small drainage areas 35 
1 1 a. Iowa State Highway Commission culvert sizes, small 

aieas 35 

12. Run-off small areas, village streets ^ 37 

13. Discharge capacity, small culverts 38 

14. Weights, cast-iron pipe 54 

15. Mesh reinforcement 55 

16. Reinforcing steel bars -. 56 

17 Approximate cost small concrete and C. I. P. culverts . 58 

18. Properties of Cambria I-beams 59 

19. Sizes of stone, Telford foundations 70 

20. Loss of crown on macadam roads 75 

21. Properties of road rocks 122 

22. Properties of road rocks 123 

23. Properties of road rocks .... 123 

24. Geological classification of road rocks 125 

25. Composition of tar products 131 

25 a. Analysis of crude coke-oven tars . . . . . . .132 

26. Composition of crude petroleum and petroleum residuums 136 

27. Effect of cross-section interval on quantities of excava- 

tion . 147 

28. Stadia reduction table . . . . 156 

29 Curve table, radii and deflections 167 

30. Tangents and externals, one-degree curve 170 

31. Sight distance on curves in cut 208 

32. Shrinkage of excavation in fill 220 

33. Radii of vertical curves 225 

34. Sight distance, vertical curves 225 

35. Table of volumes, 50' cross-sections . . * 228 



xvi LIST OF TABLES 

36. Conversion table, cubic feet to cubic yards 230 

37. Table of volumes for preliminary estimates 238 

38. Conversion table, feet to miles 251 

39. Weights of crushed stone per 100' of road different 

widths and loose depths 252 

40. Number of cu. yds. macadam per ioo' of road . . . . 255 

41. Number of sq. yds. per 100' road, different widths . . . 263 

42. No. gals, bitumen per 100' road, different rates per sq. yd. 264 

43. Cost of earth excavation 267 

44. Cost of hauling broken stone 270 

45. Cost of spreading broken stone 272 

46. Ratio of loose to rolled stone depths 272 

47. Amounts of filler and binder per cu. yd 272 

48. Proportion of sizes, crusher output 275 

49. Amount of materials for concrete 304 

50. Speed of work, value of plant, force account .... 308 

51. Cost of cold oiling ^^^ 

52. Amounts of filler (spacing of loads) 347 

53. Steam temperatures for heating bituminous materials . 349 

54. Amounts of materials for culverts 361 

General Tables and Formulae 

55. Conversion table of weights and measures 459 

56. Decimal equivalent of inches 460 

57. Areas and volumes 462 

58. Table of squares, cubes, square roots, and cube roots . 464 

59. Trigonometric functions and solution of triangles . . . 478 

60. Tables of natural sines, cosines, tangents, etc 479 

61. Logarithms of numbers 514 

62. Logarithmic sines, cosines, tangents, and cotangents 540 

63. Weights of materials 584^ 

64. Strength of materials 585* 

65. General flexure formulae, bending moments, etc. . . . 586 

66. Centers of gravity for ordinary shapes . . . . . . 588 

67. Moments of inertia of ordinary shapes 589 



HANDBOOK FOR HIGHWAY ENGINEERS 

PART I. THEORY OF DESIGN 
INTRODUCTORY 

The necessity for the permanent improvement of the main country 
roads has been so well recognized by all the States that the work 
promises in a few years to equal in magnitude that of Railroad, 
Canal, and River transportation. 

Highway construction has increased so rapidly that there are 
not enough experienced engineers to handle it. Most of the de- 
partments have been forced to use untrained men and have tried 
to make their plans "fool-proof" by standardizing the designs in 
detail. Road work is peculiarly unfitted for such treatment, as an 
appropriate and economical design often calls for changes every ioo 
feet and too much Standardization has resulted in a waste of 
money and unsatisfactory plans. 

The general public still believes that the work requires only common- 
sense and that the money spent on engineering is wasted; even in 
the Road Departments, many of the men take this view, but it is a 
relic of the old "hit or miss" style of town-road construction. There 
is no doubt that money judiciously spent in engineering is justified 
by the resultant saving in total cost; there is also no doubt that 
much of the money spent in so-called engineering is absolutely wasted. 
In order to handle satisfactorily the work already in sight, we must 
have a larger force of technically trained roadmen, who realize the 
importance of the problem as an engineering problem, and who 
understand that a good design depends on them and not on a mechani- 
cal use of Standards. As soon as such a force is developed we can 
do justice to the roads. 

GENERAL 

Highways are improved to reduce the cost of hauling and to in- 
crease the safety and ease of light traffic. The parts of the design 
are more or less important in proportion to their necessity for the 
fulfilment of these purposes, and may be ranked as follows : 
i. Selection of Roads 
2. Grades and Alignment 
, 3. Cross Sections 

4. Drainage 

5. Foundations 

6. Top Courses 

7. Minor Details 

The Selection of Roads to improve is a matter of broad policy „ 
it becomes an engineering question only when a number of roads 



2 THEORY OF DESIGN 

serve the same district, in which case the considerations of grade and 
economy govern. 

Grades, Alignment, and Section are the most permanent features 
of an improvement. The ruling grade largely controls the maximum 
load that can be hauled; section and grade combined determine the 
convenience of the road and the economy of earthwork, while align- 
ment and section affect the safety and are also important factors in 
the appearance of the highway. For these reasons these three points 
can be ranked as equal and first in importance. 

Drainage, Foundation Stone, and the Top Course keep the section 
intact and firm under heavy traffic. The bearing power of the sub- 
grade and shoulders is increased by the surface and subsurface 
drainage; the concentrated wheel loads of heavily loaded vehicles 
are spread over a safe area of subgrade by the foundation stone; 
the top course provides a surface that will withstand the abrasive 
action of wheels and horse-shoes, that gives a good footing and offers 
slight rolling resistance. At the present time the problem of the top 
course is more troublesome than all the other points combined, and 
various new styles of construction are being tried to meet the de- 
mands of both automobile and horse traffic. There is so much discus- 
sion of this one feature that it is easy to give it too much weight, and 
there is a tendency to economize on the more permanent and impor- 
tant parts of the design in order to get a higher grade top course. 
In the writer's opinion this is a mistake. The different types of 
experimental top courses will be described in detail, but as yet no 
definite conclusions can be drawn. 

Minor Details 

Minor Details include guard-rail, danger signs, guide signs, and 
other points affecting the safety and general appearance of the road. 

The steps of the design will be taken up in the order of their im- 
portance as indicated on page i. 



ROAD BONDS 

Road improvements are usually paid for by long term bonds; 50 
year bonds have been very generally used. This method has been 
justly criticised as too long a term considering the fact that a large 
amount of money will be required for construction renewals before 
the original bonds expire. Serial bonds are a more rational method 
of payment. 

The following tabulation is based on the average costs per mile for 
200 miles of 16 ft. State roads in Western New York and shows the 
cost of the permanent features and temporary parts of the different 
forms of construction. 



ROAD BONDS 



* Excavation 

* Drainage Structures 

* Foundations and sub-base 

. Surfacing 

. Edging . 

. Minor points 

* Total Permanent features 

" Temporary " 
. Probable life " " 



Brick 



Cost 
per mile 



» 2 200 

700 

63OO 

I47OO 

500 

9200 

15200 



% Total 
Cost 



9.0 

2.8 

25-9 

60.1 

2.2 
37-7 
62.3 



10 to 25 years 



Bit. Mac. 



Cost 
per mile 



$1900 

700 

3300 

5900 

500 
5900 
6400 



% Total 
Cost 



Water Mac. 



Cost 
per mile 



15.9 

5-3 

27.0 

47-5 

4-3 
48.2 
51.8 



5 to 10 years 



$1900 

700 

3300 

4000 

500 
5900 
4500 



% Total 
Cost 



18.3 

6.7 

3i-7 

38.5 

4.8 

S6.7 

43-3 



5 to 10 years 



CHAPTER I 

GRADES AND ALIGNMENT 

Grades can be divided into Maximum, Minimum, and Intermediate. 
Maximum or Ruling Grades 

It is impossible to do justice to the question of ruling grades in the 
brief discussion called for by a book of this character, but the main 
points will be covered in the following order: 

i. The relative importance of automobile and horse traffic in the 
selection of grades. 

2. The difficulty of ascent and the ease and safety of descent. 

3. The theoretical grades that fulfil certain traffic requirements, 
and the practical considerations that govern the selection. 

4. The construction of ruling grades. 

1. Under favorable conditions, gasoline and electric trucks can 
haul for about $0.08 to $0.10 per ton mile, traveling empty one way, 
while the cost of team hauling cannot be reduced much below $0.16 
to $0.18. This looks like a big advantage for the trucks, but they 
are helpless on a poor foundation and their use for general purposes in 
the country is limited by bad side-roads and snow, and for produce 
hauling is confined to the short period of the year in which the crops 
are marketed. Near cities they are coming into use for milk routes, 
gardening produce, and the rural delivery of merchandise, but only 
on improved roads and only by concerns that are able to use them 
continuously enough to warrant the investment. Farmers must 
keep horses for their ordinary work and, having them, will continue 
to draw with teams. Mechanical trucking is bound to increase, but 
there seems to be no reason to believe that in the immediate future 
it will become more important than team hauling in rural districts 
and as the machines in use have sufficient power to take them up any 
firm surfaced grade that has heretofore been considered suitable for 
horse traffic, it is evident that for heavy hauling, teams still govern 
the selection of grade. 

In Europe, mechanical tractors drawing trains of farm wagons 
have been used successfully. This style of hauling will probably be 
adopted here for limited areas, but its development into general use 
is a matter of conjecture. The number of wagons drawn by one 
machine is limited to seven or eight by the difficulties at turns and 
the danger of obstructing the road, rather than by the present grades. 
Reduced grades would lessen the fuel consumption and increase the 
speed slightly, but would not materially increase the train load. 
It would seem that such a small saving for a class of traffic that is 
to be developed in the future would not warrant any reduction of 
grade below current practice. 

Light automobiles are not handicapped as much by bad roads as 
the heavy trucks; on fair roads their ability to cover long distances 
quickly makes them adapted to many uses, but they are not now 



MAXIMUM OR RULING GRADES 



and probably never will be, as effective as horses for general use under 
all conditions. The least powerful of these light machines have no 
difficulty on firm surfaced 8% to 10% grades, which eliminates them 
as a factor in determining the maximum rate. From the preceding 
statements of the present and probable future conditions of both 
light and heavy traffic it is reasonable to conclude that the horse 
and not the machine should govern the design of the Ruling Grade. 
2. Various grades on country roads have been under observation 
for so many years that it is safer to be guided by present practice 
which 13 the result of such observation, than to trust too much to a 
theoretical discussion. The adoption of the ruling grades given in 
Table i has depended partly on the ease of maintenance as well as 
the traffic considerations; the maximum grades on which different 
top courses can be safely used, either on account of foothold for horses 
or the maintenance of the surface, properly come under a discussion 
of such courses, and will be included in chapter V. 

Table i 

Ruling Grades in Foreign Countries 



Prussia , 

Hanover 

Baden 

Brunswick 

Holyrod Road in England 



Mountainous 
Districts 



Hilly 
Districts 



5 % 4 % 2\% 
4 % 3§% 2*% 
8 % 6 % s % 
S*% 4 % 3 % 

6 % 3 i% 



Military Highway 
over the Alps Italian side 

National 
Roads 



Level 
Districts 



\\% Swiss side. .6 % 



France 



3/0 



Departmental 
Roads 

4%.... 



Subordinate 
Roads 



6% 



Ruling Grades in the United States 



State 



New York . . . 
Massachusetts 
Connecticut . 
New Jersey . . 
Michigan .... 
Missouri .... 
Washington . 
Illinois 



Main Roads 


Side Roads 


Unusual Cases 


5% 


7&8% 


H% 


5% 


7% 




5% 




— 


5% 


6-7% 


9% 


6% 







5-6% 








5% 


5% 





6% 




9% 



6 GRADES AND ALIGNMENT 

European observers claim that on a stone road, 5% is the maxi- 
mum grade that can be descended safely by a trotting team without 
the application of brakes, and that 12% is the maximum that can be 
descended safely with brakes. Safe descent with brakes need not 
be considered, as it would result in a grade far beyond ordinary 
practice; safe and easy descent without brakes very evidently plays 
a part in the selection of the ruling grade, but is more important 
for light teams with a small load, traveling at a comparatively rapid 
rate, than for heavy hauling teams which rarely trot. 

The writer knows of no records of actual maximum loads that can 
be drawn up different grades by an ordinary team; it is probably 
better to discuss this point theoretically, as any experiments would 
be affected by too many variable local conditions to be worth much 
as a basis for comparison. 

A summary of Prof. I. O. Baker's discussion of maximum team 
loads is given below, and through his courtesy we are enabled to 
include a collection of tables taken from his work " Roads and 
Pavements." 

Various trials have determined that the normal tractive power of 
a horse traveling three miles per hour for ten hours a day is approxi- 
mately one tenth of its weight; that when hauling up a steep grade 
it can exert one fourth of its weight for a short time; that for a con- 
tinuous exertion of one fourth, the grade should not be over 1200 
feet long, and if over that, resting places must be provided every 600 
to 800 feet; that in starting and for a distance of 50 to 100 feet, one 
half of its weight can be used; and that the net tractive power exerted 
by a horse on a grade equals (| its weight) — (the effort required to 
lift itself) , or approximately W/4 — W X per cent of grade expressed 
in hundredths, i.e. (W/4 — 0.04W) for a 4% grade. 

Table 2 shows the effective tractive power of a team of 1 200-pound 
horses on different grades. 

Table 2 



W = Weight of team, 
2400 lbs 

P = Per cent of grade 
in hundredths 



Grade 


Level 


2i% 


4 % 


S % 


6 % 


7 % 


8 % 


9 % 


10 % 



Theoretical 
Tractive Effort 



tVW 
w/4 -PW 
w/4 -PW 
w/4 -PW 
w/4 -PW 
w/4 -PW 
w/4 -PW 
w/4 -PW 
w/4 -PW T 



Tractive Effort 
in Pounds 



240 

540 

504 
480 

456 
432 
408 

384 
360 



This power is used in overcoming axle friction, gravity resistance, 
and rolling resistance. 



MAXIMUM OR RULING GRADES 7 

The axle friction is small, amounting to three or four pounds per 
ton for American farm wagons. 

Grade resistance (gravity) equals (Load x per cent of grade ex- 
pressed in hundredths) and expressed in pounds per ton of load equals 
(2000 x P). 

The rolling resistance varies for different surfaces and for each 
surface depends on the diameter of wheel, width of tire, speed of 
travel, and the presence or absence of springs on the wagon. The 
best diameter of wheels, best width of tires, and the use of springs as 
they affect the ease of hauling for both farm and road use are prob- 
lems for the wagon manufacturers. 

Morin, a French engineer, concluded, from a series of careful ex- 
periments, that the harder the surface of the road the less effect the 
width of tire had on rolling resistance. We are dealing with com- 
paratively hard surfacing only and with small differences in wheel 
diameters and can disregard these factors. As a matter of interest 
Tables 3, 4, and 5 are included to show the results of experiments on 
different soils and roads. 

The question of wide tires is necessary to road engineers only as it 
affects the distribution of wheel loads over a safe area and will be 
taken up under Foundations. 

Table 3. — Effect of Width of Tire upon Tractive Power 1 
Resistances in Pounds per Ton 



Ref. 

No. 



Description of the 
Road Surface 



Sod 

Earth road (hard) . . 
" (muddy) 
Sand " (hard) . . . 
(deep) .... 
Gravel road (good) . 
Wood Block (round) 



Diameters of the Front & Rear Wheels respectively 



3-6" & 
3-10" 



199 

37i 

5i 



4" 



108 

243 
162 

351 



49 



3-6" & 
3-IO" 



Width 

I*" 



268 
171 

98 
61 



304 

164 

117 
70 



3-8" & 
4-6" 



of 



if 



236 
141 

83 
35 



4" 



254 
168 

80 
46 



3-6" & 
3'-io" 



Tires 



1* 



283 
152 



239 

152 



54 



3-8" & 
4-6" 



I*" 


3" 


189 


228 


114 
265 


114 

228 


66 
28 


76 
38 



Pamphlet by Studebaker Brothers Manufacturing Company, 1892. 



s 



GRADES AND ALIGNMENT 



Table 4. — Effect of Size of Wheels on Tractive 
Resistance 1 Pounds per ton 



Ref. 

No. 


Description of Road Surface 


Mean Diameter of 
Front & Rear Wheels 


50" 


38" 


26" 


1 
2 
3 

4 
5 

6 

7 
8 

9 

10 


Macadam, slightly worn, fair condition 

Gravel road, sand i" deep, loose stones 

" upgrade 2.2%, one-half inch wet 
sand, frozen below 


57 
84 

123 
69 

IOI 

132 
173 
178 
252 

130 


61 
90 

132 

75 

119 

145 
203 
201 
303 
148 


70 
no 

173 
79 
139 
179 
281 
265 
374 
186 


Earth road. Dry and hard 


|* sticky mud, frozen below 

Timothy & blue grass sod, dry grass cut 

" " " " wet & spongy 

Cornfield; flat culture across rows, dry 

Plowed ground; not harrowed, dry & cloddy . . 

Average Value of Tractive Power 





Experiments of Mr. T. I. Mairs at the Missouri Agricultural Experiment Station. 



MAXIMUM OR RULING GRADES 






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IO 



GRADES AND ALIGNMENT 



Table 6 gives the average rolling resistance in pounds per ton of 
load on different pavements for the ordinary farm wagon driven at 
ordinary speeds. 

Table 6 1 



Kind of Pavement 


Rolling Resistance in Lbs. 
per Ton of Load 


Asphalt 

Brick 

Cobble Stones 

Earth Roads 


30 to 70 
15 to 40 
50 to 100 
50 to 200 
50 to 100 
20 to 100 
3° to 50 
30 to 80 
3° to 50 


Gravel Roads 


Macadam Roads 

Plank 

Stone Block 


Wood Block 





1 Baker's "Roads and Pavements." 

For a comparative estimate we will take a value of forty pounds 
per ton of load, including axle friction, on Bituminous Macadam, 
Waterbound Macadam, and Brick Pavement, and one hundred 
pounds per ton for earth roads in fair condition. The resistance to the 
effective tractive power of the team per ton of load is therefore 40 + 
(2000 x P) on the improved roads, and 100 + (2000 x P) for earth 
roads, and the maximum load that can be drawn on any grade equals 

( Effective tractive power of team for that grade \ 
Resistance per ton of load for that grade ) 

Using the tractive powers of the team shown in Table 2, the follow- 
ing table is constructed. 

Table 7 





Effective 


Improved Roads 


Earth Roads 












Grade 


Tractive 


Resistance in 


Maximum 








Effort 


lbs. per Ton 
of Load 


Load in 
Tons 


Resistance 


Max. Load 


Level 


240 lbs. 


40 lbs. 


6.0 tons 


100 lbs. 


2.4 tons 


2\% 


54o " 


90 " 


6.0 " 


150 " 


3-6 " 


4% 


504 " 


120 " 


4 - 2 :; 


180 " 


2.8 ' 


5 % 

6 % 


480 " 
456 " 


140 " 
160 " 


3.4 

2.0 " 


200 ' 
220 " 


2.4 
2.1 " 


7 % 


432 " 


180 " 


2-4 " 


240 ' 


1.8 " 


8 % 


408 " 


200 " 


2.0 " 


260 " 


1.6 " 


9% 


384 " 


220 " 


1-7 " 


280 " 


1.4 " 


10% 


360 " 


240 " 


1.5 " 


300 ' 


1.2 



Note. — This table is chiefly useful in comparing the effect of dif- 
ferent grades on improved and unimproved roads, but in the writer's 
opinion the theoretical loads are nearly correct. 



MAXIMUM OR RULING GRADES II 

3. From Table 7 and the preceding discussion we can pick out 
the grades that theoretically fulfil certain traffic requirements. 

I. On improved roads the same load that can be drawn up a 2 \% 
grade by the maximum exertion of a team, can be hauled on a level 
with normal exertion. This makes a perfectly balanced design from 
the standpoint of team hauling. The theoretical load is six tons. 

II. 5% is the maximum grade that fulfils the condition of safe 
descent at a trot without brakes; this requirement is more important 
for light than for heavy traffic. The theoretical load for this grade 
is 3.4 tons. 

III. The same load that can be hauled up a 7% improved grade 
can be drawn on a level dirt road in fair condition; a 7% grade there- 
fore does not reduce the load of a team which must travel over an 
earth road for part of the distance. The theoretical load is 2.4 tons. 

As a matter of fact, the actual traffic conditions, the topography 
of the country, and the money available, govern the selection of the 
grade. The theoretical advantage of a 7% grade does not really 
amount to much, as where the improved road has a small ruling grade, 
the farmers often use snatch teams to draw to the road and single 
teams for the balance of the distance. The adoption of 7% by many 
of the States depends on the topography, as will be shown later. 

The average farm wagon in New York State weighs about 1350 
pounds, and 3500 pounds is a large net load for such a wagon; even 
with larger wagons and a snatch team it is not likely that more than 
four tons would be drawn over dirt roads to the improved road. 
There is no possibility of an average team load of six tons, which 
means that a 2§% ruling grade need not be considered except in 
flat country where it can be built cheaply. A 5% grade has been 
found from experience to be satisfactory for most localities, as 3 \ to 
4 tons can be hauled, teams can descend it easily, and the cost of 
construction is usually not too great. 

In the improvement of any highway or system of highways, the 
amount of money that the community is willing to provide is often 
insufficient to build a road that the conditions demand. This limits 
the engineer to the best design he can make for the amount available. 
In such a case the grade should be consistent even if it cannot be 
reduced to a rate that would meet the traffic requirements, and should 
be designed primarily for heavy hauling. As the advantages of these 
roads are demonstrated, there is less difficulty in getting sufficient 
money for a good design. 

Take for example a road between two shipping points. It is first 
necessary to determine the portion tributary to each shipping center, 
and then the natural grade of all the hills on each portion, in order to 
decide what consistent ruling grade can be adopted without excessive 
cost. 1 There is no object in reducing a hill from 7% to 5% at a large 
expenditure if nearer the terminal there is a grade that cannot be 
reduced below 7%. It should be borne in mind, however, that the 
nearer you approach the center, the more traffic the road will have, 
and if the hills are naturally flatter the ruling grade should be reduced. 
The direction of heavy traffic on each hill should be determined and 
1 For an example, see page 151, chapter VIII. 



12 GRADES AND ALIGNMENT 

considered. In the writer's opinion there are few cases where grades 
less than 5% are required, and in hilly country 7% is satisfactory and 
a great improvement over previous conditions. 

Grades as high as 11% have been constructed in New York and 
grades as high as 9% in New Jersey and Illinois, but the general 
opinion of the Departments under which these grades were built is 
that they would not again use such a high rate except in villages where 
any material change in street elevation would damage valuable 
properties. Outside of corporations it is bad practice to use grades 
greater than 7%, for if any road is of sufficient importance to warrant 
an improvement of the class discussed in this book, it is certainly of 
sufficient importance to warrant a reduction in grade to a reasonable 
rate. 

4. CONSTRUCTION OF MAXIMUM GRADES 

Natural grades are reduced to the required rate by cut and fill, by 
new locations around hills, or by new locations giving additional length 
for the same rise. The cheapest method is usually adopted, but some- 
times where cut and fill would be the most economical in the first 
cost, the danger of drifting snow in cuts or the damage to abutting 
property from deep cuts or high fills results in the selection of the 
more expensive construction. A large reduction of grade on a long 
hill necessarily requires a new location. 

MINIMUM GRADES 

Most road books claim that level grades should not be used because 
of the liability of water standing in ruts and that a certain minimum 
grade should be adopted that would insure their longitudinal drainage. 
Baker states in his " Roads and Pavements" that for macadam roads, 
English engineers use a minimum grade of 1.5%, French engineers 
0.8%, and that American practice favors 0.5%. Let us see what 
this means: 

for a 1.5% grade the fall would be 1/5 inch per foot 
" " 0.8% " " " " " 1/10 " " " 
" " o.5% " " " " " 1/16 " " " 

The flattest crown that is ordinarily used even on bituminous 
macadam is \ ,r per foot or 2 J times as much as the greatest longi- 
tudinal fall in the above list. 1 For long ruts a longitudinal grade is 
of course effective, but the patrol system of maintenance is supposed 
to prevent their formation and for short small depressions the crown 
slope must furnish the drainage. The writer believes that there 
should be no hesitation in using a level grade; on such stretches the 
crown can be increased slightly to insure transverse drainage and the 
ditches given a minimum longitudinal fall of 0.2' to 0.5' per ioo', 
depending on the soil. 

INTERMEDIATE GRADES 

The selection of the intermediate grades affords the greatest chance 
for economy on earth work. A grade so established that the cut in 

1 See footnote, page ig. 



INTERMEDIATE GRADES 13 

every cross-section would just make the fill at that point, would 
result in the least possible excavation. This condition is never 
realized, but the nearer it is approximated, the nearer we get to the 
most economical grading design. (See chapter on Office Practice, 
page 221.) 

It may be noted at this point that economy of grading should 
never govern the profile or cross-section where there is any good 
reason oi convenience, safety, or appearance for placing the road at 
a certain elevation or giving it a certain shape. 

In determining the profile the controlling features should first be 
noted; these are high- water level of streams, elevations of existing 
bridges, railroad crossings, all points where deep cuts or high fills 
would damage the approaches to valuable property; connections 
with other highways, portions of the road that have been previously 
macadamized, and in villages the elevation that will give a convenient 
section and a finished appearance. The adopted grade must satisfy 
these conditions. However, on the greater part of an ordinary road, 
the grade can be placed at any desired elevation, and it is on these 
stretches that the saving in earthwork is effected. To get an economi- 
cal design, a rolling grade can be used if necessary; long straight 
grades are not required, a mistake easily made by engineers trained 
in railroad work. Short grades are not objectionable, and a reverse 
vertical curve rides easily if well built. It appears that there is too 
much tendency to cut the top of every knoll and fill each hollow, for 
it seems a waste of money to reduce a 4% toa3.5%ora3.5%toa 
3% grade where the ruling grade is 5%. There should be no hesita- 
tion in spending all the money that can be obtained to reduce the 
ruling grade to a reasonable rate, but it is good policy to economize 
on all grades less than the maximum. 

In conclusion, it should be stated that probably the most common 
error in the laying of a profile consists in making the excavation and 
embankment balance with short hauls, regardless of more important 
considerations, and in this connection it cannot be stated too strongly 
that the grade must satisfy the controlling points; that any resulting 
excess of material must be overhauled or wasted and any shortage 
borrowed; that the economies must be effected on the unimportant 
stretches of road, and that by the use of short and rolling grades the 
excavation can be reduced and a good profile obtained. 

Table 8 gives the excavation per mile on State roads in different 
localities and indicates the variation in amount that is required to 
get a first-class improvement. 



14 



GRADES AND ALIGNMENT 



Table 8 

Part i. — Compiled from the 1908 and 1909 Reports of the 
New Jersey Highway Commission. 



Name of Road 



May's Landing 

Rivervale 

Westwood 

Franklin Turnpike . . . 

Summit , 

Lamberton 

Westfield 

Blue Anchor 

Malaga 

Whitehouse 

English Creek 

Paterson Plank Road 

Yesler Way 

Camden 

Evesham , 

Schellenger's Landing 

Goshen 

Tuckahoe 

Hopewell 



Length 
in 

Miles 



:4.o 
5.o 
1.2 
1.6 
1.9 
3-9 
3-1 
2-3 
5-7 
6.5 
6.7 
2.3 
2.7 
2.4 
2.4 
2.1 
2.6 

4-3 
2.0 



Maximum 


Max. 


Original 


Improved 


Grade 


Grade 


7.o% 


3-2% 


8.5% 


5.o% 


5-2% 


4-5% 


8.0% 


2.8% 


13.0% 


6.5% 


2.8% 


2.8% 


4-5% 


2.9% 


2.5% 


2.0% 


4.2% 


2.0% 


12.5% 


5.o% 


6.0% 


3-9% 


Level 


Level 


12.0% 


6.5% 


6.7% 


4.0% 


6.4% 


3-7% 


3-4% 


1.1% 


3-4% 


1.4% 


4.1% 


1.6% 


7-6% 


5.o% 



Excavation in 
cu. yds. per Mile 



2,220 
4,680 
2,500 
8,200 
5,200 
540 
6,500 
3.200 
1,700 
4,100 
2,000 
(Emb.) 50,000 
5,7oo 
5,200 
3,500 
5,000 
4,500 
8,100 
3,800 



Table 8 

Part 2. — Compiled from the Records of the New York 
State Highway Commission. 

Plans for 19 11 



Name of Road 



Pittsford — North Henrietta . . . 

Indian Falls — Corfu 

Pembroke — East Pembroke . . . 
Livonia — Ontario County Line . 

Livonia — Lakeville 

Avon — Lima 

Sea Breeze — Nine Mile Point . . 

Bliss — Smith's Corners 

Wales Center — Wales 

Scottsville — Mumford 

Ridge — Rochester — Sea Breeze 

Medina — Alabama 

Pavilion — Batavia 

Parma Corners — Spencerport 
North Chili 



Character 
of Country 



Rolling 

Fiat 

Hilly 

Hilly 

Hilly 

Hilly 

Hilly 
Rolling 

Hilly 

Rolling 

50% Fat 

50% Hilly 

Rolling 

Hilly 

Flat 



Maximum 

Improved 

Grade 



5.o% 
2.6% 
5.o% 
8.0% 
8.0% 
8.0% 
8.0% 

5-5% 
8.0% 
5.o% 
i.S% 
5.o% 
5.o% 
10.0% 

6.0% 



Width of 
Section 

between 
Ditches 



24 
24 
32 
32 
32 
32 
26 
26 
28 
32 
32 
44 

28'- 3 2' 
22-30' 

32' 



Exc. in 

cu. yds. 

per mi. 



2500 
2800 
3600 
55oo 
45oo 
3300 
6600 
34oo 
57oo 
3400 
335o 

2800 
2950 

2320 



EXCAVATION TABLES 



15 



Table 8. Continued 

Compiled from the Records of the New York State 
Highway Commission. 

Plans for 19 10 



Name of Road 


Character 

of 
Country 


Maximum 

Improved 

Grade 


Width of 
Section 
between 
Ditches 


Exc. in 
Cu.Yds. 
per mi. 


Lake Part 2 & Sweden 4th Sect. 
Warsaw — Pavilion 


Flat 

a 

Rolling 
Flat 

Rolling 
60% Flat ) 
40% Hilly} 

Rolling 

Flat 

Rolling 
Hilly 

Flat 

<< 

Hilly 
Rolling 


3.8% 
5.o% 
3-S% 
2.6% 
5.o% 
2.2% ) 
7.o% ) 
3-1% 
2.4% 1 
One hill \ 
5.o% J 
4-4% 
5.o% 
4-1% 
3-6% 
0.7% 
7.o% 
3.7% 
5.o% 


32' 

28'- 3 2' 

32' 

28'- 3 2' 

32'- 4 o' 

28'- 3 2' 
32' 

32' 
3C-32' 

28'- 3 2' 

24' 

30' 
28'- 3 2' 
28'-32' 

32' 

32' 


2560 
3900 
2300 
4000 
1950 

3150 

3230 

2800 

2300 
4000 
6200 
2820 
2120 
6100 
3440 
3800 


East Henrietta — Rochester .... 
Olean — Hinsdale 


Leroy — Caledonia (1.5 miles) . . 
Shawnee — Cambria 


Roberts Road 


Sanborn — Pekin 


Oak Orchard, Part 2 


Levant — Poland Center 

Dansville — Mt. Morris, II .... 
Castile Center — Perry Center . . 
Lake Shore — Lackawanna City 
Eighteen Mile Creek 


Albion Street — Holley 

Pembroke — East Pembroke . . . 



i6 



GRADES AND ALIGNMENT 



Table 8. Continued 

Compiled from the Records oe the New York State Highway 

Commission. 

Plans for 1908 and 1909 (Selected Roads) 



Name of Road 



Hamburg — Springville Sect. I 

" II 

Collins — Mortons Corners . . . 

Clarence Center 

Orchard Park — Griffin's Mills 

County Line 

Geneseo — Avon 

Geneseo — Mt. Morris 

Alden — Town Line 

Pittsford — Mendon 

Pittsford — Despatch 

Clover Street Section I 

11 n 

Rich's Dugway 

Left Fork — German Church . 
Goodrich Road 



Hamburg — North Collins 

Lawton — Gowanda 

Chili 

Brooks Avenue 

Lyell Avenue 

Barnard's Crossing 



Character of 
Country 


Max. 

Improved 

Grade 


Rolling 


6.0% 


Hilly 


7.o% 




7.o% 


Flat 


2.5% 


Hilly 


8.0% 


Flat 


5.o% 


Hilly 


5-3% 




6.0% 


Flat 


6.0% 


Hilly 


6.0% 




5.0% 




8.0% 


Rolling 


4-5% 


Hilly 


7-2% 


Rolling 


6.2% 


60% Flat 


5.o% ) 
6.0% } 


40% Rolling 


Hilly 


9.o% 




7-5% 


Rolling 


5.o% 


Flat 


4-6% 




2.2% 


11 


4-4% 



Width of 
Section 

between 
Ditches 



30 
30' 
32' 
28' 
28' 
28'- 3 2 / 

32; 

32' 

22-28' 

32' 

24' 

28' 

32 r 

20'-28' 

28' 

26-32' 
22-32' 

32' 

28' 
24-30' 

26'- 3 o' 

22' 



Exc. in 
cu. yds. 
per mi. 



1920 
3100 
2250 
2200 
2000 
2100 
2200 
3460 
i960 
3000 
3600 
2550 
3000 
5000 
2000 

3100 

4200 
5300 
2800 
2240 
2400 
2174 



Table 8. Continued 

Compiled from the Records oe the New York State Highway 

Commission. 

Plans from 1898 to 1907. (Selected Roads) 



Name of Road 



East Avenue 

Pittsford 

Fairport 

Ridge Road 

Buffalo Road 

White's Corners Plank Road 

Orchard Park 

Transit, Sections I & II 

Hudson Avenue Road 

West Henrietta 

Scottsville, Section I 

" II 

Monroe Avenue 



Character 
'of Country 


Max. 

Improved 

Grade 


Rolling 


5.o% 




5.o% 


11 


5-5% 


11 


3-3% 


Flat 


2.0% 


<< 


3-5% 


<< 


3-9% 


<< 


4-6% 


Rolling 


3-1% 


Flat 


5-5% 


11 


4.0% 


Rolling 


$.0% 


Flat 


4.5% 



Width of 
Section 
between 
Ditches 



22' 

22' 
20-22' 

26' 
22-25' 

22' 

20' 

22' 

22' 

22' 

22' 

22' 

2 2'-24* 



Exc. in 

cu. yds 

per mi. 



8160 
5840 
6580 
2150 
1700 
4600 
4200 
2100 
7100 
3400 
2000 
2100 
1850 



EXCAVATION TABLES 



17 



An examination of the 1909 report of the New York State Highway 
Commission shows that the largest excavation per mile on roads 
built by the State from 1898 to 1908 was as follows: 

Delaware Turnpike Road ... 1.04 miles . . . 16800 c.y. per mile 
" u tl 6 c u 

North Creek-County Line 4.12 " 

Highland Lake-Tompkins Cove 5.88 " 
and the least excavation as follows: 

Main Street, Section II 

Babylon-Bay Shore 



6800 
10300 
10100 



986 
735 



Table 8 



Part 3. 



Compiled from the Reports of the Massachusetts 
State Highway Commission. 1896 



Name of Road 


Length in 
Miles 


Maximum 

Improved 

Grade 


Width of 
Section 
between 
Ditches 


Exc. in cu. 
yds. per mi. 


Andover 


• 

0.6 
1.0 

15 

1.6 
0.63 
1.0 
1.49 

o.93 

1.2 

0.56 

1.0 

1-93 

3-0 

1.62 

1.61 

1.05 

i-45 
0.97 
1.91 
1.48 
1. 16 

i-5 
2.0 


4-9 % 
3.36% 
6.0% 
5.o % 
2-7 % 
2.6 % 
4-0 % 
2-95% 
5S % 
1-25% 
4-25% 
4.40% 
i-7 % 
4.o % 
6.0 % 
3-8 % 
4-o % 
6.0 % 
5.o % 
5.o % 
4-25% 
5.i6% 
5.o % 


24 

2l' 
30' 
21' 
2l' 
2l'-24' 
2l' 
2l' 
2l' 
26' 
2l' 
2l' 

24' 
2l' 
2l' 
2l' 
2l' 
21' 
2l' 
2l' 
2l' 


6000 

2607 

1920 

3200 

53oo 

2300 

8930 

3000 

335o 

4300 

47oo 

7540 

1500 

37oo 

5600 

3800 

1200 

4500 

9700 

1500 

1810 

35oo 

3800 


Brewster 


Dalton 


Gloucester 


Granby .... 


Great Barrington 

Hadley 


Munson . . . 


Norfolk 


North Hampton 

Pittsfield 


Tisbury 


Westport 


Wrentham .... 


Walpole 


Duxbury 


Fairhaven . . . 


Fitchburg .... 


Goshen 1 


Marion 


Mattapoisett 


Lee 


Leicester 





This table is compiled to show the amounts of excavation that the 
Highway Departments of Massachusetts, New York, and New Jersey 
have been willing to use in getting various maximum grades. It can 
be readily seen that it is impossible to generalize as to how much 
excavation will be required. In the chapter on " Sections" some ex- 
amples will be given of roads for which two designs were made, using 
different widths of section and different kinds of profile, to show the 
saving that can be effected by a careful selection of the section and 
1 the use of a rolling grade. 

! is inVKnlf^^^ graC fe I2 ^ -new location used; as difficult a road as there 
is in the btate to obtain a $% grade. 



1 8 GRADES AND ALIGNMENT 



ALIGNMENT 



Sharp curves on steep grades or at the foot of such grades are not 
safe; good practice calls for a minimum radius of 300 to 400 feet for 
these cases. Right angle turns even on level stretches are incon- 
venient and often dangerous. New York State has adopted a radius 
of 200 feet as a minimum, wherever possible, acquiring new right-of- 
way when necessary, and it is very evident that the increased comfort 
has pleased the traveling public. 

On comparatively straight stretches the position of the center-line 
should be shifted to keep on the old roadbed as much as possible and 
yet give a pleasing appearance; this is done to utilize the hard founda- 
tion of the present traveled way for the subgrade of the proposed 
metaling. 

Sight Distances. — In designing a side hill road, in rough country, 
the alignment and width of shoulder often depends upon what we may 
call "a safe sight distance"; this means that the driver of a machine, 
traveling at ordinary touring speed of 20 to 30 miles per hour, must 
be able to see far enough ahead to turn out and pass an approaching 
car without the application of brakes. In attempting to reach a con- 
clusion as to what is a "safe sight distance"" we have written to 
automobile clubs throughout the country and find that, in the main, 
they agree on from 200 to 300 feet for speeds of 20 to 25 miles per hour. 

Mr. George C. Diehl, Chairman of the Good Roads Board, A.A.A. 
and County Engineer of Erie County, N.Y., gave us the following 
information for emergency stops and passing without slowing up : 

"The tests that we have conducted show that a car going at the 
rate of 20 miles per hour can be stopped at 40' and one going at 40 
miles per hour can be stopped at 140 feet with the emergency brake. 
For passing a rig going in an opposite direction this distance would 
not be necessary." 

Mr. Diehl's figures are considerably less than the distances given 
in the other answers. A minimum sight distance of 250 to 300 feet 
is the practice of Division No. 5, New York State Department of 
Highways. 

In the chapter on Office Practice, page 208, tables are given 
showing the "Sight Distance" for different curves in "cut." 

Railway Grade Crossing Elimination 

Grade crossings are being eliminated as rapidly as possible, as they 
are a source of great danger. The overhead clearance and width of 
roadway in subways are given in chapter IX. 



CHAPTER II 

SECTIONS 

Sections may be considered from the standpoints of safety, con- 
venience, and economy. 

For safety, a rig should be able to travel on any part of the road 
from ditch to ditch without overturning; for convenience, the width 
of section ordinarily used must have enough pitch to drain the surface 
water into the ditches but not enough to give an uncomfortable tilt to 
a vehicle; for economy, the section must be flexible in order to con- 
form to local conditions. 

The first questions are naturally: What is a safe slope? What is a 
comfortable driving slope? What pitch is required to drain different 
surfaces? What is the commonly used width, and what the maximum 
width of the traveled way? 

All of these points except the last two have been pretty well de- 
termined, and, while some engineers disagree with current practice, 
the writer believes from his experience and a study of the various 
State sections that the following premises can be safely adopted: 

That 3" to 1 ' or 1 on 4 is the maximum safe slope. 

That 1" to 1' is the maximum agreeable driving slope. 

That 1" to 1' is the minimum slope at which an earth shoulder will 
shed water, without too much maintenance. 

Thatf " to 1' is a satisfactory crown for a waterbound macadam 
road in order to maintain it satisfactorily, allowing for the flattening 
that occurs under traffic. 

That J" to i' is a satisfactory crown on waterbound roads having 
tar or asphalt flush coats or on bituminous macadam or mineral 
bitumen. 1 

That |" or f " to i' is a satisfactory crown for brick pavement on 
country roads. 

The width of roadway carrying the greater portion of the travel 
and the maximum width used when rigs turn out to pass are not so 
well established; these two points determine the most economical 
width of hard roadbed and the minimum convenient driving width, 
no part of which should have a transverse slope of more than 1" to i'. 

Probably the best data can be obtained from the reports of the 
Massachusetts Highway Commission, which resulted from a careful 
study of these widths on 160 improved roads during the years 1896, 
1897, 1898, 1899, and 1900. Table 9 gives the results on a few roads 
showing the form used and the variation from year to year; the 
footnote for Table 9 gives a summary of the observations on all the 
roads for the years 1896 to 1899 inclusive: this brief was prepared by 

1 New York State has adopted for their 191 2 work a crown of \" per foot for water- 
bound roads and \" per foot for bituminous macadams; this is extremely flat, allow- 
ing for the effect of traffic (see Table 20, page 75 ) . 

19 



20 



SECTIONS 



J. Y. McClintock, County Engineer, Monroe County, N.Y., and 
gives a better idea of the conditions than would be conveyed by 
printing the original table in full. 

Table 9. Showing Widths or Traveled Way 



Town or City 


County 


1 
£ 


Maximum Width of 
Traveled Way 


Width of Commonly 
Traveled Way 


1896 


1897 

16' 

13' 
12' 

2o' 
20' 

14' 
II 

15' 
12' 

13' 
16' 

20' 


1898 

2o' 
14' 
15' 
20' 
2l' 
18' 
II' 

15' 
li' 

14' 
20' 

15' 


1899 


1896 




CO 
M 

12' 
9' 

8' 

12' 

16' 

10' 

8' 

9' 

9' 

9' 

12' 

10' 


00 


CO 

14' 
7' 
10' 
12' 
18' 
15' 
9' 
10' 

7' 
10' 

15' 
8' 


1899 


Athol 

Barre 

Bedford 

Chicopee 

Dalton 

Fitchburg (W.) 
Huntington . . 

Lincoln 

Marshfield . . . 
North Adams 

Orange 

Taunton 


Worcester . 
Worcester . 
Middlesex . 
Hampden . 
Berkshire . 
Worcester . 
Hampshire . 
Middlesex . 
Plymouth. . 
Berkshire . 
Franklin . . 
Bristol 


17' 
15' 

IS' 
20' 

15' 
15' 
15' 
15' 

17' 
15' 


16' 

20' 

10-12' 
16' 

20' 


18' 
14' 
15' 
20' 
l6'-2l' 

18' 
12' 

15' 

12' 

15-20' 

20' 

18' 


io'-i 2 ' 

20' 
10' 

7' 
10' 

8' 

8'-io' 

io'-i2' 

io'-i 5 ' 


14' 
8' 

9' 
13' 

I2'-l8' 

14' 

8' 

io' 

7' 
12' 

15' 

m> -r ~l 

7-12 



Width of traveled way on 160 roads in Massachusetts, measured 
during the years 1896, 1897, 1898, and 1899, an d printed in the report 
the Massachusetts Highway Commission for 1900. 

The width of stone on these roads is given as 15' wide on 130, 12' 
wide on 3, and 10' wide on 2. It should be remembered that the 
stone is put on very much thicker in the middle than at the edges. 

The maximum width of traveled way as measured was as follows: 



9 


ft 


wide 


on 2 


roads 


l8 ft. 


wide 


on 


23 


roads 


10 


tt 




n 


" 6 


n 


19 " 




n 


1 


tt 


11 


a 




it 


" 2 


a 


20 " 




tt 


10 


a 


12 


u 




n 


" 28 


it 


21 " 




a 


10 


a 


x 3 


tt 




tt 


" 8 


a 


22 " 




tt 


1 


a 


14 

16 


u 
it 
n 




n 
it 

u 


" 23 
" 30 
" 8 


tt 

a 

(C 


24 " 

25 " 

26 " 




it 

a 
it 


2 

4 

1 


a 
a 

a 


17 


it 




n 


" 1 


a 


33 " 




u 


1 


a 


The width of commonly 


traveled 


way as measured 


was as follows : 




7 


ft. 


wide on 12 


roads 


14 ft. wide 


on 


8 roads 




8 
q 


a 
u 




1 " 17 
' " 25 


a 
a 


15 ' 

16 ' 


t it 




13 

2 


a 
a 




[O 


n 




' " 3 2 


a 


18 ' 


t 11 




4 


a 




li 


n 




1 " 10 


it 


20 ' 


I It 




2 


11 




12 


tt 




' " 3° 


a 


22 ' 


c tt 




1 


n 


- 


C3 


a 




( " 3 


it 


25 ' 


( a 




1 


11 



The author has measured a number of the New York State im- 
proved roads and found that the width of heavy travel checked the 
Massachusetts results but that the maximum widths were more, 
averaging from 18 to 21 ft.; this probably can be explained by the 



INDIAN FALLS — CORFU ROAD 21 

increase in automobile traffic since 1900, which, because of its higher 
speed, requires more room in passing. 

. Briefly stated, the widths subjected to hard wear on unimportant 
roads ranged from 8' to io'; on well traveled roads io' to 14', and in 
unusual cases 14/ to 16'. The maximum widths used varied from 
12' to 14/ on the side roads, to 17' and 18' on the main thoroughfares, 
and as mentioned above have increased to 18-21' in the last few 
years. From this data, it seems that the best practice at present 
requires a driving width for "turn out" traffic of about 22', with a 
variable width of strong metaling determined by the traffic require- 
ments and ranging from io' to 20'. 

We have now practically developed a standard for the 22' of driving 
width; the metaling that is to carry the heavy traffic has a specified 
crown for each variety and from the edge of the metaling to the 
limits of the 22', the earth shoulder must have a slope of 1" to i' or 
possibly §" to i'. 



/ "to I 'Crown^J^^^ 



Fig. 1 

The flexibility of the section depends on the portion outside of 
this 22'. The function of the extra width is to keep the longitudinal 
drainage of surface water beyond the portion used for driving. To 
do this we are limited to a minimum slope of 1" to i' to insure trans- 
verse drainage and a maximum of 3" to i' on the score of safety. It 
is by the good judgment of the designer in using various slopes be- 
tween these limits and various widths and depths of ditches, combined 
with the possibilities of different grades, that the economies in earth- 
work are effected and at the same time the design is made appropriate 
to the local conditions. 

Two examples are given to illustrate this point. 

1. INDIAN FALLS— CORFU ROAD IN NEW YORK STATE 

Original Djesign Revised Design 

Length 1.85 Miles. 

NO CHANGE IN PROFILE 

No Change in Ratio of Cut to Fill 

Width of Macadam 14' Width of Macadam 14' 

" Section 30' " " Section 24' 

Depth of Ditch 18" Depth of Ditch 14" 

Original estimated Revised estimated 

excavation 7500 Cu. Yds. excavation 5200 Cu. Yds. 

This change is section alone resulted in a saving of 2300 cu. yds. 
excavation or at the rate of 1 240 cu. yds. per mile, or in money about 
$600.00 per mile. 



22 



SECTIONS 



2. PITTSFORD — NORTH HENRIETTA ROAD IN 
NEW YORK STATE 



Length 2.67 Miles 



Original Design 



Revised Design 



" 14" 



Width of Section 24' 
Depth of Ditch i2 y 
Ratio of cut to fill 1.25% 
Maximum Grade 5.0% 
Profile : — Rolling grades 

and reverse vertical 

curves used. 

Revised estimated excavation 
6,620 Cu. Yds. 



Width of Section 30' 

Depth of Ditch 18" 

Ratio of cut to fill 1.35% 

Maximum Grade 5.0% 

Profile: — Designed with straight 

instead of rolling grades and 

tangents of ioo' between 

vertical curves. 
Original estimated excavation 
11^450 Cu. Yds. 

A saving of 4,820 cu. yds; 1,800 cu. yds. per mile, or, in money, 
approximately $900.00 per mile. 

The revised design on this road is a good example of what can be 
saved by the use of a section that fits the conditions, a rolling grade, 
and a ratio of cut to fill that we have found from experience to be 
sufficient. 

The author's experience has indicated that an open ditch does not 
have much effect on ground water; that its part in the design is to 
drain the surface water, thus preventing seepage into the road-bed 
with a resulting softening of the surface; and consequently, whenever 
ground water is encountered under drains should be used. Deep 
ditches are not only useless but dangerous, and the best practice calls 
for the least depth that will handle the surface water. The following 
section is, therefore, suitable where there is no probability of much 
surface water; it is the writer's idea of the minimum width section 
that will be satisfactory, and where it can be adopted will give the 
most economical grading design for light cuts and fills. 



El. Theoretical Grade^<> x ^^nKj^I* f'fo/' ^°" 

, <s> l< 22' _ ->| 

k - 24-' -26' —-- H 

Fig. 2 



SECTIONS 



23 



New York State 19 15 Standards 

Cement Concrete 



.,-Efev. of Theoreffcai Grade i \y 

£ ' I \Q1> 




--»/<?£- --•- £4'-0* to 32'- 

1" 
<p Crown 4 per_Ff^- : ^ 

F&T&T?' c I Sub-bottom Course if Required 

Vffi' \<---!4'-0" Or !6'-0"- --H 

Transverse expansion joints, tobe provided every JO ft., shaft be 
composed of a creosoted, yei/ow pine or tar paper strip £' thick, 
conforming to the cross section of roadway. Each strip may 
be composed of two pieces of equal ' ienath, butt jointed and 
fastened together with approved sp/ice piece of No. 26 iron 

A 



* Waterbound Macadam « 

»>W?k— -, -„ --24'-0"fo 32- '0 ->^K- 

1 I Crowns per Ff\, ^Elev. of Theoreticaf Grade II >. \%* 

1 5 ub -bo ttom Course if Required \ 



p 



ft*' 



14-0-16-0- 

B 



■--H 



^ 



Waterbound Steep Grades 

-w?j«— —24'-0" to32'-0- — ->vrf 

^c I Croyvn^perFty * Elevat ion of Theorefica Grade 

'//j Tj \5ub-bottom Course if Required \ 




Contracted Section 

I ! ^ . 
Y'Elev. of T heoretical Gr x ade ^ ^ 




Bituminous Macadam 



..^ .. 24 L 0" to 32-0"- 



>j/f|«- 



CrovynJperEf-, ^-Elev. of Theoretical Gfade \ I 







I J</£ -bottom Course if Required 
k A*'-0 or I6 L 0"- ->J 



riia 



/«?<i 

^ 



24 



SECTIONS 



• I I Crown a per Ft- 



n*£777777' x Brick 4^! 



Why 



Jf 5andly'< , 



*?'-0"/fc J? V 




If Gravel Shoulder- ^/-^ 
. _>][<<. .4/^^ I "per Ft \ 



-IS'-O" 

Expansion Joint -- 
Expansion joints, if ot poured type shall be /"thick. For premou/ded type 
they shall be fforl6'widfh J §"for20'to24'width and $" for 32 '-width. 
Half Section Half Section 

f-i F-2 



7b/? Course same as A.BorE as Specified'-^ 



7777777777777A 



Sub- base as Bottom Course 

G 



/777777777777\ 



Top Course same as A, B or E as Spec if fed 
T777777777, 



777/////"'" ' ' / / /////// ^7////7/// / 

s When lei ford replaces Sub -base, if is made 8" thick 
(bottom course to have the same thickness at 
center and edges where Sub -base or Telford is used) 
Sub-base or Telford 

H 



1,4 -Asphalt 




Class Concrete 



.1 ~" ~ a 

iy->\ \<6-8->i 
Asphalt-^ i-d Kv ?" 



Sand— -:-->'• 



7T 



M \<2 



Brick 









*ft*&* 



4 






k— /*-*—->! ^2^ Class Concrete 



TYPICAL SECTIONS 



25 



■r. ~ 

.2 

"-S to 


•ij jad „| uavojo 


5 


CN 


JS 




00 


o> 


*b 


fc 


~£ 




CO 


5: 

in 


IH 


J3 




"* 


<fr 


W) 


jappoqs * 

10 


O 


t^ 


00 


d 
_o 



U 

'a 


■^j! ^d „§ UMOI3 


£ 

cd 

cd 
U 

cd 

O 


no 
w 


s 


n|oo 

cn 


M 


NO 


00 


~d 




^4 


W 


NO 


-t 


a 


*w 


H 


XT) £-~ 

M M 


~d 


5: 


5: 

<* 


IO 


ID 


japjnoqs 


u-> vO 




00 


d 

.0 
v> 


<u 
C/3 

~cd 
y 

a 


•1J J9d „f UMOJ3 


£ 

cd 

cd 

cd 




s 


V 


5: 

O 
H 


00 




~c 


O 




+J 

to 


^ 

J3 


ro 


M 


5: 




= 1 
= c 1 - 


V- 


*o 


iappoqs 


IO NO t<> 


00 


< 

c 


"3 

U 

'5, 


"U I9d #/! UA\OI3 


"3 

3 

cd 
O 




to 

NO 


s 


M M 


5: 


00 
M 


~d 


"* 


V) 


UO 


5: 

NO 


'X 


a 


ml-* 


CO 


10 10 


c. 


"*-+ 




10 




japinoqs 


VO 


vO 


M-H 

lo 


00 



2^ 


■73" "" 


3£ 










JCC5 


,d- ^ 


in 




cj- ^* 


m-i ■- 


<u 


ed 


O- 


— 






KJ 


d- - 


<u 


DO 





d~ 


1 


<u„ ^ 


<u 


T-, 


-O- - 


u 


u 


5: rtNHN 


d~ 


<u 


ca 





M M M 


T3 





d 


0" 




o~ = 




H 




H_< 


n 


d 





















d~ 




d- - 


u 


CO 
V 

r 


X 

d^ ^ 
ed- - 


i?^ 




4) 


« 




T3 


XJ 


>^ V. 


C 


w 

D 


fi ■ 


O 


X 


a 




ori 




rt^ 






> 


d 


<u~* "* 


<u 




i) 




u, O O 


d 


fT* 


.£- 


> 


+J -»_> 


0) 

C 



be 




d 

r 


u- O O 
O CN CO 








CD~ 




J3 


iO 


Ed 






r> 


XJ- - 


T3 


l) 




II II 


u 


fr 




d 


0- - 


c ff 


■j 


tin 









- 


d 




w 


0) 


W 


H 
O 


H 
O 



^ Q 



26 



SECTIONS 



Plate 2 





MS 

I5'0". 
2I'0 
25'0 
Trap : 46 tons per 100 it 



Local -4/ 



it >r u 




15' 0:- 
2/'0„ 
25' 

Trap .; 38 tons per 100^ it. 




Local - 34 » » 







< 15 0" 

- 2I'Q" 

25'0 

Trap : 55 tons per 100 jh_ 




Local: 50 



if » tt » 




I5'0"- 
21' 
25 '0 
Trap : 4-3 tons per WO it. 




Local: 39 n 



( New 5toneNo.2 J 

(New Stone No. I.) 

[<- - iS'O"—'- >f 

(Original Width of Macadam) 



Section for Resurfacing 



«Q 



.dr' 



'/' 



72&2I&&A& 



7ZZZ7ZZZZZ%Z&ZZZZ7Z72ZZZZZ7zzz?, 

.-IS' 0- > 






Trap • 64 tons per 100 it_ 







.^ 




Local: 58 " » » 
For Village Streets 

i "to I v^ 

— 7ZZZZZZ?ZZ%ZZ7Z?ZZZZZZ7Z. 



IS'O 

Trap_ ■ 55*onsper/00_ it_ 




Local : 50 » i> v 
For Village Streets. 



MASSACHUSETTS STANDARD FOR ROAD SECTIONS 27 

Plate 2 — continued 

Note: The Backs of 'Guard- Pail Posts fobe set- 
one foot from Edge of Embankment for all Widths. 

m" A " 




V- Underdrain Cobble Filled - f 
Large Stone at Bottom, Small 
Stone and Gravel at Top. 



v Halve together over Posts 



"ft- 8'0" ft— 8'0" ----- ffi^ 8'0" ff 



U 



1 I ' ! 



U 



•to I 2 - 



2-~" 



I5 > >. ___„,! ^ 

Condition No. i. — See note below. 

Trap Rock — Lower course, No. 1 stone, 24 tons; screenings for 
binder, 4 tons. Upper course, No. 2 stone, 16 tons. 

Local Stone — Lower course, No. 1 stone, 22 tons; screenings for 
binder, 4 tons. Upper course, No. 2 stone, 14 tons. 

Total tonnage per 100': Trap, 44; Local, 40. 

Condition No. 2 — See note below. 

Trap Rock — Lower course, No. 1 stone, 
No. 2 stone, 16 tons; screenings for binder, 

Local Stone — Lower course, No. 1 stone. 
No. 2 stone, 14 tons; screenings for binder, 



24 tons. 
7 tons. 
22 tons. 
7 tons. 



Upper course, 
Upper course, 



Total tonnage per ioo': Trap, 475 Local, 43. 

Note.— For both penetration methods — grouting or the modi- 
fied Glad well method — there should be two applications of asphaltic 
oil, each f gal. per sq. yd. There may be also a third application 
of I gal. per sq. yd. for a surface finish. For surface treatment there 
should be one application of § gal. of oil per sq. yd. or two applica- 
tions of \ gal. each per sq. yd. on the finished surface of the roadway. 



Plate 2 — continued 
2". .*" 



i'tol' 



?ee: 

2' j<- 



IS'O 



,/; 



i Z 



Condition No. i. 

Trap Rock — Lower course, No. 1 stone, 19 tons; screenings for 
binder, 3 tons. Upper course, No. 2 stone, 17 tons. 



28 



SECTIONS 



Local stone — Lower course, No. i stone, 17 tons; screenings for 
binder, 3 tons. Upper course, No. 2 stone, 15 tons. 
Total tonnage per ioo': Trap, 39; Local, 35. 

Condition No. 2. 

Trap Rock — Lower course, No. 1 stone, 19 tons. Upper course, 
No. 2 stone, 17 tons; screenings for binder, 6 tons. 

Local Stone — Lower course, No. 1 stone, 17 tons. Upper course, 
No. 2 stone, 15 tons; screenings for binder, 6 tons. 

Total tonnage per 100': Trap, 42; Local, 38. 

Note. — Condition No. 1 : Bituminous Treatment — Penetration 
— lower course bound with stone screenings or sand. 

Condition No. 2: Bituminous Treatment — Surface Spraying — 
screenings of sand binder in upper course. 



Plate 3 



Shoulder Drain I wide 

at Intervals of 200. 




3 ^ini'Jlm£tC^l 




.4— ->«- q' s4<-3:. 

Laid *\I6& IZinCut >k— - 

inBox ■ I ^j 

I! 



2 ml 13 ml - 



■12 In Fill 







State of Washington Standard Section 




80- ■* 8.0'- 

1? 




S 1 

Si 



This Section is the Arc of a Circle drawn through the Points 
a.birc 
Crown for Waterbound Macadam %tot! 
rt n Bituminous ** jfiot. 

New Jersey Standard Section 

Plates Nos. 1,2, and 3 show some of the Standard Sections in use 
at the present time. 

Widths of metaling can be discussed at this point, leaving depths 
for the chapter on "Foundations." There are two sets of widths in 
general use, 12 ft., 15 ft., 20 ft. and 14 ft., 16 ft., 20 ft. 

20 ft. widths are not often required and it is evident that the use of 
12 ft. instead of 14 ft. or 15 ft. instead of 16 ft. means a large saving 



STANDARD SECTIONS 29 

(see footnote) ! and is good policy provided the narrower width serves 
the purpose. There are two ways of approaching this problem. 
The first is to build the strong metaling just wide enough to com- 
fortably take the heavy traffic, and if the natural shoulder material 
is not suitable, treat the shoulders to a width of i4 / -2o / with gravel, 
waste #2 stone, or S3 stone filled and rolled but not puddled or tarred, 
making them suitable and wide enough for the light "turn out 
traffic"; this method results in the 12' and 15' widths. The second 
way is to make the full depth of the macadam just wide enough to 
allow two vehicles to pass with a minimum safe clearance, not giving 
the shoulders any special treatment. This method results in the 14' 
width on unimportant roads. The 16' width is harder to justify, as 
on the main traveled roads it is wider than necessary for the heavy 
travel and too narrow for the automobile "turn out traffic." 

In the writer's opinion 12' should be used in preference to 14' on 
the side roads where the shoulder material is good or where gravel is 
cheap or local crushed stone is used, making it possible to get cheap 
#2 or #3 stone; the 14' width should be used in preference to 12' where 
the shoulder material is bad and gravel or stone are imported. On 
the main roads 15' is as satisfactory as 16' and is cheaper under all 
conditions, because the 16' width does not overcome the necessity 
for a good shoulder. 

The importance of shoulder treatment on the side roads should not, 
however, be overestimated. One of the New York State Highway 
engineers made a trip from Albany to Binghamton (130 miles) in 
the Fall of 19 10 and counted the rigs he passed; they averaged one 
every four miles outside of the villages; from this it would seem that 
for roads of this class shoulder treatment is not worth while unless 
fine shifting sand or heavy clay is encountered. 

The sketches given below show a number of variations of section 
for bituminous macadam which are applicable to special conditions. 
Figure 3 shows the distribution of stone on unimportant road sections. 

Figure 4 gives a good typical section for ordinary conditions on a 
main road. 



.it > Gravel- #2or#'55tone Filled and 



/"to/ 



kj. 



Rolled, butnot Puddled or Tarred. 



' . k /4'-l8 - " -*1 

K- 24-30 H 

Fig. 3. — Bituminous Macadam 
Gravel, #2 or #3 Stone ^ | About 3"deep f loose 



"~~ 



v 



1 K IZ'-I5'-- — H 

*< —— -70'-20'- 31 

Fig. 3 a. — Shoulder Treatment 

1 The amount saved per mile, 'assuming a depth of macadam of 6" and an average 
price of stone at $3.50 per cu. yd. in place would be approximately $700.00 for use 
of 12' in place of 14/ and $350.00 for use of 15' in place of 16'. 



3° 



SECTIONS 



,- Dirt Shoulders 




No Shoulder Treatment 



CM 



E[. Theoretica l Grade ^-C ra 

ca ms' Ann' .\\\\v^ .V A\vfr 

|<- is 

1 h -19'- 

k- — - 22'- 

K-- Z4'~ze' 



wnztol 

nXnnnNNVT 




Fig. 4. — Bituminous Macadam 



El. Theoretical Grade J^sOvwnf:/! %'.f. 

-^ S *777777777^ / //////\///A /S77~h7?r, ' 

Ur-r—JT— -* 



N. — 



\£ 



*— - Any Width which keeps the Top of Slope insidefHeR.oFW.—'-* 
Fig. 5 

Figure 5 shows a section adapted to the top of hills where a small 
amount of surface water is expected. If for any reason it is not 
practicable to cut into the hill beyond a certain depth and more dirt 
is needed for fill than is given by the 26' section at this depth, the 
shoulders can be widened, provided the tops of the slopes keep within 
the right-of-way. It is always best to use as shallow a ditch as 
possible, as it simplifies the construction and maintenance of entrances 
to the abutting properties. 



'Concrete 
Guardrail 




& Wooden 

§ Guard Rail- 



k-~ -IO'-20'- J 

24' 




Figure 6 gives a section showing the variations in fill. A slope of 
1" to i' beyond the 22' width is used on shallow fills; a side slope of 
1 on 4 is used for all ordinary fills up to a 7' depth; beyond a 7' depth 
it is cheaper to erect and maintain guard-rail, using a 1 on ij slope. 
The cost of guard-rail is taken up under "Minor Points." 

The section shown in Figure 7 is used for unusually heavy cuts to 
keep the excavation down as much as possible; it should never be 
used on a sharp curve because of the difficulty in seeing ahead. (See 
Alignment, page 18, and Office Practice, page 208.) 



VARIATIONS OF SECTIONS 



31 




Fig. 7 




Fig. 8. — Banked Section in Excavation 

figure 8 shows a section well suited for sharp curves on steep grades; 
the slope of j" to i' is not objectionable for slow traffic up the hill 
and makes easier riding for vehicles traveling rapidly down grade; 
this section has also been used successfully on sharp curves on level 
grades and is becoming a standard feature of the New York State 
work. 

hi 



I "to I' I "to I 




Cr own 2 1 to I ' 



15-20' M 

3Z-40' : " : -"- :: -~-^- 



Fig. 9 

Figure 9 is a satisfactory village section and by the use of a variable 
width can be made to fit conditions on most streets. 



S^ Elevation, Theoretical Grade 



k 8.0'- -* 15.0 

F -16.0'- -+- 




17.5 



Fig. 10. — Bituminous Macadam Tracks on Side 

Expansion Joint \ ~ Curbing I S S Class 

i Tie fi"c„ jr ,l- Concrete- 
z Izoand Cushion^ * T i W 



Jf 5 -2"-* Class Cone. Base .^'Concrete underground Tie i"°St.Ba\ 



-*- 



Fig. 10 A. — Village Street, Brick Pavement. Tracks in center, "T"- 
Rail Special Grooved Brick 

The preceding discussion attempts to show only the main points 
to be considered, for every road presents local conditions peculiar to 



32 



SECTIONS 



itself that require special solutions. However, if the Engineer keeps 
these points in mind, he will make an economical and appropriate 
design. 



Macadam 



Hitching Post 
/ Plain Curb 

Brick \ Crown 2 to f. 




k- io'o"-- 



>j '^Concrete 
Base 



j| 



Fig. ii. — Village Section. Combined Brick and Macadam Section 
in Front of Stores, where Horses will be Hitched Close to the Curb. 
Prevents Pawing up the Macadam 

It may be said in closing that many of the road widths, as actually 
built, do not represent the engineering judgment of the Highway 
Departments. On a road where it is evident that a 12' or 14/ width 
of metaling would amply serve the traffic there is often a strong senti- 
ment that this locality is being defrauded because some other road is 
16' wide, and if political influence can be successfully used a 16' width 
is constructed. This is mentioned to show one of the practical diffi- 
culties in attempting to build an economical road that meets the 
actual traffic requirements. The general complaint that roads are 
becoming more expensive overlooks this contributory cause, and, 
while it is true that more expensive constructions are necessary on 
account of changed traffic conditions, it can be safely asserted that in 
most cases where political expediency overrules engineering judgment, 
either in regard to widths or materials, an unnecessary expense is 
incurred. This condition is, however, sometimes due to defects in 
the Highway laws which allow too much interference by local officials 
who are not qualified to judge in such matters, and it has been demon- 
strated that better results are obtained by centralizing the control of 
the design, particularly in regard to widths, alignment, and materials, 
in some executive or commission, which is as independent as possible 
of such local pressure. 



CHAPTER III 

CULVERTS — SMALL SPAN BRIDGES — UNDER DRAINS 

This chapter deals with the smaller drainage structures only. For 
the theory and practice of reinforced concrete long-span structures, 
masonry arches, or steel bridges, the reader is referred to the standard 
works on those subjects. 

^ The conditions for transverse surface drainage to the ditches were 
given in chapter II and the minimum ditch grades that insure the 
longitudinal drainage were mentioned under the heading of "Mini- 
mum Grades," page n. Ditches on steep grades must be protected 
from wash by cobble paving, cement gutters, or loose stone, and these 
designs are considered under " Minor Points," page 115. 

I. Culverts 

Engineers do not differ much in the design of these structures. 
They should be permanent; should be large enough to take the maxi- 
mum flood flow; should, if possible, be self-cleaning; must admit of 
being cleaned easily, when necessary, and must be long enough to 
include the normal width of section between parapets. There is 
nothing more unsightly and dangerous than to have the width of 
roadway narrowed at a culvert. 

Cast-iron pipe or reinforced concrete boxes are generally used 
Cast-iron pipe culverts larger than 18" are rarely designed, as they 
are not economical. (See Table No. 17, page 58.) Vitrified pipe should 
never be placed under the roadbed proper unless encased in concrete; 
even then cast-iron pipe is preferable and probably cheaper. Where 
the head room is small, usual practice calls for cast-iron pipe, and if the 
flow is large, a double or triple line of pipe may be constructed. For 
small drainage areas the size of the culvert is determined by the con- 
venience of cleaning, rather than by the discharge capacity. Where 
sufficient fall can be obtained to make it self-cleaning, a 12" pipe is 
feasible, but where the flow is sluggish, nothing less than a 16" or 18" 
pipe will serve satisfactorily. 

The self-cleaning velocity of flow for sand and earth particles is 
about one foot per second; for coarse gravel about three feet per 
second (Ogden's Sewer Design, page 134). A pipe laid on a slope 
that gives a velocity of five feet per second when flowing one-quarter 
full should keep clean; this requires a fall of approximately two feet 
in one hundred for a 12" pipe, and is the minimum grade at which 
the 12 size should be used. 

For the smaller concrete culverts the shape of the opening should 
be designed to allow the use of collapsible forms. 

The desired size of a culvert is usually determined in the field by 
notmgthe dimensions of the old culvert, if any, and by inquiries of 
the neighboring residents and the road commissioner as to how the 

33 



34 



CULVERTS 



existing structure has handled the water in the past; any such con- 
clusion should be checked by computing the probable maximum run- 
off from the area tributary to the culvert. For the convenience of 
designers, Table No. 10 is given, showing the approximate maximum 
run-off for small watersheds in flat, rolling, and hilly country. Of 
course, it is understood that such a table is to be used simply as a 
guide for judgment. 

Table io. Maximum Run-off for Small Watersheds Using 

Dickens' Formula 

D = C^/]VP. Run-off Expressed in Second Feet 



Area in Square Miles 


Flat Country 
C 200 


Rolling Country 
C 250 


Hilly Country 
C 300 


o.i =64 acres 


36 


45 


54 


0.2 


60 


75 


90 


0.3 


81 


IOI 


121 


0.4 


IOO 


125 


I50 


0.5 


119 


149 


l8o 


0.6 


136 


170 


204 


0.7 


153 


191 


229 


0.8 


169 


211 


253 


0.9 


185 


231 


277 


1.0 


200 


250 


300 


2.0 


. 334 


4i7 


50I 


3-o 


456 


57o 


684 


4.0 


564 


705 


846 


5-o 


668 


835 


I002 


6.0 


764 


955 


1 146 


7.0 


860 


1075 


I29O 


8.0 


95o 


1188 


I426 


9.0 


1038 


1297 


1556 


10.0 


1122 


1402 


l682 


20.0 


1890 


2362 


2834 


30.0 


2560 


3200 


384O 


40.0 


3180 


3975 


4770 


50.0 


3760 


4700 


564O 


60.0 


43io 


5400 


6480 


70.0 


4840 


6050 


7260 


80.0 


536o 


6700 


804O 


90.0 


5840 


7300 


8760 


100.0 


6320 


7900 


9480 



For areas under 0.1 square mile, see Table 12. 



CULVERT DESIGN 



35 



Dickens' formula takes into consideration the rate of rainfall and 
character of the catchment basin by the coefficient "C" and is as 
reliable as any of the maximum run-off formulae. Wilson in his 
" Irrigation Engineering," page 19, gives the following values of "C": 

Rainfall 3.5 to 4 inches in 24 hours. 
Flat country C 200 
Mixed " C 

Hilly " C 



200 
250 
300 



These values are safe for 
the Northern and Eastern 
Atlantic States. 



Rainfall 6 inches in 24 hours. 
Flat country C 300 
Mixed " C 325 

Hilly " C 350 

Table ii. New York Central and Hudson River R.R. Cul- 
verts for Small Drainage Areas 



Steep, Rocky 

Ground. 

Acres 


Flat Cultivation, 

Long Vallej r . 

Acres 


Size. Diameter 
in Inches 


Equivalent Capacity. 
Pipes 


5 


10 


10" 




10 


20 


12" 




20 


40 


16* 




25 


50 


18" 


two 16" pipes 


30 


60 


20" 


two 16" pipes 


45 


90 


24 " 


two 18" pipes 


70 


140 


30" 


two 24" pipes 


no 


220 


36 " 


two 30 " pipes 


150 


300 


42" 


two 30 " pipes 


1 So 


360 


48 " 


two 36" pipes 


280 


560 


60" 




Note. — To be used only 


in the absence 


1 of more reliable infor- 


mation, particularly existing 


culverts over t 


he same stream. 



Table iia. Culvert Design. Iowa State Highway Com- 
mission l 



Size of Culvert 
Opening 


Maximum Acres 


Minimum Acres 


2'X 2' 

4 r X 4 ' 

6'X 6' 

8' X 8' 

10' X 10' 


70 

376 

1300 

2700 

5000 


28 

140 

520 

1 1 20 

2000 



36 CULVERTS 

Types of Structures Used l 

i. Box culverts and slab bridges 2' to 20' span. Not economical 
over 20' span. 

2. Reinforced concrete arches 8' to 100'. Constant tendency to 
destroy by temperature strains and settlement. 

3. Pony truss steel bridges. 30' to 8o' span with reinforced con- 
crete floor. Adapted to districts where concrete materials are scarce. 

4. Reinforced concrete girders, 20' to 50' span. Very economical, 
but require careful design. Not economical for spans over 50'. 

Where the road runs through a village, a closer computation may 
be obtained by using a sewer run-off formula. 

The Burkle-Ziegler formula for such approximations is as follows: 

Cubic ft. per sec. ] ( £v. cu- f t of ] 4 /Av slope of ground 

per acre reaching \ = C X \ ^^LltL \ X \l m ft. per 100 

No. of acres 



Svert ^ b r " e! r a ^ t u ,y ing 



I heaviest fall J T No. of acres drained 

C = °-75 f° r paved streets and built up business blocks. 

C = 0.625 for ordinary city streets. 

C = 0.30 for villages with gardens, lawns, and macadamized streets. 

Trautwine states that 1" of rainfall per hour equals 1 cu. ft. per 
second per acre approximately. 

For drainage areas of under 1 square mile, it is probably better 
to use the Burkle-Ziegler formula even for farming country, using 
the coefficient C = 0.25. 

Table 12 shows the amount of run-off computed by this formula 
assuming a maximum rainfall rate of 4" per hour for the constants 
C = 0.30 and C = 0.25 for areas up to 1 cquare mile. 

Note: — Quantities in Tables 10, 12, and 13 computed and checked 
by slide-rule; sufficiently accurate for the purpose for which these 
tables are intended. 

Table 13 gives the velocity of flow and the discharge capacity of 
pipe and box culverts for different rates of fall per 100 feet. 

Examples of the use of tables 10 to 13 dn checking culvert sizes. 

1. Determine the character and area of watershed tributary to 
culvert; say rolling country, one square mile. 

2. Determine flood flow for this area of rolling country from Table 
No. 10; equals 250 second feet. 

3. From the profile of the stream where it crosses the road de- 
termine the fall in feet per 100; say 1.0 ft. 

4. In Table 13 opposite 1.0 ft. in the "Rate of Fall" column, pick 
out the size that has a discharge capacity of 250 second feet; equals 
4/X4/ culvert. 

Where the road runs through a depression which has no outlet, a 
culvert should be placed at the lowest point to keep the water at the 
same elevation on both sides of the road, and the grade line raised 
above high-water level. 

It is our opinion that a culvert should have the same slope as the 

stream bed. If given a greater slope the outlet end tends to clog, 

and if a lesser the inlet end will plug. It is unusual for culverts to 

fill badly, except when placed at the foot of a steep hill where the 

1 See Table at foot of p. 35. 



TYPES OF STRUCTURES USED 



37 



stream velocity is naturally reduced. At such points an extra large 
structure should be designed with the idea of providing sufficient 
waterway even after the contraction caused by this settlement has 
occurred. Such a culvert should be cleaned after each freshet. 

More trouble is experienced from culverts becoming filled with ice 
due to alternate freezing and thawing weather; this is particularly 
true of small culverts draining springs. Culverts as large as 2^2' 
have frozen solid in this manner, and if this condition is anticipated 
the size should be regulated accordingly or trouble will be experienced 
during the Spring break-up. 

In designing culverts under side roads, the length must be great 
enough to provide an easy turn; many times a saving in length can 
be made by placing the culvert a short distance down the side road, 
as shown in figure No. 12, page 39. 

Table 12. Run-off for Small Areas 

Discharge in cu. ft. per second for a maximum rainfall rate of 4 
inches per hour. 





Fall of 5 


' in 1000 


Fall of 20' in 1000 


Fall of 50' in 1000 


Area in Acres 












C = 0.30 


C = 0.25 


C = 0.30 


C = 0.25 


C = 0.30 


C = 0.25 


1 


1.8 


i-S 


2.5 


2.1 


3-i 


2.7 


2 


3-o 


2-5 


4.2 


3-5 


5-4 


4-5 


3 


4.1 


3-4 


5-7 


4.8 


7-2 


6.0 


4 


5-o 


4.2 


7-2. 


6.0 


9.0 


7-5 


5 


6.0 


5.o 


8-5 


7-i 


10.7 


8.9 


6 


6.8 


5-7 


9-7 


8.1 


12.2 


10.2 


7 


7-7 


6.4 


10.9 


9.1 


13-7 


11.4 


8 


8.5 


7-i 


12.0 


10.0 


I5-I 


12.6 


9 


9-3 


7-8 


13-2 


11. 


16.5 


13-8 


10 


10. 1 


8.4 


14-3 


11.9 


18.0 


15.0 


20 


16.9 


14.1 


24.0 


20.0 


30.2 


25.2 


30 


23.0 


19.2 


32.5 


27.1 


40.7 


33-9 


40 


28.5 


23.8 


40.3 


33-6 


50.9 


42.4 


50 


33-6 


28.0 


47-7 


39-8 


60.0 


50.0 


60 


38.6 


32.2 


54-6 


45-5 


68.7 


57-3 


70 


43-3 


36.1 


61.4 


51.2 


77-3 


64.4 


80 


48.0 


40.0 


67.9 


56.6 


85.2 


71.0 


90 


5 2 -4 


43-7 


73-9 


61.6 


93-i 


77.6 


100 


56.7 


47-3 


80.2 


66.8 


100.8 


84.0 


200 


95-4 


79-5 


134-6 


112. 2 


169.7 


I4I-4 


300 


129.0 


107.7 


182.9 


152.4 


229.7 


191.4 


400 


160.0 


133-6 


227.0 


189.2 


285.6 


238.0 


500 


190.0 


158.0 


268.0 


223-5 


336.6 


280.5 


600 
640 ) 
1 sq. mile J 


216.0 


180.0 


307.0 


256.0 


387.3 


322.8 


230.0 


1 I92.0 


323-0 


269.0 


406.3 


338.6 



1 200 second feet by Dickens' formula, Table 10. 



38 



CULVERTS 



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SMALL SPAN, SOLID FLOOR BRIDGES 



39 



Main Road 



Macadam 



Side Culv. in Ditch Line 



Side Culvert Set 
Back on Side Road 




Fig. 12 



The following section shows a form of culvert often used 
in village streets where deep ditches at the culvert site would be 
objectionable: 



Sidewalk 



IN 




Drop 



6 rate 

1 kV^\^^^^\^^^^^^^^^^^^^\^^^^^^x^^j^^^^^^^^^^^.^^^^^^^^^^\^,^ l v:^^?^g 



^rw^W^'XwXw^ 



Inlet 



Sidewalk 



-4- 






^>>^>>>^ 



Fig. 



i3 



For the small-sized structures required to carry ditch drainage 
under driveways vitrified tile well laid is as suitable as any style of 
construction; the wooden boxes built by some Departments are not 
economical, which is shown in the following estimate of relative cost 
of small culverts, given by A. R. Hirsch in Wisconsin Road Pamphlet 
No. 4 : 



Kind 


Size of 
Opening 


Length 


First Cost and 

Maintenance for 

100 Years 


3 " Hemlock box 

Concrete box 


15 in. sq. 
15 in. sq. 
18 in. 
18 in. 
18 in. 
18 in. 
18 in. 


24' 
2o' 
2o' 

30' 

2S r 

24' 
26' 


$252.00 
40.OO 

35-°° 

41.00 

42.00 

166.00 

196.00 


Concrete pipe 


Single strength V. T. P. . 
Double strength V. T. P. . 

Cast-iron pipe . 

Corrugated steel 



SMALL SPAN, SOLID FLOOR BRIDGES 

Under this head are included spans of 5 to 25 feet; they are gener- 
ally designed from one of three types: reinforced concrete slabs, 



4Q 



CULVERTS 



Plate 4.— New York State Slab Bridges 




-Rods 0.25°" Net Area-, 
Spaced lE'X.toC. 
W\{Spans5'to25!) 
Plan. 



(Heights 5 'to 15.') 




, z DowehO.25^ 

ii'xtrs ;;, 

Pile Foundations tobe %_'. 
Used in Lightand Shift- 
ing Soils. Pave when 
Ordered byDiv.Engineer. 




Note 

All rods to have a deformed 
cross-section. All rib metal to be 
of medium steel. 

2d class concrete in all slabs 
and parapets. 3d class concrete 
in wings invert and abutments. 
Wing walls on the outlet end of 
all square culverts with concrete 
floors to be built parallel to the 
center line of the culvert. Round 
all exposed edges to 1^ inch 
radius. 



-Rods in Slab to be Exten- 
\ ded 24 Diams. beyond 

Neat Lines of 
\ Abutment 



Elevation. 



Bottom Width of the 
Abutments not less than 
j~ of Total Height from Bottom 
of Abutment to lop of Slab. 

Section onCenterLine 



For Typical 

Section "F" 

Where culvert covers 
become a part of con- 
crete base for brick 
pavement, transverse 
reinforcement should be 
extended 12" beyond 
back of abutment intc 
concrete base. 




Rods in Slab to be 
Extended 24 Diams. 
beyond Neat Lines 
A of the Abutments. 



"Rods 0.25°' 
NetArea-, , 
Spaced IZ 
C.toC. 



NEW YORK STATE SLAB BRIDGES 



41 



! 

Span 


Thickness of 
Slab 


Net Area 
of 

Rods 


Rod 

Spacing 
C-C 


Length 

of 
Dowels 


5 


8" 


o.25sq." 


4*" 


12* 


6 


9" 


it 


4" 


u 


7 


10" 


o^gsq/' 


- 3'/ 
54 


u 


8 


IO" 


11 


si" 


a 


9 


II" 


it 


5" 


u 


10 


12" 


a 


4-r 


a 


11 


12" 


o.s6sq." 


er 


a 


12 


13" 


u 


6" 


l8* 


13 


13" 


It 


- 3// 
54 


a 


14 


14" 


It 


-3// 
58 


11 


15 


14" 


a 


5" 


it 


16 


15" 


it 


.2 If 
44 


11 


17 


i5' r 


a 


44 


ti 


18 


16* 


u 


A 1 " 

42 


ti 


19 


17' 


u 


44 


a 


20 


18" 


o.77sq." 


,-10 

54 


a 


21 


18" 


a 


si" 


a 


22 


19" 


u 


5" 


24" 


23 


19" 


it 


S" 


11 


24 


20" 


a 


.5// 

4s 


11 


25 


21* 


i.oosq." 


r-1" 

58 


11 



For Spans 5' to 19' W = 18" For Clear Height 10' or less 
5' to 19' W = 24* " " " ii' to is' 

" " 2o' tO 25' W = 24" " " 

For Clear Height 7' or less E = 3'- o" 

" 8' to 10' E = 4'- o" 

above 10' E = 5'- o" 



15' or less 



42 CULVERTS 

steel I-beam stringers supporting thin reinforced concrete floor 
slabs, or plain and reinforced concrete arches. 

Central piers will often reduce the cost of culverts having a long 
span with small height. 

For structures of this class more care must be taken in determining 
the span and height. On streams requiring spans of more than 10 
feet there are generally existing structures above and below the 
proposed bridge site which will afford the best basis for judgment. 
While it is usually good policy not to reduce the span of an existing 
structure it is often found that the present bridge, particularly if it is 
a steel bridge that has been sold to the town by an enterprising bridge 
company, has a needlessly long span. 

If the freshet velocity of the stream is high the stream bed and the 
abutment foundations may be protected from scour by riprap. 
However, it is not often necessary to take this precaution for small 
span bridges. According to Trautwine a velocity of eight miles an 
hour, or 12' per second, will not derange quarry rubble-stones 
exceeding half a cu. ft. deposited around piers or abutments. A 
rough approximation of small stream velocities can be made by 

assuming a value of 60 for the constant C in the formula V = C \/RS 

where V = velocity of flow in feet per second; constant C = 60. 

„ ,* , .. ,. Cross sectional area of flow 

R = Hydraulic radius = ^ r~^ — = 

Wetted Perimeter. 

S = slope of stream. 

Example. To approximate the freshet velocity of the stream shown 

having a fall of i.o' per ioo', or 53' per mile 




2S.0' 

v = cvrs 

C = 60 
IOO 



R 



25 



S = = 0.01 

100 

V = 60^/4 X 0.01 = 6o\/^°4 = 60 X .2 = 12 ft. per second. 
Plates No. 4 to No. 6 c show the standards for culverts and small 
bridges as used by various State Departments. 

Under Drainage 

The purpose of under drains is to intercept the ground water before 
it reaches and softens the subgrade. On a side hill road the drain is 
usually placed under the ditch on the up-hill side (see Figure No. 14, 
position No. 1, page 52), where the greatest depth can be obtained 



NEW YORK STATE I-BEAM BRIDGES 



43 



Plate 4 a. — New York State I-Beam Bridges 



Expanded Metal Embedded in 
6"Concrete( '2* 'Class) \ 

Length of Culvert — - d 




V-1'6"-^ 



Exp.Metal- 
Steel Bars 



I- Beams Spaced 
as/Shown In 
.A\ Table/. 






' " Conor 
Cover 



&& 



' j : ? , 



[VWc 



• no more than 4. 
l-'-oj 



r 



3 




« 



Cross Section of Parapet 
Showing Reinforcing. 



'-■'■■■■'ff.-iWSIlSTO 



2 Steel Bars- 



^ ? ^ 

55 ^ .',' 

2 -Class Concrete 
Parapet 



3 




Paint all Beams 
p\ 2 Coats Lead 
and Oil. 



Round all Exposed 
Edqesto2£Rad. 
Exp. Metal to be 
3 6' "or -6* 12' 'Mesh, 
weiqhinq not less 
than 1. 2 lbs. 
persq. ft. 



- — . __: — -L_____ _' _J£! 

Longitudinal Section. 




PartEnd Elevation. 








I- Beams Spaced as Shown 

on Table I. 
Expanded Metal 
Embedded in 6" 

?d r//-rcc rnnrre+t 



h- -x 

6 'tolZ'high, r=24+(lix2{") 
I3'to20'" ,x=24+(Hx3 n ) 

Spansl8to30Feet. 
6-2?aa 






c 




k---x~>| 

6 'tol2'high, x=ldt(tlx2fj 
I3'to20'f f x=ffl(Hx3") 

Spans 6 to 17 Feet 




Length of Culvert 

'L enqth of Culvert is taken as the 
'Distance from Outs, to Outs ide of Para- 
pets or from 0. toO.ofOuardRailand Meas- 
ured on a Line at Right Angles toC.L.of Road. 
Span is Taken as me Distance bet. Abutm'rs 
Measured on a Line parallel to the C.L.ofRoad. 
- 'at Top of I- Beams. Angle of Skew is the Angle 
bet. the C.L.of Culvert and a Line atR.Angles to C.L.ofRoad. 
ti= Total Height of Abutment 
A and B = Deflection of Wings in Degrees. 
L and M= Length of Winqs. 
P = Length • of Abutment Measured along Face of lop. 

Skew Culvert. 



44 



CULVERTS 



ii^h ^\d 'u " u n 


O 00 O CN ^tO 00 O cn "^-vo 00 O N *tO CO O N "tO 00 O cn rj- 

M M CN CN CN CN <N rOfOtOtOf)'t , t^' , t , tiOiOiOio l/")0 O O 




O cn ^t-O 00 O CN 'tO 00 O CN 'tO 00 O CN ^tO 00 O CN 'tOOO 

cn cn cn cn cn totocotOfO , t'tt , t , tmininio lOO o O o O 


S9?[idg spunoj 


"tO 00 O cn "^O 00 O cn "tO OO O cn TtO OO O cn 'tO 00 O cn 

CN CN CN tOtOfOt / )< / )^ , t^t , tl^l010lO U)^) VOVOOO t^> t-~ 


g.3 


q^2u9-j 

}00J I9J 


O fO^O O CN tOOO H ttNO fO>0 O CN IO00 H ^NQ COO O CN 
tO'OrOcO , t , t , t 1 O l O iOO OOO M>. t^OO 00 OO 0*00*00 

M 


qiSugq; 
;ooj £s 


10 CN cn ro-rj-iOM rOfONOO CNOO <t O OOO 00 00 00 CO CSVO O 
lOlO^tt (OM CO CN CO CN CN l^lO't't'tH M M M M M CN CN CO 

00 O O m cn oo 't >oO r^.00 O O m cn co »oO r^-00 OO w f^t 

MHWMMMHMMMCNCNCNCNCNCNCNCNCNCOrOCOCO 


Cu. Yds. 2d Class 
Concrete Cover 
and Parapets 


}OOJ I9J 


lONOO N ^O OOOwcOvoOmpO -to 00 O cn tJ-O r-» O w 

M M M CN CN CN CN CN CO' / )fOfOtO^ ,, t'tt , t>01010IJHO U")0 

6 6 6 d 6 d 6 6 d 6 6 6 6 d 6 d 6 d o d 6 6 6 6 6 


}OOJ Ss 


^00 CO cOOO 00 GO O CO O Ow O h m -rj-O cocO cn O O O cn 00 

1J"> O O O CNOO "t M N^IHOO O ^0 ^ W t-^'tO NtO^HOO T}- 

«t io voO t» r^-oo OOO m m cn co -t 10 10O r-- r^-oo O O O m 

MMMHMMMI-1MMMMMCNCNCN 


CO X 


qigug'j 

lOOJ I9J 


oO O O w cn co "3" ioO r>-00 O m cn ro "*t 10*0 t-^co O O w cn co 
hwhhmmmmihmCncncncncncncncncncocococo 


q;§n9i 
;ooj Ss 


OioO^OioO<oOioO>oio0 1 oOioO'oOioO^Oio 
OnionO«")nOw' / )N(nionOnionO«ionOn 

CN CN CN CN tOfOfOtO^ - ^" T t^" l 01^ U-JO 0*0 t*» f-» t-» t^OO CO 


M 
<cj 

u 
+J 

CO 


sreg f 
;qSi9^ 


m OO "* cn u->o 'too hionhooo O m cn t O r^oo OOO 

HMCNCNCNCNCOCOCOCO»OVO 100 t^OO O O O O 


9ZIg 


»h<liraWipjHimHirj|'*t-|*'-l«> H=o-c!oort|a>HeOi-<("*'Hh!'«:-*^ i^i«|N-!t)H|fiH|NHM 


r/J 

a 

a 
a> 

PQ 

i 

i— i 

<u 

CO 




O inOM CN COrt-loOiO t>-00 M COO CO O CN rto 00 O V)0>^ 
O toioOiOf^ONO co*£> O^O O^O O i^OfONH ioOO m 


•}j i9d 
*1A\ 


CN lO IOOO MHMliOlOMMMMI-lCNCNCNCNCNCNCNlClDlOU-) 
M W M M CN CN CN CN CN COcOcOCOCO T t' : t't' ; t't' , t ,, t 1 O l Ol010 


}93J 

q^Sug^j 


CO O O m cn co rt ir,\o t-»oO O m cn co ^ ^00 r-00 O »-* cn co 

MMMHMMMMMWCNCNCNCNCNCNCNCNCNCOCOCOCO 


Sup'Bds 


•"' "^' ^' ^' ^' ^' ^' ^' ^' ^' ^' ' ^' ^' ^' v 1 "J ' ^' ^' ^' ' 

CN rOcOCN cOCN cocOcocoCN rocOcOcOcOCN CN cOcocOfO 


s9qouj 
q;d9Q 


O t>i t^GO OOOO O CN CN CN CN N lo IO >0 V) m 10 IOOO 00 OO 00 


t/3 

<D CO 

C V 

<a 
£3 

§3 

rt en 

.as 

£^ 
a o 
O 4 " 


M9^S 


rt- rcO O r^00 OOOmmcncO'+tI- ioO O t^OO 00 O O m co 
"t "f ioO r- t^-OO OOOMCNCNco't't u">0 O t^cO O O O m 

MMMMMMMHMMMMMMCNCN 


M9^S 


O O CO OO <0 OO CN O^O CN 0\\0 CN O^CNCO l^5CN00 IOMOO 
CN O O I-^O UO CO CN M OOO Nlfl'tfOH O O r^-O io CO CN M O 

lAo o t^-oo o d h cn cn co 4- too r^-oo t>t>6 h cn nt>nm 

HMMMMMMMHHHMCNCNCNCNCNCNCN 


AV9^S 

.Si 


O O CO 0<O co OO CN O^^CN OlOCNOOO CNCO 1OH00 lflHOO 
CO *■» t^O 0*0 V)10V)tttfOtOfOM CN CN IH M M O O O O* 

u>*o t^oo O O m cn co "t io*0 t^co O O m cn co 't >o*0 r^oo OO 

MHHMMMMMMMCNCNCNCNCNCNCNCNCNCN 


Span, all 


Culverts 


O t^oo O O m cn co ■* mO r-^00 O O m cn co -^- too r^oo O O 

(HMMMMMMMMMCNCNCNCNCNCNCNCNCNCNCO 



QUANTITIES IN CULVERTS 



45 



o 

LO 

M 

II 

pq 

o 

CO 

II 

< 

w 

m 

o 

LO 

HI 


Cubic Yds. 

each ft. in 

length of 

Culvert 

more or less 

than 25 ft. 


Xjuosej^; 


M N ^t CO ^O^C O CN TJ-X-- <M Q\O0 GO M 

01 -^ N O COO OO O •^■OcOCO COO 

M M HI CN CN CN CO CO 4 4 4 IO lOOO 


9}9JDUOJ 


CO TtOSLO^"*fr<N O O H T^ OO IO 

O cn rfO Onoi \o HI LOCO CO N HI O HI 

O M HI HI HI CN CN CO fO fO 4 4 IO lOO 


Cubic Yards 

Third Class 

Masonry 


s3m YV * 


hi -3- iO\Q 00 hi O CO 'sJ-'O CO 10 q COO 
O 6 lO HOO NO hi -4" 00' 4 ^N H 

MMcscNco^rOr^coO'NTtoo 

H M M HI HI 


s^nqy z 


n O t-^O cn h 10 ^tO co ^pOO NoO ^f 

00* n dNio coco co b hi co 1000 

CN CO "^ Tj" IOO NOO O O CN CO ^ IOO 

HI HI HI HI HI HI 


Cubic Yards 

Third Class 

Concrete 


sSujav i~ 


CN 00 Q\ CO CO N O O lO'tN HOO 0*0 

lOCO CNOO* rf HI d^CO^CO COOCO OO 

HI HI CM CO CO IOO N Q\ HI CN rf N 

HI HI HI HI 


s,inqy z 


<N O -^O CN <N LOGO O NO H H (ON 
4 OM^HOO LO CN O O lOO O NOO 6 

(N cn cO'^-'^-ioO NOO OO hi <N ro 10 

H HI M HI HI 


S3 


Lengths of 
VVings 


% 


N O COO O <N O O CN LOOO CN lOCO M 
O t HOO lOCOO N IT) CS O N -^- M Qn 


co ^O NOO O cn t}-ionO0 *n i-o N 

HHHHHH(1N(Nflfl 


J 


HO cno cn N CN 00 COCO hi 00 Tf O rj- 

LO O O HI N CN OO CO^O^fHI IOMO CN 

CO LOO OO O HI CN 4'ONO^O CN f) IO 
MHIMMHIr-lCNCNCNCN 


o 


CO 

II 

PQ 

o 

CO 

II 

< 

H 

H 

o 

HI 
< 

H 


Cubic Yds. 

each ft. in 

length of 

Culvert 

more or less 

than 25 ft. 


a!iuos'bj\[ 


N moO lOLoO O O O hi -tj-CnNO n 

M Tj-O O CN LOCO ^00 CO N M O HI O 

HHHHNCNlNrOCO^^t 1 ^ IOO O 


919JDU03 


TNOO COCOO -4" hi NIOIOO O lOCO 
O HI COO OO M ^- O CON H LOO ThO 
O HI HI M HI CN CN COCOCO^^IO^^O 


Cubic Yards 

Third Class 

Masonry 


sSujav "t 7 


10 a rf n cn hi hi coioo "^"t^o t> - r t 
do" <N ^i-od -4- m 6 oJiohi 

M H CN CO CO ^"O NCJ\H CO 1Y) IN 
HI HI M H CN 


s^nqy z 


IOCOIOC010C0 10N(N CN lOCO CONIO 

CO 4" O N ^j" <N 6 ^r"^-^"--i- lOO' N C> 

CN CO 't -t V)0 NOO O O HI CN CO^LO 

HI HI HI HI HI HI 


Cubic, Yards 

Third Class 

Concrete 


sSui yv * 


LO CN 00 i" Tj- TT H LO -^f* Tj- CN O T^- CN LO 


lo C> co O *0 «0 cn 10 OO WOO lo-3-O O 

HI HI <N CO 'i" IOO OO O H COION 
HI HI M HI 


s^nqy z 


COCOO O 't COCO CN LOO O HfXJ NO 
COOO 400COO< s 'HHHHHCI't 

cn cn co tJ" ^ IOO NOO On O hi cn co ^T 

HI HI HI HI M 


CM 


h3 


% 


N O COO O ON O O CN LOCO CN LOCO M 

COO COO N LO CN 0\N Tt H OO CO M 

CO»ON d 6 CN t ^NC^H CN tJ-O CO 
HHIMMHIHICNCNCNCNCS 


h3 


N O COO O CN O O CN LOCO <N LOCO M 
00 O COO N-LOCN O N -vf HI OO CO HI 

CO *0 N q\ 6 CN TJ- LO N C\ M <N tJ-O 00 
HIMHIHIHIHICNCNCNCNCN 


iu9tii:mqy 
jo ;i{Sj3H 


w 


O NOO OO HI CN co rf LOO NOO O O 

MMMMMMMMMM CN 



4 6 



CULVERTS 



o 
O 

II 

pq 

o 
to 

II 

< 

W 

w 
co 

o 
to 

^r 


Cubic Yds. 

each ft. in 

length of 

Culvert 

more or less 

than 25 ft. 


Xjuosbj^; 


10 O NO OO rO 0\rj- O Om io cn m co 
O O ^^"^^O O CMOO NroO N ^ 
H CN CN CN CO CO ^t -4 tOO O* NOO 00 O 


9;3iouo3 


xt co tO OO 'tO O O H NO 00 M On 
<00 C> cn O O ^ <N N COOC Tt NrO 
M H H CM CN CO CO 4 4 IO lOO N N 00 


Cubic Yards 

Third Class 

Masonry 


sSu IM ^ 


00 cn hoooo O 't qv O tJ--^-oo n no 

O H N co h h H r^coC>J>-l>.C>rj-H 

H H CN CO Tf tOO 00 O M CO tOOO M 
H t-4 H M CI 


s^nqy z 


10 1000 to to cm 10 to coco OOOOO 

O OCO 0606 OO* h to O to 6 N co cn 

rf ^ tosO NOO O cn co TfvO OO O h CO 

MHMMMMHCNCN 


Cubic Yards 

Third Class 

Concrete 


s2u IAV ^ 


ION IO CO <N HOOOO H O O 00 H H 


to On ^f O N to tJ-OO h NrOH m H/ o^ 

H CN CM CO Tt" tO NOO O CN "^"O OO 

IH H M H H 


s^nqy z 


O ^ <*? p O ^-topooo NO OO O 
COOOO t^O to to to N O "^- O co OnvO* 

co ^ -^t too noo O m co -1- to noo 

MHMHWMHCN 


! 




% 


rJ-O On m CO lO N O CM ^rO CO O CM rf- 
CM CO "^-00 NOO Oh CM UTtiO NOO O 

tJ-OOO O CN -rj-O Om COION 0\H CO 

MHMMMCNCNCNCNCNCOCO 


tl 


O )-* ^O MO mO hO mO HO hO 

co too CO Oh cn ■^•lOt^.O'O H CO"4" 
HMHMHHCSCNCMCN 


o 
to 

H 
II 

PQ 

o 

co 

II 

< 

W 

M 

CO 
o 

o 

CO 


Cubic Yds. 

each ft. in 

length of 

Culverts 

more or less 

than 25 ft. 


Xiuos^p^ 


lOCO'tvO O to-^-coO i-^00 O "^" h O 
COO OCNO OcoO ^OThO to h N 

MMHCNC-4<NCO"^j _T 4""4" tOO O N N 


949IDU03 


O co O N NOO cmoOOcoONNO"^" 

O CO tOCO H tJ-00 ^OO CONN N COCO 
HHHMCNCNCNCOCO^^tO tOO O 


Cubic Yards 

Third Class 

Masonry 


sSm^w t 7 


00 CO 00 N O ^ tOOO to CO CN N ^f CM 

O H NfOH O H N CM O N N O "3- H 

H H C4 CO Tt" tOO CO Q\ i-^ CO tOCO H 

H H M H Ci 


s^nqv ^ 


cocnO NO O co cm N tJ-O O to O O 

COO N io t cn cn OO cn -cf N O '^■CO 

co ^" ^t" too t^CO O H cn co "tf-O t^CO 

n i-i m y* n n h 


Cubic Yards 

Third Class 

Concrete 


sSujay t 7 


000 tcn ONNco^-^OnCN h toto 

tOCO "4 1 O O ^ COCO H O CN 1H M CO00 

m cn cn co ^- to r»oo O cm ^-o 00 

M M M W M 


s^nqy 3 


O CO lorONO O t^O O O NOO O 

t^ CN 0\^0 CO H O tOO N00 Qs CN TfoO 
cn CO CO "^ toO l>»00 O O h <N rt- 10O 


fei 


1.1 

►3 


3 


t^-O G\ >-f co to X^ O cn -^-O O0 O N ^t 
TJj-iOOCO OO h co^toO NOO h 

^-Ood O* CN IONOH COtONOCN "4- 
MMfHHHClCNCMCNCNCOCO 


h1 


^■o^t-o^o^t-o^t-o^-o^-o^- 

co^rO t^OO °q cotoOOO O t-t cn t^- 

HHHHH HHCNCNO) 


}U9ui:mqv 
jo iqSpH 


ffl 


O t^oo O O h cn co ^r too i>-oo O 

" 1 



CULVERTS 

Plate 4 a — continued 



47 



Table No. 6 


Number I- Beams 
For Concrete Covers only 












P ^3 T pnrrf Vi r\( AKntmontc 




Spacing 








Length of Culvert 
























2'- 6" 


2'- o" 


3'-o" 


15° Skew 


30 Skew 


45° Skew 


18 


5 


5 


4 


18.64 


20.79 


25.46 


19 


5 


5 


5 


19.67 


21.94 


26.97 


20 


6 


5 


5 


20.71 


23.09 


28.28 


21 


6 


6 


5 


21.74 


24.25 


29.70 


22 


6 


6 


5 


22.78 


25-40 


31.II 


23 


7 


6 


6 


23.81 


26.66 


32.53 


24 


7 


6 


6 


24.85 


27.71 


33-94 


25 


7 


7 


6 


25.88 


28.87 


35-36 


26 


8 


8 


7 


26.92 


30.02 


36.77 


27 


8 


8 


7 


27-95 


31.18 


38.18 


28 


9 


8 


7 


28.99 


32-33 


39.60 


29 


9 


8 


8 


30.02 


33-49 


41.01 


30 


9 


9 


8 


31.06 


34-64 


42.43 


31 


10 


9 


9 


32.09 


35-So 


43-84 


32 


10 


9 


9 


33-13 


36.95 


45-26 


33 


11 


10 


9 


34.16 


38.10 


46.67 

1 



Application of Tables 

Quantities for a 30 Skew Concrete Culvert, concrete top, length 
30 feet, opening 13 feet high and 12 feet wide. From Table 1, an 
opening 12.12 ft. wide 30 Skew is a 14-ft. span requiring (see 30-ft. 
length, Table 6) 9 I-B earns spaced 2 r -9" c. to c. (9 X 400) = 3600 lbs. 
I-Beams; 218 lbs. Bars; 400 + (5X16) = 480 sq. ft. Ex'p'd Metal; 
9-78 + (5 X 30) = 11.28 cu. yds. 2d class Concrete 32 lin. ft. Pipe 
Rail. An opening 13 ft. high will require Abutments, 16 ft. high 
(13' + 2' in ground + 10" I-Beam = 15'- 10"). From Table 4, 
Abutments = 118.0 cu. yds., Wings= 102.9 cu. yds. (5X4.79 = 23.95 
cu. yds. 5 ft. extra length of Culvert) 118. o + 102.9 -f- 23.95 = 
244.85 cu. yds. 3d Class Concrete. 

For Spans of more than 17 feet, use Masonry Tables for Con- 
crete Abutments and Wings. 



4 8 



CULVERTS 
Plate 5 





k- W - ->j 

End Elevation. 
General Dimensions Semi-Circular Arch Culverts 



s 

Span 


Thickness at Springing 
Line 


Thickness of Ring 


Height of Haunch 


T 

Concrete 


K 

Masonry 


C 
Concrete 


R 
Masonry 


J 
Concrete 


V 

Masonry 


6 
8 

10 
12 

14 
16 

18 
20 


2'-6" 
2 , -6" 

3'-o' / 
3'-6" 

3 , -9" 
4 '-o" 
4 '-6" 
■>'-o" 


2'-6" 
2'-6" 

3'-o" 
3'-6" 

3'-9" 
4 '-o" 

4 '-6" 
S'-o" 


10" 
11" 
12" 

14* 

15" 
16" 
18" 
18" 


10" 

12" 
12" 

15" 
15* 

15' 
18" 
18" 


iV 

2'-6" 

3'-°" 
3'-6" 
4 '-o" 
4 '-8" 
S'-o" 
S'-o" 


2'-0" 
2'-6" 

3'-°" 

3'-9" 
4 '-6" 

S'-o" 
S'-6" 
6'-o" 



CULVERTS 



49 



Plate 6 





Alternative 

Cross Section for 

Collapsible Forms. 



k- 6'6"or- 

' 8'0" 



Longitudinal Section. 




( All 1^2'and 2'x2' 

Culverts to be Bui It with 

EndWa/h.) 



End Wall. 




c 
a 




- t 

.ZOO 

.c x> 
1- < 


2|3 


2'0" 


6" 


12" 


a 5 


3'0" 


6" 


12" 


/.2 


4'0" 


6" 


12" 


/2 


S'O" 


8" 


/2" 


/.2 



Table of Dimensions. 



Reinforcement^ 
^«9 



|. , d:o'd'. , 'a:o"c, , ,r».i.Y' 



mt r*r ■ • • — ■ — ' 

Longitudinal Section. 



Slope 



m 



^Dowels 0.25°" 
NetArea , 
I'Olon^lZC.ioC. 



Part 
Cross Section. 



New York State Small Box Culverts 



So 



CULVERTS 



Plate 6 a. — Massachusetts Standard for Concrete Arch Culverts 
|4--4'6"--->i f*\ 



!F\&y 



-* 



</8- 



OneEnd 0.88 cu.yds. 
5'6"----H icffH 



s 



0.064- cu.yds. 
perft. 




One End 1.14 cu.yds. 

e'e" — *\ M^ 




One End 1/39 cu.yds. 




fc-23"H 



0.089 cu.yds. 
per ft. 



K/ftl 




K- 2^"-^ 



O.U4cu.yds. 
perfr. 



K-- — To"— — >i 




(*!% 




* — 
Si 


f, 

<-/8> 


^.1 <i- 



One End 1.61 cu.yds. 
* 



7 r ^\ 

24 






*n* 



i\ 



A. 



*18* 



One End 1.91 cu.yds. 




k- 30*-M 

0.123 cu.yds. 
per-fV. 




0.18 cu.yds. 
per -ft-. 



with the least excavation and where the water is caught as it flows 5 

out of the hill. . . * , i 

Some engineers place the drain in position No. 2 (figure 14; but > 

this requires more excavation for the same depth, and, in the writer s 

opinion, it is more likely to be broken. 

The usual depth for drains is three feet below the surface. 

Where the road is on a descending grade, the water will flow out ot : 



CULVERTS 



Si 



Plate .6 b 




See Note 
below. 



__1 



,# 



Concrete 



k— 5'— >l 
Assumption for Live Load. 



-J 



xt 
i 



Longitudinal Rods 20"to27'C.toC. 



5 of k 

sEvery o/fte/- Rod bent J i v 



•ir / 



■'t 

r 



* 



71 



Long. Rods not 

*■ Spans less than 8 ft 

Corners not less than 6. 
Long. Rods Same SizeasSides 
and Bottom t. 



Cross Section of Culvert. 



-fr-'No Corners 
' ; or Corner Rods 
• or Reinforcing 

n for 5 ides and 
\ Bottom t on2' 
\ and 3 'Spans. 



U» Q 



d — ■* 

•r T d <3 






u 

ri 



CO 



c 



ccj rt 

a a 

CO CO 



a 

CO 



a 

CO 



C 
a 

CO 



a 

CO 



OOl^t^NrOtOWMOOO»fO T tOMO<NOOt^"*Ol^^tMMMMMTj--^-^J-TtTl- 
f^t^M M MOO lO<N 0~0 -^"(N M M CO CO O O O >-< t^ Ol 't t^ tO f) t^ ^t"00 O* f) O ^ 



>H g 



m to toO vo rf io^O CO O O co O 00 "*H00 m O NO O O 00 "O io^- coiohvO c* t^ 
O* m iooO m O fOO r^-O fONH tJ- Q\ co ^ t^. O tJ-00 O ^t O t 3" | - ,v O m \0 O *0 m t-.cs 
Ohhhnnnnn to (O to 't 't ■+ io^O *0 t^ t^ r^ O O O O O O O O n w to fO ^ 



lo'C 



d y 
o o 



3 



OOoOMoOoOooOOOOOooOOONNMNWNMN't^^Tj-^ 

v' *0x*0» M M *M *M M M *M 00*00 CO'oO CO 00 CO CO CO 



u 

a 

CO 



VOMDVO "3-Tj-Tt-C* (N NOMDOO tOtOtOtOtOtOtO^ N OS CN <N CS tN CN <S 



M 

J 



a 

CO 



o> o 0> Oi Oi Oi o 
i ii i i i T 


o 


O W N *N C* 


fOtO^oWWNN 


t-~ 
i 


j^^O O^OvO^O 


H <N to« co 'd" eo ^■^O^oo^J- 100 


co ■* »OvO t^OO O co -^ iOO 


^.00 


O O 

M 


H 


% ^ » i * i % 

*0 OO rt tJ- rf CS 


<N 


NvoivO^O 


cococococOcococN cn 


<N 


rs 


CI e* 


CS 0* 


7n 



►J 



^S:*:^**:^*:^*:*^^* 



* % %: 5: 5; 



MMMMMMMMWCSCNCSCNCNCNCNCNCNCNCNCOCOCOOOCOOOCOCOCO 



OOO rj-^t^cs CN NVOOOO CO0OCOCO0OCOCOCN CN <N N N N M CN <N 



3 



■bii ah-h.xxxxxx °2222'???P'?'i , ""?V???'?-?"?-'?T f 



<N M tOcOfO^'t^'^TO 



\Q vO O 00 00 



Oi O H H m w M M M cococococococococo 



a 



00 00 »0 io IOO0 00 00 r*»-f>. r^O vOOcX)C00000O^OOOOOO v 0\0O'O<5vOO ( O^0 



Tj-Ttioioiovoioioiovo io^o voO'OO t^t^r^.t^ t^oo oooooooooooooO 00*0*0*0* 



^ % H|^H|nH|n ^ * ^ H|n«l«H|NHt1H|NHlNH|NH|Nrt|t<H|tl O O O O O O O 

tJ- rf 10 lo u-)vO *0*0*000 !>• r* t^00 OOOOOOmmmmmmm 



MHNtOHNtONtO^'MtO'tNtO't'ONtO* lOO X>-00 <N CO ^ 10*0 t^OO O 



- ^ 









lo^=l 



a-a 

O -t-> 

-M U 

-1-1 0) 
O M 

28 

cu T3 

^ CCj 

.y «« 

&^ 

^u 

'o »-• 

en ^ 

<u o 

CO O 

. d 

oS 

+j d 



■&.§ 



iooooooooooocoooOooooodoccooooooooooooooOoooooooocooooooooooooooooooo; 






=3 O 

o <u 
ad 
Q <^ 



52 



CULVERTS 



& ^Macadam 



!! 

-Si 




Side 
Hill 



Position No. 2 



^ at Direction 
of Seepage 
Position No. I 



Fig. 14 



the hill directly under the stone and the drain is placed as in figure 15, 
position 1, or two drains are built in position 2. Position 1 is the 
usual practice, being cheaper and more effective. 

The argument for the two side drains is, that in case the throat 
becomes clogged, a side drain can be taken up without disturbing the 
macadam. This rarely occurs in a center drain, as it is better pro- 
tected than those in position 2 and in case the center drain does clog, 
side drains can be constructed at any time. 




Position No. 2 



<xj ^H Open Throaty 

I Position No. I Position No. 2 

Fig. 15 



\<--?.0-y j<-20-->{ 

• w ^y/ ^^'^ - ■■ ■ 

Bcrckf/H^KM^ 'mMm^-Packfill 
No. 4 Stone-; 




No.2 Stone or Gravel*^ 
Farm Tile-. Joints \ , S ~ 
Wrapped in Burlap* 1 - * **P» 

Fig. 16 



Open Throat 



There are two kinds of drain in general use : 

No. 1 is built entirely of stone with an open throat roughly laid as 
shown; it is satisfactory in a water-bearing strata of gravelly loam 
or clay, but does not work so well in quicksand, which is liable to fill 
it up. It is generally cheaper, however, than No. 2. 

No. 2 is built of porous farm tile or vitrified tile of a suitable size 
(usually 3" to 6") with open joints, wrapped with a double or triple 
layer of burlap; the pipe is surrounded and covered with clean gravel 
or f " crushed stone to a depth of 6", the remaining depth of the 
trench being filled with large stone. If this drain has a good fall and 
the outlet is kept free, it will rarely clog even in bad quicksand. 

The author has successfully used the following method to prevent 



UNDER DRAINAGE S3 

the outlet from clogging: after being brought out from under the 
macadam, the drain is continued under and across the ditch line, 
then keeping outside the ditch line, and using a slightly smaller 



1 



mt 



v , f ,/,>>'. ^ n An i n , !rr=:j . 



I! 

Fig. 17 

gradient than that of the open ditch, the tile is continued down the 
hill until it reaches a point eight or nine inches above the ditch grade. 
Here it is turned into the open ditch through a small concrete head- 
wall and what little material it tends to deposit is washed down the 
ditch by the surface water. (See figure 17.) 

In planning the drainage for a road improvement, it is well to make 
as few changes as possible from the existing scheme. New culverts 
or a change of direction and amount of water discharged through 
farm land is almost certain to result in some friction with the owners 
of the properties affected. 



54 



CULVERTS 



OO 

o 

o 



3 





& 


M 


n 


Ph 


H 


to 


< 


o 


U 


c^ 


O 


t-H 


rfl 


H 

ro 


CO 

< 


< 


CO 


Ph 

O 

m 


P4 

O 


H 


r* 


W 


H 


o 


H 



w 



££ 



CO M 

M 
o 

w 

H 



CO 



a 

H 



!^ < 
< w 

« H 

<I 

P* ^ 

H o 

a* 



Q 

H-l H 

Q ° 

«£ 

So 
o 





,a 


o 


o o o o 


o 


o o o o 


o o o o o 




4-> 


M 


O VO t^ CN 


() 


io O O lo 


00 o o o o 




PI 


<N 


CO ^t-vO ON 


(N 


LO ON CO t^ 


vO ^ LO OnvO 














<u 


0) 






M 


H H CN CN 


OO lO N 0> ^ 


a 










M 


-»-> 














f4 
















o 


O COOO N 


o 


M fO N Ol 


^ o o o o 


£ 


4-) 


OO 


LOOO lovO 


o- 


0\00 H <J\ 


VO O LO lo O 


o 


H 


CN co lo N 


u 


CN LO 0\ CN 


O LO CN <N LO 




Ph 






M 


M M M CN 


CO ^vO 00 O^ 

H 


^ <n 


CO 


<M lO O00 


LO 


M O^O fO 


vO NOO 00 vO 


U en 


^- lo LOO VO 


t- 


oooo ao 


H COIONO 




a 








M 





bo 



Lo O O Lo O 

O 00 CO CN lo 
CS CM -3-VO OO 



O O lo O O 

O O <n O O 

M T^- t^ M LO 

H H M CM CN 



OOOO 
LO O LO O 

COOO lovO 



CO «frsO 00 O 



+-> 


H 


COOO 


H 


00 


j>- r-oo 


O 


CO 


CN 


OOO 


t«- 


CO 


o 
o 


!>. 


CO LO 


CN 


O 


M 


VO 


CO LOOO 


ON 


o 


LOVO 


00 


H 


CN CO LO t"^ 


ON 


H 


"* 


J>- 


O 


^ 


o 


*fr 


H 


o 












H 


H 


M 


CN 


CN 


^ LO 


*>. 


ON 



O in 



LOOO H VO CN 
Tt Tt LO LOVO 



SO 



J>-O0 OO ON 



O CN co lo i>- 



S3 
p. 

•4-* 

rd 


Xi 

-t-> 
to 
d 

(U 


^- O O O lo 

OnvO O J>-vo 


lo O O O O 

OO co O O O 

ON CN LOOO M 
M H M CN 


o o o o o 

O O lo O O 

oq^ O^ ^ w^ q^ 

CN -^- LO t^ ON 


o 
o 


CN 

vd 

H 


t^- CO LOOO 

H CON to 
CN CO "^J-vO 


h io q q o 

CN CN LO O LO 
OO O CN LO f^- 

H H H M 


CO CO CN t^ O 

CO co ^f M 6 
CO co lo ON lo 
CN co tJ- lo n 


H 


tn 
en 

(D 


CN 


LOOO M t^ 
rt ^t LO LO 


cn vO O io O 

vo vo t^- t^OO 


ON CO LOOO CN 
CO O W CN tJ- 

i-i i-i i-i i-i 







<u 






H 




Q 


3 




s 




H 


w 


Ph 


ffi 


H 


T3 


O 


O 
O 


i— i 


c 


J 


Uh 


3 




O 

o 


o 




M 





LO O O ^^ lo 

N r}-N HOO 
M CN CO LOO 



O lo O O O 
^ i^ O lo O 
00 O co LOOO 



o o o o o 

lo O O lo O 
T^- lo n m O 

oT co ^vO^OO^ 



LO O 00 ON M 

4 d 6 cn n 

M CN CO -^t" LO 



LOVO CO CN O 

<N ONOO d> o 

i>-00 O CN LO 



(N NNION 
tJ- h m cn vd 

O ON ON M VO 
<N CN CO LOO 



^ S 



ON cn rl-vO O 
CO ^f ^" ^" lo 



rh 1>> O ^ J>- 

lo lovO vO vO 



vO OO ON O vO 

N.00 ON M CN 



saqouj 
l^uiuio]yj; 



co "tvo OO O 



CN rtvO OO 



tj- OvO NOO 
CN co co ^ Tf 



WEIGHTS OF EXPANDED METAL 



55 



o 

Ph 


Weight 

in Pounds 

per 

Sq. Ft. 


OvO rj- o Tf O n^h r»vo -*tO 
vOOOO cn "<t cn co vooo O cO00 cn 

666666666mm6m 


Note. — Expanded metal for small 
culverts is generally specified as 
weighing a certain number of pounds 
per square foot and having a mesh 
approximately the size shown on the 
plans. 


Sectional 

Area in 

Sq. In. per 

Foot of 

Width 


co cooO r-O O O cn co tj- O vooo 
O vooo 00 to^OO *3- cn o ^O 

cs<NMqMqi-iMcjfo , 4'«Nro 
6666666666666 


H 

r 

< 


-G 
cn 

CD 
N 

to 


M "^ coo c^TOooobobobob cs w 

xxxxxxxxxxxxx 

i-t|N«|-* ih <N co co co CO co co tO^O vO 


o 
w 




00 « W^OO^O N O O O N't"* 




cn 
C 

<£* 

,a co 


OO ^O 00 00 t- O O ^ 'd'OO 
\0 VOOO vO ^t" co "<t vo voO t>- 

66666666666 


1 O -d § 
<<CO PQ 


OOOOOOOO^OOOOO 

CN ^O O 00 't ^VO ^ <N <N M O <N 
MCNMCN-^CNCNMI-IMMCNCNM 




Hjr CD -> 

CO 


vo vo vo vo O lOifllOcOfO COO «o CO 




cn 
<U 

CL)T3 

c 

OO 


cn "cn cn "cn "cn "cn "cn "cn "cn "cn ^ *cn "cn 

Xooooooooooooo 
^ob^obobcooooooooooooooooo 
5 XXXXXXXXXXXXX 

COO -<t voo O <0 ^tvO vo vo -tf vo vo 


H 
W 

o 
w 


cn 

CO 


ts^lf)^l0 1fl«5N N W CN 

xxxxxxxxxxx 

rl|C< r-l|P» r-l|?< r-l|C< H?* HC< H?» 

coco<N<ncncnmmmmm 


w 

o 
o 

Hi 


►> CO 


^tOOOoOOOOOoOt^-CN TtO 

t^-OO f>. VO CN VOO Ol CN CO O "^"OO CN 
M M CN " H 


s 

< 

u 

h 

Q 

< 


Section 

Area per 

Foot of 

Width 


O vo r^.vo cooo 00 r>-0 O O "1 vooo 
O M OOoo >t t^O vo O O O "^-vO 

CNCNCNMOWMCNCO 'tO O CN CO 

66666666666666 




CO -<-> M 

CO o 


Standard 

< < 

Light 

Standard 

Heavy 

Ex " 

Standard 

Heavy 

Old Style 

Standard 

Heavy 




<u 


O cn O N ^vO vO vo "fr to 




CCJ -•-> 

o°3 


cX)cocNCNvOOOOO v OOvO' : t ,, =t 

MMMMMMMMM M 




,-fi 






e* 


cn 


m CN cococococococo ^1"nO O 



56 CULVERTS 

Table 16. Table of Round and Square Bar Weights 



Round Bars 


Plain Sq 


uare Bars and Twisted 
Square Bars 


Diameter 


Area 


Weight 


Dimension 


Area 


Weight 


1 

4 


.0491 


.167 


1 

4 


.0625 


.212 


_5_ 
16 


.0767 


.261 


A 


.0977 


•332 


3 

8 


.1104 


.376 


3 

8 


.1406 


.478 


A 


.1503 


•511 


7 
T6~ 


.1914 


.651 


i 

"2 


.1963 


.668 


1 
2 


.2500 


.850 


A 


.2485 


.845 


9 
16 


.3164 


I.O76 


5 

8 


.3068 


1.043 


5 

8 


.3906 


I.328 


\i 


•3712 


1.262 


11 
T6 


•4727 


I.607 


3 
4 


.4418 


1.502 


3 
4 


.5625 


I-9I3 


^4 
16 


.5185 


1-763 


13 
16 


.6602 


2.245 


7 
8 


.6013 


2.044 


7 
8 


.7656 


2.603 


ti- 


.6903 


2-347 


15 
16 


.8789 


2.988 


i 


•7854 


2.670 


I 


1 .0000 


3.4OO 


ii 


..9940 


3-38o 


i* 


1.2656 


4.303 


ii 


1.2272 


4.172 


i| 


1.5625 


5-3I3 


if 


I.4849 


5-049 


if 


1.8906 


6.428 


ii 


1. 7671 


6.008 


if 


2.2500 


7.650 



Diameters expressed in inches. Areas expressed in square inches. 

Weights expressed in pounds per foot of length. 

The twisted square bar is known as the Ransome Bar. 




RcmsomeBar. 



Kahn Cup Bar. 





Corrugated Bars, 




Diamond bar. 



ThacherBar. 



ROUND AND SQUARE BAR RATES 



57 



•8 






O 



■Q 

N 

< 
PQ 

c 

B 

B 
I 

1 
& 

Q 

fa 

o 

w 

< 

W 

< 

o 

P 

u 
u 

CD 

Q 

< 

« 
O 

w 

w 


n 

pq 

CJ 
O 

B 

s 


X! 


cn ^t-oo co q\0 ^ co 

6 6 O H H « Wj IT) 


< 


CN H O M COO O CO 

O "t^ OMD O Q O 
O w cn co to ^ O to 

000000* m 


M 

c3 

pq 

M 

D 
rC 
(J 

CJ 

Xi 
H 


X! 


n coO O cooo ^t" O t*- 

dddoHHNfOfo 


M 

< 


^ o 

^f O CO 00 m u->m O O 

O M M (N ^ lO N O^ H 

dddddddoH 




a 
w 

H 
M 

1-4 
O 

U 


-t-> 

X! 


vO to»T)iO O 
OO OnO «*■ CO 
O M CN CO *0 


V 

< 


to O r^ O O 

CN ION O lO 
d O O H M 


Ih 

PR 

M 

en 

'£ 
H 


x 


cncnOOOOOOO 

cn omnio^(-t|-ioion 

CN -rfOO CO OO ^ CO CO 

OOO^'-iCNcO'^'^O 




tOO O o too o o to 
cnCOOcnvoO^ocn 
O "3- to oo o o o o 
Omcncoi-O^Ocnlo 
OOOOOOmmm 




H 

w 

PQ 

$ 


XI 

IS 1 

'53 


cn co tJ-oO co O CO CO 
O OOO tONH t^ 
to CO coO NupWiO 

OOwcNcncO'sJ-io 


< 


OOO too O O to 

OOOCNtOO^OCN 

rf to o^^ o o o o 

M CN co>-Ot^O cn to 
OOOOOmmm 


Nominal 

Size of 

Bar 


iHl-*»lQCH|NiO|00e9i^H°0 iH|0CiH|tJ( 
H M M 



58 



CULVERTS 





CO 

H 

> 
•J 

u 
w 

PL, 

1— I 
Ph 

o 

1— 1 
1 

H 

CO 

< 




O 0* rfvOOO O <N -^-vOCO O <N Tj-vO CO O 

<N CN Ot CN W I , OfOtOt<3^'t^ - ^ , ^-'t>0 






w Ph 


r~» m vo O «o 
O ro io OO O 

M H M H CN 


O 

4 




*5 

n Ph 


CO M O r-~ VO 

OO O m to >0 

H M H M 

4& 


VO 

q 

co 




oo 9* 

m Ph 


cn co ^ O »o 
t^> co O vn co 


vN 

vO 






m rt r^ o t)- 
vo !>. 00 O m 

M M 
S9= 


CO 






CN CO •"+ <+ *0 
iO VO t^ CO O 
4£= 


o 

oq 






Tt- CN M O OO 

Tf to vo vo *>. 


M 








CO 

H 
t4 

W 
> 

u 

w 

H 

w 
u 

o 
u 


O 

w 
O 

o 

H 
N 

CO 


X 

»o 


O m co -^-vo t^OO O m co rj- io t^OO O M 
t^CO O O m <N co >ovo r-»CO Ov O m co ^f 


o 

to 




X 


r^oo 00>0 O h m cn c\» coco^Tfioio 
Tf tovo NdO H W (O* u->vo x^co O O 

HMHHHNNNNMMNNOin^ 

©9= 


CS 

to 




"Vo 
X 


t*. t>»vo vOvOioio^l-Tt'^-cococococvi oi 
CN CO "^ lOO t^-00 ©O H N to^t IOVO r^ 
MHHMMMMHCviCNCNvNCNCNMCvj 


CO 

00 

4 

6^ 




X 


t^VO lOrJ-fON M O OCO f^vo *0 rf co CN 
<N co rt tovO t^OO O O O M <N CO "^- vovO 
MMMHHHMt-IMCNCNCNCNCNCNCN 



to 

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CAMBRIA STANDARD I-BEAMS 59 

Table 18. Properties of Cambria Standard I-Beams 



Depth of 


Weight per 


Area of 


Thick- 
ness of 
Web 


Width of 


For Fiber Stress 
of 12,500 lbs. per 
Sq. In. for Bridges 


Beam 


Foot 


Section 


Flange 


Inches 


Pounds 


Sq. Inches 


Inch 


Inches 


Coefficient of 
Strength 


3 


5.50 


I.63 


•17 


2-33 


13,790 


3 


6.50 


I.QI 


.26 


2.42 


14,950 


3 


7-50 


2.21 


.36 


2-52* 


16,180 


4 


7-50 


2.21 


.19 


2.66 


24,850 


4 


8.50 


2.50 


.26 


2-73 


26,480 


4 


9-50 


2-79 


•34 


2.81 


28,110 


4 


IO.50 


3-09 


.41 


2.88 


29,750 


5 


9-75 


2.87 


.21 


3.00 


40,300 


5 


12.25 


3.60 


,36 


3-*5 


45,390 


5 


14-75 


4-34 


•50 


3.29 


50,490 


6 


12.25 


3.6l 


.23 


3-33 


60,520 


6 


14.75 


4-34 


■35 


3-45 


66,6lO 


6 


17-25 


5-07 


•47 


3.57 


72,740 


7 ' 


15.00 


4.42 


•25 


3-66 


86,260 


7 


17.50 


5-15 


■35 


3.76 


93,290 


7 


20.00 


5-88 


.46 


3-S7 


100,430 . 


8 


18.00 


5-33 


.27 


4.00 


118,490 


8 


20.25 


5-96 


•35 


4.08 


125,400 


8 


22.75 


6.69 


•44 


4.17 


133,57° 


8 


25.25 


7-43 


•53 


4.26 


141,740 


9 


21.00 


6.31 


.29 


4-33 


157,260 


9 


25.00 


7-35 


.41 


4-45 


170,260 


9 


30.00 


8.82 


•57 


4.61 


188,640 


9 


35-oo 


10.29 


•73 


4-77 


207,020 


10 


25.00 


7-37 


•3i 


4.66 


203,500 


10 


30.00 


8.82 


•45 


4.80 


223,630 


10 


35-oo 


10.29 


.60 


4-95 


244,050 


10 


40.00 


11.76 


•75 


5.10 


264,480 


12 


31.50 


9.26 


•35 


5.00 


299,740 


12 


35-oo 


10.29 


•44 


5-09 


317,030 


12 


40.00 


11.76 


.56 


5-21 


341,540 



6o 



CAMBRIA STANDARD I-BEAMS 







Table 18 


. Continued 




Depth of 
Beam 


Weight per 
Foot 


Area of 
Section 


Thick- 
ness of 
Web 


Width of 
Flange 


For Fiber Stress 
of 12,500 lbs. per 
Sq. In. for Bridges 


Inches 


Pounds 


Sq. Inches 


Inch 


Inches 


Coefficient of 
Strength 


15 


42.00 


12.48 


.41 


5-50 


490,840 


15 


45.OO 


13.24 


.46 


5-55 


506,490 


15 


50.00 


14.71 


.56 


5-65 


537,130 " 


15 


55-oo 


16.18 


.66 


5-75 


567,770 


15 


60.00 


I7-65 


•75 


5.84 


598,410 


18 


55-oo 


15-93 


.46 


6.00 


736,620 


18 


60.00 


17-65 


.56 


6.10 


779,440 


18 


65.00 


19.12 


.64 


6.18 


816,200 


18 


70.00 


20.59 


.72 


6.26 


852,970 


20 


65.00 


19.08 


•50 


6.25 


974,6oo 


20 


70.00 


20.59 


.58 


6-33 


1,016,490 


20 


75.00 


22.06 


^5 


6.40 


1,057,340 


24 


80.00 


23-32 


•5o 


7.00 


l,449,46o 


24 


85.00 


25.00 


-57 


7.07 


1,505,430 


24 


90.00 


26.47 


.63 


7-i3 


1,554,450 


24 


95.00 


27.94 


.69 


7.19 


1,603,470 


24 


100.00 


29.41 


•75 


7-25 


1,652,490 



Explanation of the coefficient of strength in the above table and 
examples showing use in practice. 

The coefficient of strength for each sized beam represents the 
maximum uniformly distributed load, in pounds, that will produce a 
fiber stress not exceeding 12,500 lbs. per sq. inch multiplied by the 
span in feet. 

If the load to be investigated is a concentrated load it must be 
changed to an equivalent uniform load in order to use the values 
given. This is done by multiplying the concentrated load by 2. 

Example: Suppose that it is required to determine the size I-beam 
that will carry a 40,000 lb. load in the center of a 15' span and a 
uniformly distributed load of 20,000 lbs. The coefficient of resistance 
for the concentrated load will be 2 (40,000) X 15 = 1200000 
Uniform load 20,000 X 15 = 300000 

1500000 

The required beam must have a coefficient of resistance of 1500000 
plus the coefficient due to its own weight. A 24" beam weighing 90 
lbs. per foot has a coefficient of 1,554,450. 

The beam weighs 90 X 15 = 1,350. The coefficient for the beam 
weight is 1,350X15 = 20,250, which deducted from 1,554,450 gives a co- 
efficient of 1,534,200, which is slightly greater than required and is safe. 



CHAPTER IV 
FOUNDATIONS FOR BROKEN STONE ROADS 

Concrete foundations are considered under Brick Pavements in 
chapter V. 

The real foundation of a road is the earth subgrade; generally, 
however, the term foundation is used in speaking of the lower course 
of stone, gravel, etc., used to distribute the concentrated wheel loads. 
A discussion can 'be developed under the following heads: 

i. The bearing power of different soils. 

2. The concentrated wheel loads on improved roads. 

3. The distributing action of foundation courses and the depth 
required for different soils. 

4. The different kinds of foundation courses. 

5. The distribution of the stone in the foundations. 

6. Special cases. 

1. Bearing Power of Soils 

The subgrade develops its greatest bearing power when dryo 
In the following discussion we assume that the soils are protected by 
a well-designed drainage system. 

Mr. W. E. McClintock, Mem. Amer. Soc. C. E., Chairman of the 
Massachusetts Highway Commission, published in the 1901 report 
of that Commission a valuable statement of the results of their 
investigations on the bearing power of soils and the distribution of 
wheel loads by the macadam. The conclusions have been well tested 
in practice and found to be satisfactory. 

"The Commission has estimated that non-porous soils drained of 
ground water, at their worst will support a load of about 4 lb. per 
square inch; and having in mind these figures the thickness of broken 
stone has been adjusted to the traffic. 

"On a road built of fragments of broken stone the downward 
pressure takes a line at an angle of 45 degrees from the horizontal 
and is distributed over an area equal to the square of twice the depth 
of the broken stone. If a division of the load in pounds at any one 
point by the square of twice the depth of the stone in inches gives a 
quotient of four or less, then will the road foundation be safe at all 
seasons of the year. On sand or gravel the pressure can be safely 
put at twenty pounds per square inch. . . . 

"Acting on this theory the thickness of the stone varies from four 
inches to sixteen inches, the lesser thickness being placed over good 
gravel or sand, the greater over heavy clay, and varying thicknesses 
on other soils. In cases where the surfacing of broken stone exceeds 
six inches in thickness, the excess in the base may be broken stone, 
stony gravel or ledge stone; the material used for the excess depending 
entirely upon the cost, either being equally effective." 

61 



62 FOUNDATIONS FOR BROKEN STONE ROADS 

2. Concentrated Wheel Loads 

There should be some limit placed by law to the maximum load per 
lineal inch of tire for vehicle using improved roads. The roads can 
then be designed for this load with no danger of failure from unreason- 
able pressures. Road work is handicapped in this country by the 
lack of wide tire statutes and the regulation of traction engines using 
sharp lugs on the wheels. At present it is necessary to assume a 
loading that will probably not be exceeded by the unregulated traffic. 
Many engineers favor a law limiting the load on improved roads to 
700 to 800 lb., to the lineal inch, which is a reasonable limit; with a 
six inch thread this would mean a load of nine tons for a four wheel 
truck provided the load was uniformly distributed. This is beyond 
the limits of team hauling. 

Most of the mechanical trucks in present use have tires wide enough 
to reduce the pressure below this limit. Near some of the large cities, 
however, mechanical trucking has increased to proportions that 
amount to a regular freight line and excessive loads are carried; the 
load and speed for such trucks must be regulated, for no road can 
stand abuse of this character. 

The following regulations governing the control of motor trucks 
and traction-engines were prepared by the New York State Highway 
Commissioner to go into effect in 19 14. 

Regulations for State and County Highways Adopted by the 
Commissioner of Highways of the State of New York 

Sec. 1. No traction-engine, road-engine, hauling-engine, trailer, 
steam-roller, automobile truck, motor or other power vehicle shall 
be operated upon or over the state or county highways, the face of 
the wheels of which vehicle are fitted with flanges, ribs, clamps, 
cleats, lugs or spikes. This regulation applies to all rings or flanges 
upon guiding or steering wheels of any such vehicle. In case of 
traction-engines, road-engines or hauling-engines which are equipped 
or provided with flanges, ribs, clamps, cleats, rings or lugs, such 
vehicles shall be permitted to pass over said highways provided that 
cleats are fastened upon all the wheels of such vehicles, and are not 
less than i\ in. wide and not more than if in. high, and so placed 
that not less than two cleats on each wheel shall touch the ground 
at all times, and the weight shall be the same on all parts of said cleats. 

Sec. 2. No traction-engine, trailer, steam-roller, automobile 
truck, motor or other power vehicle shall be operated upon or over 
the state or county highways; nor shall any object be moved over 
or upon any such highways upon wheels, rollers or otherwise, in 
excess of a total weight of 14 tons, including the vehicle, object or 
contrivance and load, without first obtaining the permission of the 
State Commission of Highways as hereinafter provided. No weight in 
excess of 8 tons shall be carried on any one axle of [any such vehicle. 

Sec. 3. The tire of each wheel of a traction-engine, road-engine, 
hauling-engine, trailer, steam-roller, automobile truck, motor or 
other power vehicle (except traction-engines, road-engines, and 
hauling-engines) shall be smooth, and the weight of such vehicle, 
including load, shall not exceed 800 lb. upon any inch in width of the 



CONCENTRATED WHEEL LOADS 63 

tire, wheel, roller or other object, and any weight in excess of 800 
lb. upon an inch of tire is prohibited unless permission is obtained 
from the State Commissioner of Highways as hereinafter provided. 

Sec. 4. No motor or other power vehicle operated upon any state 
or county highway shall be of a greater width than 90 in., except 
traction-engines which may have a width of 1 10 in. 

Sec. 5. No traction-engine, road-engine, hauling-engine, trailer, 
steam-roller, automobile truck, motor or other power vehicle, carry- 
ing a weight in excess of 4 tons, including the vehicle, shall be operated 
upon any state or county highway at a speed greater than 15 mi. 
per hr.; and no such vehicle carrying a weight in excess of 6 tons, 
including the vehicle, shall be operated upon any such highway at a 
speed greater than 6 mi. per hr. when such vehicle is equipped with iron 
or steel tires, nor, a speed greater than 12 mi per hr. when the vehicle 
is equipped with tires of hard rubber or other similar substance. 

Sec. 6. The State Commisssioner of Highways, upon proper 
application in writing, may grant permission for the moving of heavy 
vehicles, loads, objects or structures in excess of a total weight of 
14 tons over state and county highways, upon proper application in 
writing being made therefor, and under such restrictions as the Com- 
missioner may prescribe. 

Sec. 7. The owner, driver, operator or mover of any vehicle 
over any state or county highway shall be responsible for all damages 
which said highway may sustain as a result of a violation of any of 
the provisions of the foregoing Rules and Regulations, and the amount 
thereof may be recovered in an action of tort by the State Commis- 
sioner of Highways or by any County Superintendent of Highways 
of any county or by any Town Superintendent of Highways of any 
town in which said violation occurs. 

1 Sec. 8. These regulations take effect October 20, 1913. 

"Section 24 of Chapter 25 of the Consolidated Laws entitled 'The Highway Law' 
provides that any disobedience of any of the foregoing rules and regulations shall 
be punishable by a fine of not less than $10 and not more than $100 to be prosecuted 
by the Town, County or District Superintendent, and paid to the County Treasurer 
to the credit of the fund for the maintenance of such highways in the town where 
such fine is collected." 

Under these regulations properly enforced any of the ordinary 
foundation courses can be successfully used except on the heaviest 
traffic roads (see Classification page 74) provided the depth is varied 
to meet the soil conditions. 

Heavily loaded farm wagons exert a pressure of about 350 lb., per 
lineal inch of tire width as determined from the records of produce 
dealers in Western New York, and the author believes that a road 
designed to distribute a 4,200-pound wheel load on a six-inch tire 
would be safe. 

Note : — The length of wheel bearing on a well-constructed mac- 
adam road is about 1". 

The use of this loading and the application of the rules for distribu- 
tion of pressure given by Mr. McClintock in the preceding quota- 

1 This provision for enforcement does not work well; enforcement should be in the 
hands of the State authorities. 



64 FOUNDATIONS FOR BROKEN STONE ROADS 

tion results in a depth of 15" for heavy clay or a fine sandy loam, and 
a depth of 5" for gravel, which check his results. 

The thickness to be used in the intermediate cases must depend on 
the judgment of the engineer. The following examples are intended 
only as a guide for the more common cases. The amount for special 
cases often depends on trial. 

Sand and gravel require from 4" to 6"; New York State uses 7" 
as a minimum where motor trucking is expected; Massachusetts 
uses the following section on good gravel. 

A 






ZZZZZZZ2EZZZIZZZ 



■ ' ■ ■'■■'■'■ • • 1 > m — 



is! ^4"to5' 



Fig. 18 

Wherever the total depth is less than 5" the stone should be laid 
in one course and classified as top stone. 

For a light clay loam an average depth of 7" to 9" is sufficient in 
cut; for fills over 2' deep 7" is enough; high fills even of clay after 
having once settled rarely give trouble with 7" of stone. 

Heavy clay requires at least 12" in cut; if the soil is springy and 
especially hard to drain, 15" to 18 " is advisable. 

For shallow fills (see figure 19) : 

Old Surface 
Good Materia!^ 



Fig. 19 

In shallow or "pancake" fills, clay or fine sandy loam should 
never be used where the natural surface at this point is of a better 
variety, as they are almost certain to become saturated with water 
and will either squeeze or heave out of shape; long, shallow fills are 
to be avoided, which is considered in placing the grade fine, but where 
unavoidable, the best available material should be obtained and the 
original surface well broken up to form a bond with the new fill. 
Where clay is used, it should be treated as in cut. For fills of inter- 
mediate depths [i' to 2'] 8" to 9" is satisfactory. 

A fine sandy loam is difficult to drain because of its strong capillary 
action. Mr. Charles Mills, Chief Engineer of the Massachusetts 
Highway Commission, in the report for the year 1902 states that a 
loam of which 30% or more will pass a 100 sieve will require from 
10" to 15" of stone. 

To illustrate the different stone depths that may be used in a short 
distance, an extract follows from the construction report on founda- 
tions for " Clover Street, Section 1," a road near Rochester, N.Y. 
This was built in 1907-1908 and has held satisfactorily under farm 
traffic. 



KINDS OF FOUNDATION COURSES 



65 



Clover Street Road, Section i 
The normal depth of stone on this road was 7" > ** ^°P 



Station to Station 


Character of Subgrade 


Total Depth 
of Stone 


180 183 + 25 
183 + 25 186 -f 25 

186 + 25 187 

187 190 

190 191 

191 193 
193 200 


Cut in sand and gravel 

Clay fill 

Clay cut 

Sand, gravel and clay 

Clay cut 

Clay loam fill 

Sand and gravel 


6" 
8* 

n" 

7" 
12" 

7" 
6" 



PREPARATION OF SUBGRADE 

It is evident from the pressures to which a road is subjected that 
the subgrade must be well consolidated before placing the foundation 
stone. This is usually effected by rolling with a 10 or 15 ton steam 
roller, exerting a pressure of 350 to 500 pounds per linear inch of 
wheel width, and is continued until the grade is firm and compact. 

The difficulties of consolidation in different soils and the methods 
of overcoming them will be included in chapter XL 

KINDS OF FOUNDATION COURSES 

The foundation courses in ordinary use are as follows : 

1. Crushed stone 

2. Screened gravel 

3. Field stone sub-base 

4. Pit gravel sub-base 

5. Field stone-sub base bottom course 

6. Pit gravel sub base-bottom course 

7. Quarry stone base or Telford. 

1. Broken Stone Bottom Course. 

This style of construction is the one in most general use. Where 
local stone is abundant and well distributed, such a course will cost 
from S2.00 to $2.50 per cubic yard rolled in place; where imported 
stone is necessary, the cost depends largely upon the freight rate and 
the length of haul and may run as high as S5.00. Bottom of this 
kind is generally used where the total depth of stone metaling does 
not exceed 6" to 8" after rolling. Beyond these depths it is often 
cheaper to substitute sub-base or sub-base bottom course for a part 
or the whole of the broken stone course. 

The method of construction by the New York State Highway 
Commission is shown in the following extract from their 191 1 specifi- 
cations : 



66 FOUNDATIONS FOR BROKEN STONE ROADS 



Stone Macadam Bottom Course 

" After the subgrade has been prepared and has been accepted by 
the Engineer, a layer of broken stone of the approved size and quality 
for bottom course shall be spread evenly over it to such a depth that 
it shall have, when rolled, the required thickness. The depth of the 
loose stone shall be gauged by laying upon the subgrade cubical 
blocks of wood of the proper size and spreading the stone evenly to 
conform to them." 

"The roller shall be run along the edge of the stone backward and 
forward several times on each side before rolling the center. Before 
putting on the filler the course shall be rolled until the stone does 
not creep or weave ahead of the roller. In no case shall the screenings 
or sand for filler be dumped in mass upon the crushed stone, but they 
shall be spread uniformly over the surface from wagons or from piles 
that have been placed on the shoulders. It shall then be swept in 
with rattan or steel brooms and rolled dry. This process shall be 
continued until no more will go in dry, when the surface shall, if 
required by the Engineer, be sprinkled to more effectually fill the 
voids. No filler shall be left on the surface, and surface of bottom 
course stone shall be swept clean before covering with top course. 
Only such teaming as is necessary for distributing the materials 
will be allowed on the bottom course. Any irregularities or depres- 
sions, the result of settlement, rolling or teaming, if slight, shall be 
made good with broken stone of the same size used in the bottom 
course, otherwise the stone shall be removed and the subgrade re- 
graded and rolled. Such removal and restoring of the surface shall 
be made at the expense of the Contractor. Screenings shall not be 
used in leveling up irregularities or depressions." 

Massachusetts uses no filler; otherwise their construction is 
substantially the same as New York. 

Where imported stone is specified or the local stone is suitable for 
both top and bottom courses, the size used for bottom course is 
known commercially as "No. 4 stone" and ranges from 2f " to 3!" 
in its greatest dimension; the smaller sizes are used for the top 
course, for concrete and for filler; where the local material is only fit 
for bottom, the course is made up of stone ranging from i n to 3!" 
in order to use up the total output of the crusher. The stone smaller 
than 1" is used for filler, on the shoulders, and sometimes for the 
cheaper grades of concrete. In specifying the sized stone for a 
particular job, economy is considered. Stone sized from 1" to 3%" 
is perfectly satisfactory. The only reason for limiting the usual 
size from 2f " to 3!" is that it leaves the 1" to 2f " stone for the top 
course; a uniform grade is important for the top and the size men- 
tioned gives a smooth finish. 

The ratio of loose depth to rolled depth is given on page 272. 

Where filler is not used in the construction of the bottom course 
more binder is required for the top; it is our opinion that the use of 
filler is the better construction. 

The clause concerning teaming in the quoted specifications is a 
dead letter; teaming helps to consolidate the bottom provided it is 



KINDS OF FOUNDATION COURSES 67 

distributed over the full width and care is taken in watching the 
course to prevent loss of shape when the traffic is first turned on or 
after a long continued rainfall. 

2. Gravel Bottom Course. 

Screened gravel 1" to $%" in size is used in place of crushed stone; 
the course is constructed in the same manner as described above, 
except that a filler containing some clay or clay loam is preferable 
to a coarse sand, and it is often necessary to wet the course in order 
to consolidate it satisfactorily. 

A gravel bottom should be made somewhat thicker than a crushed 
stone bottom as the fragments do not interlock as firmly as crushed 
stone. 

The choice between a screened gravel or crushed stone bottom 
depends entirely on the relative cost. Under favorable conditions a 
screened gravel bottom course will cost from $1.30 to $2.00 per cubic 
yard, rolled in place. 

3. Field Stone Sub-base. 

Field stone sub-base is constructed, as shown in the cut, of field 
boulders roughly placed and rilled with gravel, waste No. 2 stone 
or stone chips; no attempt is made to finish the top of the course 
exactly to line and grade, as any small inequalities can be filled 
with bottom stone. The depth varies from 5" to 12" depending on 
the soil encountered in the size of the available field stone. In 
designing a bottom course of this kind, care must be taken to have 
accurate data as to the average size of stone available. If the de- 
mands of a foundation were fully satisfied by a 5" sub-base course, 
it might still be more economical to use a 7" course if the stone aver- 
aged seven inches, because the extra work of sorting and sledging 
to a 5" size would result in a higher cost per square yard than for a 
7" depth. 

Top Course,^ ^!o , : Bottom Course 



ia&jkmrf 




es 



■Sub-Base 



Fig. 20 



^ The amount of stone and filler required per cubic yard in place is 
given on page 272. 

Under favorable conditions this sub-base can be constructed for 
$1.00 to $1.50 per cubic yard. 

4. Pit Gravel or Creek Gravel Sub-base. 

Stony gravel is a satisfactory material for sub-base; it can be 
readily constructed for any depth from 2" to 24" if required, and 
where a pit or creek bar is near, the cost of such a course should run 
from $0.80 to $e. 2 5 per cubic yd. 



68 FOUNDATIONS FOR BROKEN STONE ROADS 

The ratio of loose to consolidated gravel for such a course is given 
on page 272. 

5. Field Stone Sub-base Bottom Course. 

Sub-base bottom course is essentially the same construction as 
sub-base, except that, as the top course is placed directly upon 
it, the stone must be more carefully assorted as to size, more 
carefully placed as to line and grade, and a better grade of filler must 
be used. 

Crushed stone (crusher run) or coarse gravel make a satisfactory 

filler. 




/Top Course 



1 

^Sub-Baw Bottom Course 



Fig. 21 

The course can be of any depth from 5" up, depending, as for sub- 
base, on the soil and average size of stone; it is practically impossible 
to make a large stone bottom of this kind conform exactly to line 
and grade; a variation of 1" either above or below grade is usually 
allowed and the inequalities taken out with the top stone; this 
requires that the top course must be at least 3" deep after rolling. 

Sub-base bottom is especially applicable for long stretches of road 
requiring a depth of 9" to 12"; it usually costs from $1.30 to $i.;o 
per cubic yard in place where fence stone is available, and by its 
use the item of higher-priced bottom stone is reduced. However, 
on a hard foundation it is generally better to use 4" to 5" of ordinary 
broken stone bottom course instead of the sub-base bottoin course 
even if more expensive, because the small stone construction is more 
uniform in its resistance to heavy loads and the top course will wear 
more evenly and longer. . . 

An extract from the 1915 New York State Specifications is given 

below. „ 

Sub-base Bottom Course 

When field or quarry stone is used for constructing the foundation 
course it shall be of a hard, sound and durable quality, acceptable 
to the Engineer; the stones shall be placed by hand so as to bring 
them in as close contact as possible. When quarry stones are used 
they shall be placed on edge. The depth of the stone shall m no 
ca^e be greater than the depth specified for the course, the width 
shall not be greater than the depth, nor more than six inches; and 
the length shall not be greater than one and one-half times the depth, 
nor more than 12 inches. The distribution of the stone shall be ol a 
uniformity satisfactory to the Engineer. The long dimension sha 
always be placed crosswise the road. After laying^ this course shall 
be thoroughly rolled with an approved roller weighing not less than 
10 tons, and shall then be filled with stone or coarse gravel as directed 
and again rolled until the stones are bound together and thoroughly 



KINDS OF FOUNDATION COURSES 69 

compacted; but no gravel shall be used for filling except under 
written permission of the Engineer. .All holes or depressions found 
in rolling shall be filled with material of the same quality and the 
surface shall be rerolled until it conforms to the lines and grades 
shown on the plans. When field stone is used approved tailings 
may be used for filling. In all cases a sufficient amount of fine 
material shall be used to fill all voids. In limited areas where the 
use of a roller is impracticable heavy tampers may be used to con- 
solidate the material. 

6. Pit Gravel Bottom or Sub^Base Bottom. 

A stony gravel containing not over 1$% of loam makes a satis- 
factory course; the depths vary from 4" to 18"; pit or creek gravel 
even when unusually coarse has from 40 to 60 c ~ c of fine material; 
a suitable gravel for pit run bottom should not contain more fine 
material passing a j" screen than coarse material retained on a J" 
screen. If there is a large excess of fine the gravel should be screened 
and remixed at the bin in proper proportions. 

The great difficulty in this construction is to get proper consolida- 
tion without too much delay. It is advisable to lay a course of this 
kind at least two weeks ahead of the top stone in order to give traffic 
and rains a chance to help consolidate the course. The addition 
of 10 % of loam to clean gravel will quicken the consolidation. This 
can be done either at the pit by leaving a thin layer of loam when 
stripping which runs down with the gravel in loading or by placing 
from \" to 1" of loam on top of the gravel as spread on the road; 
the author has succeeded in getting rapid consolidation by snatching 
loaded teams over the loose course with the road roller; the roller 
continually smooths out the gravel and eases the haul for the teams; 
the horses' hoofs and wagon wheels punch into the gravel and pack 
it down rapidly. Sprinkling helps. A gravel bottom consolidates 
unevenly and it is always necessary to reshape it somewhat after 
consolidation; about So. 05 per cu. yd. should be allowed for this re- 
shaping of crown and elimination of humps and hollows. A prop- 
erly consolidated gravel bottom will permit a 4-ton load on 3 V tires 
passing over it without making a wheel mark over \" deep; this is 
a simple available construction test. We have gone into some detail 
covering this construction as it is the most economical type of bottom 
in a large number of cases but is not generally favored because it is 
harder to consolidate than, the other types of bottom. With a 3" 
or preferably a 4" madacam top it has proved perfectly satisfactory 
on all but the heaviest traffic roads. 

The cost of a gravel bottom ranges from $0.80 to $1.50 per cu. yd. 
in place provided the hauls are short. 

The depths of gravel is gauged by blocks or lines and the ratio 
of loose to rolled depth is approx. 1.2 (see page 272). 

7. Telford Base. 

Telford base is rapidly going out of use in the United States because 
of the difficulty of maintaining a top course laid upon it. It seems 



70 FOUNDATIONS FOR BROKEN STONE ROADS 

to be too rigid and is. more expensive than sub-base or sub-base 
bottom course, costing about $1.80 to $2.00 per cubic yard under 
favorable conditions. 

A good description of a telford construction is given by Mr. William 
Pierson Judson in " Roads and Pavements." The following quota- 
tion is an extract from his book: 

"On this subgrade are then placed by hand the stones forming the 
telford foundation, which may vary in size as shown below: each 
stone must be set vertically upon its broadest edge, lengthwise across 
the road and forming courses and breaking joints with the next course, 
so as to form a close and firm pavement. The stones are then bound 
by inserting and driving stones of proper size and shape to wedge the 
stones in their proper position. All projecting points are then broken 
with a sledge or hammer so that no projections shall be within four 
inches of the finished grade fine. 

"The telford foundation is then rolled with a steam roller of ten or 
more tons weight, until all stones are firmly bedded and none move 
under the roller. All depressions are then rilled with stone chips 
not larger than two and one-half inches, and the whole left true and 
even and four inches below the fine of finished grade and cross-section. 

"A good workman will average about twenty minutes in setting 
a square yard of this telford foundation, which may be formed of any 
kind of quarried rock which is most available: cobble-stones are not 
suitable. 

"The practice in 1901 in the states named is here shown:" 

Table 19. Sizes of Stone for Telford Foundation, in Inches 



State 


Depth, as 
set on 
Edge 


Width, as 
set 


Length set 
across Road 


Remarks 


Max. 


Min. 


Max. 


Min. 


Max. 


Min. 


New Jersey . 

Mass 

Conn 

New York . . 


8 
6 
8 
8 


8 

5 
8 
6 


4 
10 
10 
10 


4 
6 

4 


10 

15 
18 

15 


6 
8 
6 


Alternate end-stones 
double length. 

Two inches gravel rolled 
on subgrade as base. 

Macadam covering 
formed in one layer. 

Used only on unstable 
ground as foundation for 
macadam. 



Distribution of Stone in Foundations. 

In the discussion of sections, Table 9 shows that most of the traffic 
keeps to the middle 10 or 12 feet; to make a consistent design the 
foundation should therefore be thicker in the middle than on the 
sides for the ordinary crushed stone bottom, and where sub-base is 
required it is often unnecessary to place it the full width of the 
metaling. 



KINDS OF FOUNDATION COURSES 71 

Figure 22 is an example of such a foundation course for ordi- 
nary soils as used by the- New York State Highway Commission 
in 1910. 




4 to 8 

Fig. 22 

Figure 23 is an example of an economical sub-base for a light 
traffic road as used by the Illinois Highway Commission in 19 10. 




Fig. 23 

On a heavy traffic road, however, the writer does not believe that 
the width of sub-base should be less than the width of metaling. 

Special Cases. 

Long stretches of comparatively level ledge rock, peat, muck, and 
vegetable loam may be placed under this head. 

Where a road is on the surface of ledge rock for any distance, the 
usual cross-section of part cut and part fill cannot be used because 
of the high cost of shallow rock excavation for ditches; the grade 
should be lifted to make the normal section fill and the best avail- 
able material (not clay) used in its construction. Where conditions 
of this kind prevail, dirt is usually hard to obtain and often a stone 
fill is cheaper and also more satisfactory. 

The construction shown below was used for a stretch of two and 
one-half miles on the Leroy-Caledonia State Highway in New York, 
where ledge rock was encountered as described. 

The price for the stone fill was $1.23 per cubic yard in place con- 
structed as shown; the road was built in 19 10 and has given satisfac- 
tion; such a base, however, is very rigid, which will probably cause 
a more rapid deterioration of the top course than if earth were used; 
the minimum thickness of top for such a fill is 3" as it is impossible 
to construct it exactly to line and grade; it was found that by allow- 
ing a variation of 1" either above or below the grade elevation, the 
fill could be readily constructed, and these small inequalities were 
taken out with the top stone. A top course having such a variable 
thickness should be paid for by weight and not by volume in place. 
(See page 268, Cost Data.) 



72 FOUNDATIONS FOR BROKEN STONE ROADS 



Screened Gravel or \' ''^E^in£f Top j ^rusher Run abovej 

Broken Stone 'j-^ ^^jL,^ ' »^__ -Lj£ ^_ ,- Best Available 



■ uravetoroKen '^\ ' Ledge Rock- 
Stone, Fence or / J 

Quarry Stone Fill./ 

^Method "A*! j ' <N Method "B 1 ! 



V .... . u A i> 



Fig. 24 

Fill can be made of fence stone, gravel, quarry spalls, stone chips, 
or run of crusher stone over f " in size. 

Method A. — Boulders up to 2 cu. ft. can be used, placing the 
largest in the bottom of the fill; the top layer must be fairly uniform 
and not over 8" in size and must be roughly placed by hand to reduce 
the voids as much as possible, provided this layer of large stone is 
within 4" of the bottom of the top course. The top 8" to be filled 
with stone chips or gravel and a cushion of at least 2" of screened 
gravel, stone chips or crusher run of broken stone over f " in size to 
be placed on top to bring the fill to the correct grade and crown for 
the top course. 

Method B. — Same materials and manipulation as Method A, 
except that provided the top of the boulder fill is more than 4" from 
the bottom of the top course the top layer of the boulder fill need 
not be placed by hand. (See sketch, Method B.) 



Peat, Muck, Vegetable Loam, or Silt. 

Where the material is semifluid the only solution is a pile and 
grillage foundation. 

Swamps, as ordinarily encountered, can be treated successfully 
by using a corduroy or mattress foundation covered with a deep 
fill of gravel or large stone. In some cases where the muck is com- 
paratively stiff, a gravel or boulder fill alone will give a satisfactory 
foundation. 

Where swamps are crossed by improved roads, the location usually 
follows the old road which has often been corduroyed in the past; 
in such a case the old foundation should not be disturbed; a sufficient 
additional depth of stone can be added to keep the shape of the section 
intact. 

As an example, the Scottsville-Mumford New York State im- 
provement crossed a 1000 ft. stretch of muck on the old road location; 
it was found that the original cedar corduroy was in good shape; an 
18" depth of large boulders was placed on the old foundation and 
surfaced with 6" of broken stone macadam. This stretch of road 
has kept its shape and has not settled; it affords a good example 
of the statement made on page 61, that in many special cases 
the depth of the stone is determined by trial; the boulders were 



KINDS OF FOUNDATION COURSES 73 

put on in successive layers of 6" each until there was no material 
movement under the roller and then surfaced with the broken stone 
macadam. 

Under a heavy load the whole road-bed will vibrate for 100 feet, 
but the shape remains intact. 




Swamp <■'!-'■ ■■u^:^0^^':.^o/a/ Corduroy?. : '" r - 'Black Muck' K 

Fig. 25 

Economical Foundation Design Macadam Roads 

The economical design of foundation courses may be summarized 
as follows. 

For moderate traffic use pit run coarse local gravel if available 
varying the depths to suit the soil. If gravel is not available use a 
macadam bottom for ordinary soils and field stone sub-base or sub- 
base bottom for bad foundations. The economy in the design of 
macadam roads is greatly increased by utilizing local material, pref- 
erably uncrushed, to its fullest extent. We wish to emphasize this 
point (see design report page 210). If the supply of local material 
is limited it should be used for as much of the road as possible and 
advantage should be taken of the different local supplies by changing 
the design to allow their use with short hauls. 

Uniform designs which disregard limited amounts of local materials 
often raise the cost from $500 to $1,000 per mile. 

Conclusions. 

In the design of a road, the amount of material required for the 
foundation courses can be only approximated. This is the only item 
in the preliminary estimate that cannot be figured within definite 
limits. It can be closely estimated if careful data on the soils is 
obtained from local people and from the preliminary survey (see 
page 151), but a certain leeway must be given the constructing 
engineer so that he may vary the estimated depths to meet the 
construction conditions and build a consistent road. 



CHAPTER V 
TOP COURSES AND THEIR MAINTENANCE 

The selection of the most economical top course that is suitable 
for a given road is the hardest problem of Highway Engineering. 

The relative economy of the different constructions is theoretically 
expressed by the sum of the first cost and the capitalized cost of 
maintenance and renewal. The first can be readily estimated, but 
the cost of maintenance and renewal cannot be figured with any 
degree of accuracy for single special cases, and even on large systems 
it can only be approximated because of the new factor of motor 
vehicle traffic. The life of any surfacing is comparatively short, 
a fact generally overlooked in most of the popular literature on Good 
Roads. 

On any road the amount and class of traffic will fluctuate, and 
roads that are designed for light travel will often fail under temporary 
heavy traffic which, for some reason, is diverted from its normal 
course. The first improved roads built in any locality will for a 
time carry more than their share of the traffic, which is naturally 
reduced by the subsequent construction of adjacent improvements. 
It can be readily seen that it is difficult to judge the amount of traffic 
a road will handle and that a short-time traffic estimate is valueless 
as a basis for a definite conclusion. 

The design of the top course is usually based on a comparison of 
the actions of different kinds of previously improved roads that serve 
districts similar to that under consideration. Roads may be divided 
into four general traffic classes. 

Class I. Main trunk roads, for 5 to 20 miles out of cities of say 
5o,coo and upwards and in the business sections of villages, which 
carry the concentrated farm and truck garden traffic of a large area 
and are subjected to continuous auto truck and touring car traffic. 

Class II. Main through automobile routes, at greater distances 
from the cities, which have a large touring car traffic and medium 
heavy farm produce traffic. 

Class III. Secondary or feeder roads and cross roads having a 
medium heavy farm produce traffic and light auto traffic. 

Class IV. Pleasure roads or scenic routes that have a heavy 
touring car and light steel tire traffic. 

This chapter describes the advantages and disadvantages of the 
various types and in the discussion of maintenance indicates in a 
general way their economic limitations. 

Waterbound Macadam 

Waterbound macadam is constructed of crushed fragments of 
suitable rock, filled with rock dust and sprinkled and rolled until 
firm and hard. The cost varies from about $3.50 per cubic yard 

74 



TOP COURSES 



75 



where local materials are available to $6.00 where the stone is im- 
ported and the haul is long. A fair average price for roads in Western 
New York would be $4.30 per cubic yard, or 35^ per square yard for 
a three-inch depth. 

Depth of Course. 

As the top stone is relatively more expensive than the bottom 
course a good design calls for the least thickness of top which can be 
successfully constructed and maintained. 

In 1901 the thickness used for top-course macadam in Massachu- 
setts, New York, Connecticut, and New Jersey was 2", and the size 
of the top-course stone fragments ranged from \" to \\" in Massa- 
chusetts to 1" to 2" in New York. Experience demonstrated that 
with a course as thin as 2", the larger stone fragments tended to 
"kick out" under traffic and that the top wore out by raveling rather 
than by the abrasive action of the teaming. For this reason the best 
practice at present calls for a 3* depth of finished top course, using 
stone ranging in size from ij" to 2! "; this depth makes it possible 
for the large stone fragments to interlock more firmly than in a 2" 
course. 



Crowns. 

The crowns used on plain macadam are \" to i' to f " to 1'; while 



V to 



1 is satisfactory when first built, the gradual loss of crown 
due to traffic and weather action soon makes it too flat to shed the 
water. Mr. Charles Mills, Chief Engineer of the Massachusetts 
Highway Commission, reports the following loss of crown on State 
roads in Massachusetts and concludes that an original crown of f " 
to i' is advisable, except in villages where the traffic is in two lines. 
A f " to 1/ crown has proved satisfactory in Xew York State. 

Table 20. Tests Made in December, 1901 



Date of Original 
Construction 


Number of 
Tests 


Original Crown 
(Inches per Foot) 


Present Crown 
(Inches per Foot) 


1895 
1896 

1897 
1898 
1899 


7 

9 

12 

7 
2 


O.694 

O.583 
O.645 
O.625 
O.688 


O.500 

0.5I4 
O.500 
O.500 
O.625 



From the Massachusetts Highway Report for 1901. 
Maximum Grades. 

Waterbound macadam gives a good footing for horses on the 
steepest grades that are ever constructed; the limit of grade for this 
construction is determined by the cost of maintenance; on steep 
grades macadam washes badly and the cost of maintenance is high. 
Good pracjtice limits its use to grades of 5% or under, although 



76 TOP COURSES 

it has been used and maintained successfully on grades as high as 
12%. 

Advantages and Disadvantages. 

Waterbound macadam does not require particularly rigid inspection 
during construction and can be built under almost any weather 
conditions except freezing. By its method of construction the voids 
between the large stone fragments are completely filled with solid 
material and there is no tendency to squeeze or creep as in some of 
the asphaltic macadams. If carefully built it maintains its longi- 
tudinal and transverse shape and is an easy riding road for both team 
and motor traffic. 

Plain waterbound roads generally loosen up during the spring thaw 
and if subjected to much traffic at this time are liable to ravel. This 
trouble is not experienced with the bituminous macadams. Under 
heavy automobile traffic a plain waterbound macadam is not satis- 
factory as the machines remove the fine dust particles between the 
larger stones, leaving a rough surface which "kicks out " under team 
traffic. For this reason waterbound roads which are receiving much 
motor traffic are generally being treated with some kind of a dust layer 
or a bituminous protecting coat, that will better resist the wear of 
automobile travel. 

Waterbound Roads Treated with Dust Layers or Protected by Flush 
Coats. 

If waterbound macadam is kept moist by sprinkling with water, 
rapid disintegration under light machine traffic, traveling at medium 
speeds, is prevented. For light traffic, city or village streets, this is 
feasible, but the cost of sprinkling long stretches of country roads is 
prohibitive, and where the speed is high, as usually occurs on the 
main improved country roads, sprinkling alone will not satisfactorily 
protect a plain macadam. 

The application of calcium chloride to a road surface keeps the 
dust down for a longer period than sprinkling with water, as this 
salt has the property of absorbing moisture from the atmosphere 
and condensing it on the road surface; on side roads two applica- 
tions a season have kept the surface in good condition. The salt 
is applied with an ordinary agricultural drill, using about i§ pounds 
per square yard for the first application and less for the succeeding 
applications. In Western New York the cost of the first applica- 
tion i2 r wide has been approximately $100 per mile. Complaints 
have been made that the application of too much calcium chloride 
has caused soreness to horses' feet, but using the quantities given 
above, no trouble has been experienced, to the writer's knowledge. 1 

The application of calcium chloride does not build up the road or 
form a wearing cushion that protects the stone; it merely prevents 
the fine surface dust from being blown away or removed by the 
machines. 

1 We are indebted to Mr. Frank Bristow, Superintendent of Repairs, New York 
State Department of Highways, for much of the data on Calcium Chlorine, Glutrin 
and Cold Oiling. 



WATERBOUND MACADAM 77 

Glutrin. 

Glutrin is a trade name for the liquid which is run out of sul- 
phide tanks in the manufacture of pulp; it is distilled and the acids 
neutralized. It resembles molasses in color and consistency, is 
soluble in water, and is applied by sprinkling the surface of the road 
with one part glutrin dissolved in one or more parts of water, using 
from 0.3 to 0.5 gallons of the glutrin mixture per square yard treated. 
The road surface need not be swept if the dust is not more than \" 
deep. It hardens the surface to a certain extent, and, apparently, 
prevents raveling if applied twice during a season on roads receiving 
a moderately heavy traffic. According to Hubbard an addition of 
5% to 15% of semiasphaltic oil to the glutrin prolongs its efficiency, 
but such an addition tends to produce an oily mud in continued wet 
weather; glutrin alone does not produce this objectionable condition. 
Glutrin has been laid in New York State under an agreement with the 
Robeson Process Company of Ausable Forks, at a cost of $0.04^ 
to $o.o6| per square yard of surface actually treated. 

Cold Oiling. 

Macadam surfaces treated with light refined tar or asphaltic oil 
give a nearly ideal surface after the slippery, sticky condition has 
disappeared. 

The road to be treated is swept clean of dust and the oil is applied 
by pressure sprinklers, using from 0.2 to 0.3 gallons per square yard. 
The surface may be dry or slightly moist when the oil is applied. 
It is then covered with a good quality of pea gravel, stone or slag 
screenings or a sharp, coarse sand. In Western Xew York the cost 
has ranged from $0.02 to $0.04 per square yard, including sweeping, 
materials (oil and cover) and the labor of placing. 

To derive a season's benefit from the application of light oil or tar, 
the surface of the macadam must be thoroughly impregnated with 
the bitumen. Some of the lighter oils will evaporate. The cover 
will absorb some more. To get the greatest degree of saturation of 
road surface therefore, with a resultant freedom from dust and dis- 
integration, the cover should be the smallest amount of stone that 
will smooth out or eradicate that "toothy" or " mosaic" effect of 
small shallow voids between the firmly locked top stone. (See 
page 100.) 

On medium traffic roads, one application a season is sufficient and 
on light traffic roads one application will sometimes last for two 
seasons. 

Hot Tar and and Asphaltic Residuum Flush Coats. 

Bituminous flush coats are applied by sweeping the macadam 
carefully to remove all surface dirt as well as the stone or sand filler 
to a depth of about \" below the top of the larger stone fragments. 
On this rough, clean, dry surface a heavy refined tar or a bituminous 
residuum of the binder grade is spread hot, using from 0.2 to 0.8 
gallons per square yard. The binder is applied at temperatures 
ranging from 250 to 400 F., and is spread either by hand-sprinkling 



78 TOP COURSES 

pots or is sprayed on by specially devised pressure sprinklers. It is 
then covered with a layer of clean No. 2 stone (J"), or dustless 
screenings and thoroughly rolled. A well constructed surface of 
this kind resembles asphalt. It protects the macadam from raveling, 
is ^waterproof, forms a surface which takes the wear of the traliic 
from the large stone fragments, and gives a pleasing appearance. 
However, it cannot be laid in wet or cold weather; like asphalt, it is 
slippery and will not give satisfactory footing for horses on grades 
over 4%, and, unless laid evenly, will develop short, sharp waves or 
humps, which are very disagreeable for fast-moving automobile 
traffic. Some engineers advance the argument that by successive 
applications of such a flush coat a road can be maintained indefinitely 
without recaping, but as far as the writer has been able to observe, 
the roads become so humpy from continued treatment of this kind 
that recapping will be necessary to even up the surface on the score 
of comfort alone. 

The use of a hot tar application on a concrete road will be dis- 
cussed on Page 87. For use on an existing macadam road as 
repair, the authors believe that there is just one condition where a 
hot application should be specified; where an old road has begun to 
disintegrate unexpectedly, has passed the stage where cold oiling 
would rejuvenate it and funds are not available in the current year 
for resurfacing, then the hot oil or tar treatment may be used as a 
stop-gap to save it from complete disintegration for another year. 

The cost of flush coats exclusive of covering ranges from $0.12 to 
$0.16 per gallon, or about So. 09 per square yard. If applied to a 
macadam road during construction the cost of the plain macadam is 
increased approximately So. 10 per square yard, making So. 45 per 
square yard a fair comparative figure for flush coat and waterbound 
macadam construction. 

The crown ordinarily used on flush coat roads is \" to 1'. 

All bituminous binders have the following practical disadvantages 
whether applied as surface coats or as binders in bituminous mac- 
adams. The composition of residuum products is so complex and 
so easily varied that, to get uniform results, each shipment must be 
sampled and analyzed to insure certain required properties. In 
heating, care must be taken not to char the binder, as this destroys 
its life and effectiveness. They cannot be applied in wet or cold 
weather, which reduces the length of the construction season, and 
unless evenly spread a rough, humpy road results. 

Bituminous Macadam. 

Bituminous macadams are constructed in two ways, by the pene- 
tration method and by the mixing method. 

Penetration Method. 

Most of the bituminous roads in Xew York State have been built 
by this method. 

The larger stone fragments, ranging in size from 1" to 2" ', to 1" to 
25*, depending on the depth of the course, are spread and rolled; 



BITUMINOUS MACADAMS 79 

a heavy grade of refined tar, residuum bituminous material, or fluxed 
natural asphalt, is then poured hot, either by hand or machines, 1 
into the voids of the stone so that the stone fragments are covered 
with a thin coat of bituminous material; No. 2 stone, or dustless 
screenings are spread over the surface and broomed and rolled until 
the voids are filled; if a flush coat is to be used the excess filler is 
broomed off and the surface coat applied in the same manner as 
described for plain macadam. Where the flush coat is not applied, 
a wearing coat of clean screenings is spread over the surface. 

The amount of bituminous material used as binder varies from 
1.25 gallons to 1.75 gallons per square yard, depending on the depth 
of the course. The amount used for flush coats ranges from 0.2 to 
0.5 gallon per square yard. 

The cost of a one-coat 2" bituminous top, using 1.25 gallons per 
square yard, will range from $0.35 to $0.45, and a 3" one- coat top, 
using 1.75 gallons per square yard, from $0.50 to $0.60 a square yard. 
The flush coat using 0.4 gallon per square yard will add about $0.06 
to the above costs. For the purpose of comparison with madacam 
a fair set of prices is, 

2" Bituminous top, one coat of bitumen . .$0.40 per square yard 

2" " " flush coat $0.45 " 

3" " " one coat of bitumen .$0.55 " " " 

3" " " flush coat $0.60 " 

Depth of Top Courses for Bituminous Macadams. 

In 1910 New York State adopted a depth of 2" using 1.25 gallons 
as binder and 0.5 gallon as flush coat per square yard. 

In 191 1 a 3" depth was used with 1.25 gallons per square yard as 
binder and 0.4 gallon as flush coat. 

In 19 1 5 a 3" depth was used with 1.75 gallons as binder and 0.5 
gallon as flush coat. 

A2" bituminous top will not fail by raveling, the defect mentioned 
for a 2" waterbound macadam course, but it has certain construc- 
tional difficulties. To construct a 2" course no stone should be over 
2" in its largest dimension. Because of the tendency to crack under 
concentrated wheel loads, none of the stone forming the main body 
of the course should be less than one inch in size. These limits of 
size are so narrow that difficulty has been experienced in procuring 
sufficient stone for top when crushing local material, and even when 
the stone is obtained from a commercial plant the same difficulty 
is often encountered. Also in spreading such a depth with stone 
ranging in size from 1" to 2", there will be places where the metaling 
is only one stone deep and the fragments do not fit as closely together 
nor have the same chance to interlock as in a deeper course. The 
spaces between these stones are filled with the No. 2 (f ") size, which 

1 The author has had better success with hand pouring for the first coat than with 
machine work. For thin flush coats, however, a pressure machine is absolutely neces- 
sary. If bitumen is poured by hand it must be poured across the road (never along 
the road) as this method of work largely eliminates humps formed by overlap. It 
is much easier to control the hand spread than the machine spread as to amounts 
and the stone spread is not disturbed or rutted up during the pouring. 



80 TOP COURSES 

wears more rapidly under traffic than the larger pieces and the road 
tends to become rougher than would occur if the ij" stone fitted 
closer together. This last argument does not apply to flush coat 
roads. 

The argument is often made that a 3" top will last one and one- 
half times as long as a 2" top because it has one and one-half 
times as much material, but the life of a top course rarely depends 
on its total thickness, as it will become so badly out of shape 
before the general elevation has worn down an inch that it will need 
recapping. 

In attempting to meet these difficulties, %\ w and 3" courses have 
been built; as far as the author has been able to judge, the 2\" 
depth remedies the defects. 

When pouring bitumen in the penetration method, a pocket of 
fine stone, dirt, etc., will sometimes hold the binder near the top in 
too great quantities; during hot weather the bitumen swells and, as 
the voids are full in these spots, it rises to the surface and forms a 
hump or wave. This trouble is not so frequent on either 2 \" or 3" 
courses as on the 2" depth. 

The writer's present opinion is that a 2\" depth, using about 1.4 
gallons bitumen per square yard in one coat, will give satisfaction. 

Crowns. 

The crowns used on bituminous macadams range from \" to 1' 
to |" to i'; \" to i' is generally used and is apparently satisfactory. 

Footing. 

A single coat road affords good footing on any grade that will be 
adopted as suitable for heavy hauling; such a top course will not 
wash, which makes it easy to maintain on hills. 

A flush coat, however, cannot be used to advantage On grades over 

4%. 

Advantages and Disadvantages. 

Bituminous macadam without a flush coat provides good footing 
for horses; it will not ravel, is easy to repair for small depressions 
and ruts, is comparatively dustless and keeps its longitudinal and 
transverse shape well, making a comfortable riding road for fast 
travel. On the other hand, it will probably wear more rapidly than 
the flush coat construction as the traffic comes directly on the stone; 
it is subject to the practical disadvantages of construction of all 
roads where bituminous materials are used; it is not waterproof 
when first constructed; this last defect, however, is remedied by 
the traffic which grinds up the surface wearing coat and forces it into 
the voids. As a matter of fact, the combined action of traffic and 
weather puddles the road, and after about six weeks' use we can say 
that the road has a bituminous bond and a water-puddle finish. 

Flush coat bituminous macadams are more dustless than the single 
coat, are more nearly waterproof when first built, look smoother at 
first, and will probably cost less to maintain. However, they do not 



BITUMINOUS MACADAMS 81 

give as good a footing as the single coat and are liable to develop 
waves and humps disagreeable to fast traffic. 

If a flush coat is used there seems to be no advantage in a bitumi- 
nous binder, as the flush coat alone prevents raveling, and, if such is 
the case, the binder used throughout the depth of the course is a 
waste of money; a waterbound bituminous flush coat course might 
better be used. In choosing between a flush coat construction or a 
single coat bituminous madacam, the author believes that a single 
coat bituminous macadam is the better design; although it will 
probably cost more to maintain, the increased safety and comfort 
to the traveling public is worth the expenditure. 

Mixing Method. — Open Mix. Type I. 

The stone and bitumen are mixed hot in specially designed machine 
mixers. The mixture is then spread in the same way as sheet asphalt. 
A flush coat can be used if desired. The 191 5 New York State 
specifications call for No. 2 stone (f to 1})" — when finished thickness 
is to be two inches or less and a mixture of No. 2 and No. 3 stone 
(ij to 2\)"\ when finished top course is greater than 2", the stone to 
be proportioned as directed by the Engineer. Approximately 18 
gallons of bituminous material to each cubic yard of loose stone. 

In this "open" mix, it is unavoidable that pockets of mixed 
top material will be placed which have a greater percentage of voids 
than the average. Whether or not a seal coat is used, these pockets 
will wear more rapidly than the surrounding pavement. In a similar 
manner, variations in the size of the stone will cause uneven wear. 
Both conditions tend to produce a humpy pavement after some use. 

Mixing Method. — " Tight Mix " or " Topeka." Type II. 

The stone, sand and bitumen are mixed hot in specially designed 
machine mixers. The mixture is then spread in the same way as 
sheet asphalt. The thickness varies according to the foundation. It 
is generally a consolidated depth of 2" on a concrete foundation and 
2^" on a firm macadam foundation. The various sizes of the mineral 
aggregate and the percentages of each are specified within certain 
limits varying slightly to meet gradations peculiar to the material 
available. 

Because of the fine aggregate used in work of this type, there is 
not sufficient stability to withstand a mixed traffic and the surface 
ultimately forms in disagreeable waves. 

Attempts have been made to prevent this waving by using a high 
penetration asphaltic cement which will permit the pavement to 
iron itself out. However, if a heavy slow-moving traffic be carried 
on this type of road, the surface will rut. 

Apparently, the best results in mixed Bituminous Macadam have 
been secured when the coarse aggregate was used — stone between 
three-quarter inch and one and one-half inches in size, which were 
filled with a matrix of fine material of sand and bituminous material. 
Such pavements have sufficient u body" to materially decrease the 
"creeping" under use and take a more even wear than the open 
mixed type. 



82 TOP COURSES 

The prices for this type of top course run from 

Type I, 6ii^ . $1.10^ , 

-JJL — > lr to - ? per sq. yd. 

Type II, 66^ $1.25 ^ H 

'Natural Rock Asphalts. 

Sandstones and limestones containing a certain percentage of 
bitumen are known as rock asphalts. The most common source of 
supply for the Eastern States is Kentucky, and the product is known 
as "Kentucky Rock Asphalt." It is a sandstone containing about 
7% to 10% of maltha. It is pulverized at the mine and is shipped 
and applied cold in the following manner: 2" to 2i"of stone, ranging 
in size from f" to i|", are spread and rolled slightly. The rock 
asphalt is run through a shredding machine and spread over the stone, 
using approximately forty pounds per square yard. The whole mass 
is then thoroughly rolled, preferably with a six or eight ton tandem 
roller; forty pounds per square yard of pure rock asphalt is then 
spread as a wearing coat and well rolled; the rolling is continued 
intermittently for a number of days after the traffic is turned on the 
road. The cost of such a course has been about $0.70 per square yard 
in Western New York. 

The crown ordinarily used is \" to i'. 

Advantages and Disadvantages. 

The road is pleasing in appearance, is not as slippery as sheet 
asphalt, and will not ravel under motor traffic. However, it is hard 
to construct in cold weather, is not uniform, and will ravel in spots. 
It has defects in common with sheet asphalt of showing wear by de- 
veloping short humps and hollows disagreeable to fast traffic. The 
steepest grade on which it can be used advantageously is about 5%, 
as it becomes slippery in cold weather, and in warm weather it some- 
times softens enough to make hard pulling for heavy loads. 

Amiesite. 

Amiesite, a patented material made of crushed stone coated with 
asphaltic cement, has been used on many miles of road with good 
results. It is shipped cold in a friable and granulated state, spread 
on either macadam or concrete base and well rolled. Amiesite 
screenings are then spread and rolled, forming the surface. This 
construction costs about $1.00 per sq. yd., 3" thick. It resembles 
asphalt in appearance and has the advantages and disadvantages 
of all roads of this class. It is particularly adapted for small jobs 
where it would not pay to set up an asphalt plant or where suitable 
asphalt materials are not locally available. 

For further information see chapter on Cost Data and Specifica- 
tions. 

Other Surfaces of a Bituminous Nature. 

There are any number of patented pavements that can be classed 
under this head to which we cannot give space. 



BRICK PAVEMENTS 83 

Sheet Asphalt and Warren Brothers' Bitulithic are used in unusual 
cases, but constitute such a small percentage of the mileage that 
for information concerning them we refer the readers to books by 
Richardson, Hubbard, Tillotson, etc. We includes some notes on 
inspection of construction, page 351. 

Brick Pavements. 

The ordinary brick pavement construction is probably familiar to 
most readers. On a concrete foundation 5" to 7" in thickness a 
sand cushion varying in depth from 1" to 2" is spread and the paving 
brick are laid on this sand bed so as to break joints; the brick are 
well rolled and the joints are rilled with sand, cement grout or pav- 
ing pitch. Longitudinal expansion joints of bituminous material are 
provided next to the curbs or edgings; transverse expansion joints, 
space 30' to 50' apart, are used by' some designers. The latest 
practice tends to make the sand cushion as thin as possible, acting 
merely as an evener of the concrete surface. It is also rare to find 
any material but cement grout used for filler. The use for traverse 

• J Jg Pitch Expansion Joint 

Concrete ;M^^^2:C6ncr e^Bwe:°5' t o d.-o.-r 3 .-^ 

Note t Transverse Expansion Joints Spaced 
K ton 30 to 50 ft may be used. 

Fig. 26. — Brick Pavement, Flush Edging 

expansion joints is also being relegated to the back ground. Pre- 
molded alsphaltic strips are designed for longitudinal expansion 
joints in most recent practice. In the last few years the former 
theory that the i\" sand cushion prevented crushing of the brick and 
gave the amount of resiliency necessary to a pavement of this type 
has been disputed, and apparently successfully so, by the increased 
use of a cement sand bed. Upon the prepared foundation a bed 
of cement and sand consisting of one part cement to four parts of 
approved sand is spread not more than 1" in depth. The sand and 
cement are thoroughly mixed dry until a uniform color is obtained, 
struck off with a template and rolled with a hand roller weighing 
about 300 lbs. After the brick are laid thereon and before grouting, 
the rolled bricks are thoroughly wet by sprinkling. It is important 
that the bricks be well wet so as to set up the cement sand bed. . It 
is probably true that the use of a mortar cushion reduces the tendency 
of the brick to loosen near cracks. 

In 19 1 5 several experimental brick pavements were constructed 
where the mortar cushion and brick were laid upon concrete which 
was still plastic. Concrete foundation was shaped by template and 
the brick laid, inspected and rolled with a hand roller before the 
cement had taken its initial set. This is immediately followed by 
grouting. It is too early to say whether or not this so-called " mono- 



84 TOP COURSES 

lithic " construction will be successful. The expense and difficulty of 
manipulation are increased and it is doubtful if any material advan- 
tages are attained. 

Brick Pavement construction is essentially rigid, intended to with- 
stand heavy traffic. The cost, including foundation and surfacing, 
ranges from about $1.60 to $3.00 per square yard, the average price 
in Western New York being about $2.00. 

Brick pavements on heavy traffic roads have been extensively used 
in Ohio and New York. Macadam foundations for brick surfacing 
have not proved satisfactory in the Northern States, as the surface is 
too rigid and cracks under the heaving action of the frost. Even 
on a concrete foundation longitudinal cracks often develop from this 
same action. It is more difficult to prevent this on country roads 
than in cities where the sewers keep the earth sub-grade comparatively 
dry, and the necessity for a center drain under the concrete base is 
being recognized by many designers. Some engineers believe that 
the 1 to 1 cement grout in general use is too strong, and that if a 
weaker grout or a sand filler were adopted in its place the heaving 
frost action would merely separate the bricks slightly instead of 
breaking them and that as the road settled they would fall back into 
close contact. This is an attempt to make a theoretically rigid 
construction flexible and seems to be striving to adapt the construc- 
tion to conditions for which it is not fitted. 

Longitudinal Cracks. — These cracks have been carefully studied, 
as they seem to be the most discouraging feature of brick pavement 
construction on country roads. 

Mr. Wm. C. Perkins, Chief Engineer of the Dunn Wire Cut Lug 
Brick Co. states from a careful examination of a large mileage of brick 
roads built under his supervision, that longitudinal cracks have always 
occurred within 2' or 3' of the center of the road; that the cracks 
extend down through the concrete base and that less difficulty is 
experienced in preventing them as the crown of the pavement is 
reduced. From these observations he has been led to experiment 
with a concrete base having a perfectly flat bottom, as shown in 
figure 2 6 A, crowning the road by making the concrete thicker in the 
middle than on the edges. The claim is made that this style of 
construction is helping to prevent such cracks. 

Transverse Expansion Joints. — The use of transverse expansion 
joints has not been successful locally. Difficulty has been experi- 
enced with the brick loosening at these joints, and whenever a tem- 
perature heave has occurred it has appeared at the joint. Their 
use has been abandoned for rural roads in Western New York. 



.Sand Cushion .Longitudinal 



m 



V » ' ''^Concrete Foundation 



Fig. 26 a 



ASPHALT BLOCK 85 

The crowns in use on brick pavements range from \" to 1', to 
f " to i'. For the methods of figuring ordinates for parabolic crowns 
see page 262. 

Brick pavement does not give a good foothold for horses on grades 
above 5 % unless some special form of brick is used. For steep grades, 
on heavy traffic roads, it is better practice to use some form of stone 
block. 

Stone block pavement, including concrete foundation, costs from 
$2.70 to $3.30 per sq. yd. It is suitable for the steepest grades that 
are constructed. 

.' Pitch Expansion Joint 



Slopelj«ULJ^ 



Concrete ^M^k^i^^^Co nc'rei^Baieis^to 6 'l?M **- 2"Sand 



w« 



S5J0W 



Lm"j' Note : If Pitch Filler is used between StoneBlock, 

^ * no Special Expansion Joint is needed. 

Fig. 27. — Stone Block Pavement, Flush Edging 

Where stone blocks are used on hills it is better practice to use 
second quality blocks; these blocks are identical with the first quality 
blocks as to material but are not dressed as carefully and cost about 
fifty cents per square yard less; their rougher surfaces and wider 
joints afford better footing. For the difference in size and joints 
see specifications, Medina Block, page 396. 

The first cost of brick pavement for country roads restricts its use 
to roads where it can be conclusively proved that macadam will not 
be suitable. 

Asphalt Block 

The asphalt block pavement laid in New York State has been very 
satisfactory. The proportion of ingredients is about 70% crushed 
rock, usually trap, which has passed a \" ring, about 20% limestone 
dust to act as filler and approximately 10% of asphaltic cement, 
molded under a pressure of 2 tons per sq. inch of block having a 2" 
depth. This produces a dense asphalt much superior to the ordinary 
sheet. 

The asphalt used is Trinidad. This is refined and fluxed so that 
the resulting A. C. may be varied as to adhesiveness, penetration, 
etc. to meet varying conditions peculiar to different localities. 

The penetration is made high enough to give a certain amount of 
pliancy to the block, to avoid crumbling at the edges and to make 
the joints self-healing. 

The use of blocks containing steel anchors, laid across the road, 
approximately fifteen feet apart, has eliminated any movement of 
the block under traffic. These blocks are placed at more frequent 
intervals on curves. Block pavements have been laid using a longi- 



86 



TOP COURSES 



tudinal row of these anchor blocks in place of edging. The results 
appear satisfactory. 





Sfeel Reinforcement ■ 




/' 




\ 


%s . . . 


_J 



Plan 




''Mortar Bed'. 



""^V -p, * a; ^ > ,^>M >■> a; i;^^K- ^^v-^ bi- 



section 

Fig. 27 a 



^Foundation 



After the base is prepared a mixture of 1 to 4 Portland cement 
mortar is spread \ inch thick. This mortar bed is carefully screeded 
and the block laid thereon, joints being broken at least 4 inches. 

Asphalt Block Data 



Highway 

No. 


County 


\ Mileage 


Bottom 
Per sq. yd. 


Top 
Per sq. yd. 


Per Mile 
16'— 26' 


5357 


Westchester 


0-95 


$0.61 


$1.49 


$26,593 


5375 


n 


1-34 


Old Mac 


I.69 


18,114 


5388 


Rockland 


2.16 


a a 


1.70 


1 27,025 








0.59 


I.70 


1 32,525 


ii53 


Niagara 


0.97 


O.60 


1-37 


1 31,800 


5482 


Westchester 


1. 16 


O.66 


1-50 


29,270 


1167 


a 


1.28 


O.Ol 


1.38 


24,245 


io53 


(C 


1-45 


Old Mac 


I.60 


21,205 


5528 


Warren 


0.61 


o.59 


I.60 


35,990 


5356 


Westchester 


0-53 


Old Mac 


I.63 


1 26,960 


536i 


ci 


0.68 


0.61 


I.44 


1 23,5 12 


5302 


Ci 


0.25 


0.67 


i-37 


25,569 


53°4-A 


u 


0.31 


0.47 


1.47 


23,166 


5373 


tc 


2.85 


0.58 
Av. 0.599 


1-52 





• 




Av. 1.533 





1 Costs from preliminary estimate. 

All costs not marked with star from bid prices. 



CONCRETE PAVEMENTS 87 

An interesting comparison with brick occurs in the " pinning in" 
at curbs. Instead of bats being broken by hand, a large mechanical 
shear is used. Each fractional block is measured and cut to fit 
exactly. 

After being laid, the pavement is given a light coat of sharp sand 
which is broomed into the joints. Traffic is permitted in four or 
five days. 

Advantages. — The pavement shows a smooth, uniform surface, 
dustless and practically noiseless. Its life has yet to be determined: 
Pavements that have been down ten or fifteen years are still in good 
shape. Within a reasonable freight radius from the point of manu- 
facture, it can be laid for approximately the cost of brick. 

Disadvantages. — A mist or light rain makes the pavement very 
slippery. It should not be used on grades over 4%. 

CONCRETE PAVEMENTS 

Introductory 

Inasmuch as there is some difference of opinion as to the value of 
this type each author has written his interpretation of the available 
facts. 

Concrete Pavements 

By W. G. Harger 

Many miles of these roads have been constructed in the last few 
years. 

The construction has varied from poor 1 to 6 pit run gravel con- 
crete to first-class 1: if: 3 stone concrete 6" to 9" thick. 

There is enough data to conclude that cheap concrete is a failure. 
An effort was made to protect the surface of such a mix with a thin 
bituminous surface coat of asphaltic oils or tars. These coats have 
not been successful as they peel off and produce an unsightly, rough 
riding and a high maintenance cost road. 

The 'type of concrete road now being built and which has many 
enthusiastic supporters is a first-class 1: ij: 3 stone or screened 
gravel concrete which takes the traffic directly on its surface. The 
concrete is carefully manipulated (see specifications, page 443). 
The ordinary section used is shown in figure 27B. Expansion joints 
of creosoted wood or patented steel plates with tarred paper filler 
are provided at intervals of approximately 30 ft.* The cost of this 
pavement has been from $1.10 to Si. 50 per sq. yd. They have the 
advantages and disadvantages of all rigid types of construction. 
They should not be used on grades over 5%. 

Pavements of this class have been built on roads having light, 
medium and heavy traffic and are advocated by Cement Manufac- 
turers as an economical road under all classes of traffic. The author 

* The author personally believes that better results will be obtained by eliminating 
these joints altogether. The artificial joints are sources of weakness in that they 
tend to localize the wear. Apparently less wear occurs at a natural crack and it is 
certain that a smoother riding road is obtained. 



/ 

88 TOP COURSES 

believes that while this type has its place that a great mileage is being 
constructed which from an engineering viewpoint is not justified. 
The roads have not been down long enough to obtain reliable data 
as to their length of life before resurfacing. Considering in a general 
way, however, what we know of the material and the action of the 
weather and traffic on rigid types of pavement, an allowance of 10 
to 15 years would appear liberal. When they arrive at the point 
when they need resurfacing a large expense is involved. It has been 
demonstrated that cheap thin bituminous coats have not been suc- 
cessful; it is not possible to successfully resurface with a thin layer 
of concrete which means that probably Asphaltic Concrete, Asphalt 
Block, Brick or some other form of block or cube pavement will 
be used at a cost of from $9,000 to $16,000 per mile. The fact that 
resurfacing when it occurs requires such a large expenditure eliminates 
this type from use on any but the more important roads which con- 
stitute a small percentage of the mileage of any large system. 



4"fo6' ^^mrn^^ZF'^ 8 





Fig. 27B 

With the data at hand the indications are that this type is a good 
design for the heavier Class II traffic roads where it is desirable to 
keep the first cost as low as possible and where it is. expected that the 
necessary money will be available in later years for an expensive 
resurfacing. 

The fact that the first cost is moderate and the maintenance is 
low for a number of years blinds a great many highway officials to 
the final cost of upkeep, or if they are not blind many of them figure 
that the roads will outlast their tenure of office and what do they 
care about their successors. 

Concrete Bituminous Roads 
By E. A. Bonney 

Some four or five years ago, a tremendous wave of publicity swept 
concrete roads into the limelight. The construction at that time 
consisted of a second-class concrete base with a skin coat from \" 
to \" in depth, composed of screenings, mixed with hot oil or tar, and 
sometimes a combination of the two. The base was laid without 
joints and gravel or any kind of stone was used for aggregate. 

Under this type at least a dozen patented pavements were devel- 
oped practically none of which have to any degree borne out the 
extravagant claims made at that time. 

The bituminous skin coat has not been satisfactory. It is subject 
to all the disadvantages of other bituminous macadams and with 
few exceptions has not adhered to the concrete for any length of 
time. 



CONCRETE BITUMINOUS ROADS 89 

There is a road known as the Bedford- Golden s Bridge State High- 
way in Westchester County, on which 2.67 miles of concrete base 
had been laid when the original contract was canceled. The un- 
finished portion was covered with an experimental skin-coat treat- 
ment which today is as sound and intact as when laid. Work was 
finished in the early summer of 191 5. The road was subjected to 
the enormous automobile traffic peculiar to W r estchester County 
all season. A brief description follows: 

The concrete was cleaned, all dust, dirt or caked material removed. 
It was then coated with a cold application of low carbon tar, very light 
grade, almost a creosote. This was spread about jq gallon per sq. 
yd. and allowed to dry for two hours. About f of a gallon per sq. yd. 
of Bit. Mat. U T" low carbon binder was then applied hot and covered 
with approximately 37 lbs. of No. 2 stone per sq. yd. A second coat 
of J gallon per sq. yd. was then applied and covered with about 32 
lbs. per sq. yd. of No. 1 stone. 

This treatment so far looks extremely well and has not broken away 
from the concrete. It is still too early to classify as a success. 

The cost of the top course only was 17^ per sq. yd. 

Base cost 6Sc' making total of 85c. 

Concrete Pavements 

By E. A. Bonne y 

1— 1 J— 3 Mix 

Concrete pavements are showing as each season passes by, that they 
are worthy of much more consideration than has been given them up 
to the present time. For roads subjected to heavily loaded and slow 
moving vehicular traffic or for roads so located or so traveled that 
any type of macadam road would be subjected to costly maintenance, 
the concrete pavement has come to stay. The wear seems to be 
inappreciable and because of the flat crown, traffic is spread over the 
entire width of metal. 

Great care must be exercised in the selection of aggregates. Many 
sands that are considered good enough for ordinary concrete work 
will not give satisfactory results in concrete pavement. Stone or 
gravel should be limited to those showing a high coefficient of 
wear. 

Considerable attention should be paid to the percentage of voids in 
the sand and stone. Experiments should be made to determine 
approximately the mixture giving the lowest percentage of voids. 
The authors do not believe in the blind adoption of a specified mix. 
It is often essential that the mix be varied to correspond to the grada- 
tion of available sand and voids in coarse aggregate. 

Several containers of uniform volume and a pair of scales are all 
the apparatus necessary to show whether or not the specified mix is 
the best mixture for the aggregates available. 

The approximate percentage of voids may be found by water. 
By making up several concrete cubes or cylinders of the same vol- 
ume, beginning with the specified mix and varying the others as 



90 TOP COURSES 

indicated by the percentage of voids, the heaviest product will indi- 
cate the proper mixture. 

Any data given herewith is based upon a one-course road. The 
authors are not personally familiar with two-course roads. 

Bulletin No. 249 of the Office of Public Roads, U. S. Department 
of Agriculture, cites the advantages and disadvantages of concrete 
highways as follows: 

"Advantages: 

1. As far as can be judged, they are durable under ordinary sub- 
urban and rural traffic conditions. While it is true that there are 
no very old concrete pavements in existence, the present condition 
of many of those which have undergone several years' service would 
seem to warrant the above statement. 

2. They present a smooth, even surface, which offers very little 
resistance to traffic. In the past the surface of concrete pavements 
have sometimes been roughened in order to insure a good foothold 
for horses. This practice has now been abandoned, except on very 
steep grades, because it tends greatly to accelerate deterioration of the 
pavement, and because the smooth surface has been found to afford 
a fairly satisfactory foothold under all ordinary conditions. 

3. They produce practically no dust and may be easily cleaned. 

4. They can be maintained at comparatively small cost until 
renewals become necessary. 

5. They may be made to serve as an excellent base for some 
other type of surface when resurfacing becomes desirable. 

6. They present a pleasing appearance/ 5 

"Disadvantages: 

1. They are somewhat noisy under horse traffic. 

2. There is no method of constructing necessary joints in the 
pavements which will entirely prevent excessive wear in their vicinity. 
Furthermore, joints do not altogether eliminate cracking and wherever 
a crack develops it must be given frequent attention in order to pre- 
vent rapid deterioration of the pavement. 

3. They cannot be readily and effectively repaired as many other 
types of pavements." 

This summation of concrete roads in general seems eminently 
fair. We believe, however, that to the disadvantages should be added 
the inevitable rut which appears between the edge of the .concrete 
and the earth shoulder. These ruts are dangerous to fast-moving 
traffic and require constant maintenance for their elimination unless 
the shoulders are armored with crushed stone or gravel for two feet 
or more from the concrete. 

The questions of reinforcement and joints are still the subjects 
of much discussion among engineers. 

The item of reinforcement largely increases the cost of the roads 
and it is yet too early to say that the added expense is justified. 

The joint problem affords an unlimited field for a variance of opin- 
ions. Few engineers are satisfied with any of the existing armored 
joints, patented or otherwise. 



CONCRETE PAVEMENTS 



91 



The author believes that experience to date has divided the prob- 
lem of joints into two fields: i. e. on roads under continued mainte- 
nance a bituminous joint- will prove satisfactory and is renewable 
at small cost; on roads which receive spasmodic maintenance or none 
at all, some sort of steel joint should be used. 

On New York State work where maintenance is continuous the most 
satisfactory joint to date is of premolded asphalt, which is so placed 
that it projects from f " to \" above the surface of the concrete; thus 



Premolded Asphalt 
Joint as Laid 




A combination of hot weather and traffic spreads the asphalt out in 
this manner, leaving a bituminous mat over the joint. 



Premolded Asphalt 
Joint as it becomes 
under Traffic 




For concrete roads not under maintenance, the better joints are 
being made of soft steel tempered to the same relative hardness as 
the concrete. A hard steel joint simply transfers the point of wear 
from the joint-edge proper to the concrete back of the joint. 

The proper length of Concrete slabs between joints is another 
subject of speculation. Many roads are now being built with vary- 
ing distances between joints in an endeavor to determine how few 
can be used with success. 

The average cost of this type in New York State lor 6" depth of 
pavement is $1,121 per square yard of pavement only. Total 
average cost for mile of completed highway, including excavation, 
drainage structures and pavement, is $15,320. 

Small Stone Block Surfacing. 

In Germany, Hungary, Austria, and England a surfacing made of 
granite blocks, ranging in size from 2V to 4", has been used success- 
fully. This pavement is known as Kleinprlaster in Germany, and 
as "Durax" armoring in England. The stone cubes must be cut 
with considerable accuracy in order to give a smooth and durable 
surface. 

The blocks are laid on a thin sand cushion of about f " depth, on 
either a macadam or concrete foundation; they are thoroughly 



9 2 



TOP COURSES 



rammed to give a firm bearing and the joints filled either with clean 
sand flushed in, or a bituminous filler. The joints do not exceed \" 
in width. The courses of cubes are laid either diagonally to the 
direction of the traffic or in concentric rings. 

Where the stone is broken by hand the cost is high and it would 
be impossible to consider its use for rural roads in this country. A 
machine * has, however, been developed in Europe for breaking 
these cubes which is claimed to produce a satisfactory product at a 
reasonable rate. It is a belt-driven friction drop-hammer having 
a stone chisel mounted on the anvil; the hammer head is shaped like 
a stone-cutter's sledge. The power needed for each machine is about 
ij H. P. 

About 400 of these machines are in operation, and a plant in 
Sweden is turning out 700,000 square yards of pavement per year 
with 62 machines. 

Provided the pavement can be laid for $1.00 to $1.25 per square 
yard, it seems a type that must be seriously considered. A price as 
low as this, however, would necessitate the use of convict labor in 
the manufacture of the cubes. 

McClintock Cube Pavements, by W.G. Harger 

This is a patented pavement devised by J. Y. McClintock, County 
Engineer of Monroe County, N. Y. It is very similar to "Klein- 
pflaster" except that under his patent artificial cubes as well as stone 
cubes are proposed. It appears to be a very promising type. 

The construction is essentially as shown in figure 28 and consists 
of a top course of 2|" cubes placed on a thin sand cushion supported 
by either a macadam or concrete base. The cubes have been made 
of concrete, vitrified paving brick material and stone as in Conti- 
nental practice. 



Gravel or Stone 

Shoulders '-, 




^Macadam Foundation 



FlG. 28 



They are loaded, hauled and dumped like broken stone; laid in 
close contact by means of a pallet and rake 128 at a time on a sand 
cushion \ to \" thick, no care being taken to break joints. They are 
then rolled to bring to an even and firm bearing; the joints are filled 
with a sandy loam and the surface treated with a light coat of light 
road oil or cold tar if the foundation is macadam. The joints are 
grouted if the foundation is concrete. Temporary shoulders of 
2" plank are put down during the laying of the cubes after which they 
are removed and replaced with broken stone or gravel as shown in 
figure 28. 

1 A detailed description of this machine is given in Engineering News, March 27, 
1912. 



CONCRETE PAVEMENTS 93 

The experience of the past six years has shown that this form of 
construction using a sand-tarred joint is flexible under frost action 
which makes it suitable as a surfacing on a macadam base. It 
keeps its shape under traffic and shows no tendency to ravel or 
break down at the edges and can -be successfully held with a 
macadam or gravel shoulder without the formation of a rut along 
the edge which is a difficulty always encountered where a rigid edg- 
ing is designed. It gives a satisfactory surface in both wet and dry 
weather and can be laid late in the season. The cubes require com- 
paratively little inspection and can be successfully used as a patch 
in maintenance with simple manipulation. They reduce the tonnage 
and freight cost where imported materials are required. Concrete 
cubes have not served satisfactorily, failing in spots, but this is to 
be expected as it is not a reliable material for a road surfacing of 
this nature (that is for such small units). Vitrified shale cubes with 
wide sand joints laid on a macadam base have shown ability to stand 
medium traffic. Vitrified shale cubes with close tarred joints laid 
on a thick macadam base serve very satisfactorily under moderately 
heavy traffic, and the indications are that these cubes laid on a con- 
crete foundation and grouted will meet all but the heaviest traffic 
satisfactorily. 

Consider briefly the present tendencies in highway construction. 
There are two distinct types; the flexible form represented by the 
macadams and the rigids types, such as brick, asphalt, stone block, 
etc. having concrete foundations. Each has a distinct field and their 
relative economy depends largely on the traffic. 

It is sufficient for this discussion to note that macadams are suit- 
able for light and medium traffic (Classes II and III); that they 
are able to withstand climatic changes better than the rigid pave- 
ments and that with a moderate yearly expenditure they can 
be kept in good condition when used under the volume of traffic 
stipulated. 

They fail either under high velocity traffic or heavy hauling; the 
first being a surface failure and the second a foundation failure for 
most of the roads in this locality but a surface failure for some which 
have a thick well-consolidated base. That is, if some better flexible 
surface can be used on a first-class macadam foundation, this type 
of road will be able to handle a heavier volume of traffic than at 
present with a moderate maintenance charge. The indications are 
that the Brick cubes with sand-oiled joints will serve this purpose. 

The rigid roads develop defects due to temperature changes; 
frost heave and the settlement of fills. Subsequent movement is 
localized along these lines and eventually expensive repair and re- 
construction is necessary. Under heavy traffic, however, the cost 
is less than for the macadam type and the inconvenience of continual 
repairs is avoided. 

The first cost of Brick and Asphalt block which are generally con- 
sidered the best of the rigid types is so high that designers often 
hesitate to use them where they are actually needed. If it were 
possible to reduce the cost and yet obtain practically the same class 
of improvement a larger mileage could be used to advantage. 



94 TOP COURSES 

The indications are that the Brick cubes on a concrete foundation 
will serve this purpose at a cost of about $0.40 per sq. yd. less than 
the present paving brick. 

Highway designers do not hesitate to use madacam for the light 
traffic roads or expensive rigid constructions for the extremely heavy 
traffic; the great mileage that lies on the verge of either form of 
construction offers the real difficulty. It is for this class of road 
that the cubes are particularly adapted by reducing the cost of brick 
and increasing the efficiency of macadam. This applies also to the 
resurfacing of concrete and macadam roads. 

The author believes that provided this type fulfills its present 
indications that it will meet a recognized need in highway construc- 
tion and for this reason has given more space than perhaps is justified 
to a method which has not been tested out by a large mileage of 
construction. 

A reasonable cost of the brick 2" cube surfacing is approximately 
$0.95 per sq. yd. in Western New York. This form of road material 
is adaptable to manufacture by convict labor. 

Rocmac. 

Rocmac is another patented pavement which deserves mention, 
as the roads which the author has seen built by this method compare 
favorably with other types of construction. The claim is made that, 
under favorable conditions, it will cost only fifteen cents per square 
yard more than plain macadam. The only available example of 
cost details given below is hardly a fair sample of what can be done. 

We quote an extract from the 19 10 report of the New York State 
Highway Commission: " Experimental pavement according to the 
Rocmac System as laid over the westerly portion of Buffalo Road, 
Section No. 2, County Highway No. 83, located in the Town of Gates, 
County of Monroe, New York. 

"The Rocmac system differs from ordinary macadam construction 
in that the aggregate of crushed stone is cemented together by a 
matrix composed of limestone dust (as rich as possible in carbonate 
of lime) mixed with a solution of silicate of soda and sugar, the silicate 
of soda combining with the carbonate of lime, an unstable compound, 
forming silicate of lime, which is a very stable compound. 

"The materials used in this experiment were Leroy limestone flour 
for the matrix, being the entire crusher product which would pass a 
screen of J-inch mesh, and Akron limestone No. 3 size with some 
No. 4 size mixed for the aggregate. The No. 3 size being retained 
on a screen of ij-inch mesh and passing a screen of 2-inch mesh, 
the No. 4 size being retained on a screen of 2-inch mesh and passing 
a screen of 3|-inch mesh. 

"The delivery point for material shipped by rail being Cold water 
Station, a dead haul of one mile to the beginning of the work. 

"The supervision given this work consisted of occasional inspections 
by the division superintendent of repairs and the inspector in charge 
of this section, neither of whom could devote much time to this 
particular work without interfering with other duties. Had the 
work been constantly directed by a competent foreman more progress 



ROCMAC 



95 



would have been made and the cost probably would have been 
decreased. 

"The method pursued during the laying of this surface was to 
scarify by hand the original foundation course, removing all loose 
material by brooming, upon this prepared foundation to spread the 
matrix composed of limestone dust and solution, to an average depth 
of about two inches, upon this spread the crushed limestone aggre- 
gate to such a depth as would give finished rolled thickness averaging 
about 3f inches when properly crowned, then rolling same until 
thoroughly consolidated and continuing rolling and sprinkling with 
water by hand until the matrix which flushed to the surface in the 
form of grout has nearly disappeared, when the pavement is covered 
with a light coat of screenings and considered complete. 

"The total length of this resurfacing extending from Station 237 
to Station 275+ 76 is 3,876 lineal feet, aggregating an area of 6,890 
square yards surface upon which was used 1,094 tons of No. 3 and 
No. 4 crushed limestone, 520 tons of limestone flour and 4,050 gallons 
of silicate of soda solution. 

"Deducting from total expenditure materials not used and expense 
of labor trimming shoulders and ditching would leave total cost of 
this resurfacing including all material and labor necessary to form 
pavement complete in place $6,400.82 or $0.9288 per square yard. 

This expense is itemized as follows: 



Item 


Total 


Per Sq. Yd. 


Cost of Stone f.o.b. cars delivery point. 
Cost of Rocmac solution 


$2,026.59 
617.28 

1,408.79 
408.61 
547-28 

1,341.64 
50.63 


$0.2941 
O.0896 

0. 2044 
O.0593 
O.0794 
O.1947 
O.0074 


Cost of teams hauling stone, solution, 
water and coal 


Freight and duty on solution 


Roller and coal 


Labor 

Tools, tank, blacksmith, oil and wood . . 


Total 


$6,400.82 


$0.9288 





"The average price paid per ton for all stone f.o.b. cars at delivery 
point is $1.25 J; price paid per hour for labor $0.22; for teams $0.56^ 
per hour; roller rent $10 per day. 

"During the progress of this resurfacing traffic was not interfered 
with at all, all traffic being permitted to go over the work in whatever 
stage of progress. This is an advantage worthy of consideration. 

"The finished surface after five months' traffic has the appearance 
of a well-constructed macadam road, being hard, smooth, well bound, 
and clean, no discoloration being apparent except immediately after 
a rain, when it shows light brown in spots, due to the solution, which 
being soluble in water comes to the surface. 



96 TOP COURSES 

"No ravel developed during continued dry weather when freshly 
laid and under traffic; road is relatively dustless; this, however, 
depends upon the percentage of silica in the stone used. The theory 
being that whenever the pavement becomes wet the solution is 
brought to the surface, resulting in absorbing and hardening 
down any fine material which had been produced by the abrasion of 
tires. 

"It can be laid in all excepting freezing weather, and while smooth 
yet it is sufficiently rough to afford good footing for horses and rubber 
tires. There is nothing entering into the construction to soften 
under high temperature and nothing to form mud in wet weather. 
It is claimed to be self-healing, due to continual chemical reactions 
taking place whenever the road becomes wet." 

CONCLUSION 

In this chapter the authors have attempted to, show the approxi- 
mate costs of the different styles of construction in general use or 
such experimental tops which they have seen that promise well. 
The costs given can be considered as relative only, to be used in a 
comparison of the various constructions and are based on roads in 
Western New York. 

In selecting the kind of pavement for various traffic requirements, 
good present practice calls for Brick, Asphalt Block or Asphaltic 
Concrete for Class I traffic at a cost for a i6' road ranging from $20,000 
to $28,000 per mile. 

For Class II, Bituminous Macadam, First-Class Concrete, Water- 
bound Macadam with Bituminous flush coats, Amiesite, and in the 
near future probably small blocks or stone cubes at a cost for a 16' road 
ranging from $11,000 to $18,000. 

For Class III, Waterbound Macadam treated with Calcium 
Chloride or light road oil or tar at a cost for 12' to 16' road of from 
$8,000 to $11,000. 

For Class IV, Bituminous Macadam, Concrete, Waterbound 
Macadam with Bituminous flush coats, Amiesite, Asphalt, etc. at a 
cost of $12,000 to $20,000 per mile. 

The type selections as given are based on satisfactory performance 
under traffic and moderate maintenance cost. 

MAINTENANCE 

In the development of any system of highways the methods and 
cost of maintenance become increasingly important. The rapid 
growth of motor traffic in the last few years has changed both methods 
and cost, making it necessary to give new figures which are reliable 
for present traffic conditions. We have therefore confined ourselves 
in the discussion to recent costs with which we are familiar in order 
that in stating general conclusions proper allowance is made for 
unusual conditions not shown in the reports of various State Highway 
Departments. 

The discussion will be based on the general maintenance costs 
and methods employed on 5600 miles of New York State Highways 



MAINTENANCE OF IMPROVED HIGHWAYS 97 

of all types for the year 191 5 and detail costs on 600 miles of roads 
in Western New York for a term of years. 

We are indebted to Mr. Frank Bristow for the following discussion 
of general maintenance methods and summarized costs. It should 
be borne in mind that the discussion and costs apply to territory 
subjected to severe winters. 

Maintenance of Improved Highways 
By Frank W. Bristow, 
N. Y. S. Dept. of Highways, Division of Maintenance 

Maintenance comprises keeping the paved roadway surface in 
as nearly perfect condition as possible, keeping the earth shoulders 
smooth and safe for traffic; the drainage system free from obstruc- 
tions; all structures in good repair; removing obstacles to vision as 
brush or overhanging branches; and cutting tall weeds and grass. 

If the work of maintaining improved roadways is consistently 
performed through successive years it is certain that the efficient 
life of such roads will be lengthened. Maintenance should commence 
when construction leaves off, because in order to effectively and eco- 
nomically maintain improved roads it is necessary that the roadway 
be in a good state of repair at the time the maintenance work begins, 
and should the pavement be so worn as to be structurally weak it 
is not economy to postpone resurfacing. 

Maintenance work, including surface treatment with bituminous 
material and cover, should be distinguished from extensive repairs 
involving resurfacing or reconstruction. 

Maintenance of Macadam Roads 

It is especially desirable that all surface treatments be completed 
as early in the season as possible; say by mid-summer to permit 
traffic to enjoy the greatest benefit from such treatment, the season 
of heaviest motor traffic being from the middle of July to the middle 
of September. So far as practicable the correction of surface defects 
such as ruts and depressions should precede the surface treatments. 

While the elimination of dust on macadam roads is desirable as 
adding to the comfort of the traveling public, it is necessary from the 
maintenance point of view, inasmuch as dust means deterioration 
of the road which if permitted to continue results in a raveled con- 
dition and the macadam will disintegrate. Surface treatment with 
oil or tar also tends to seal or waterproof the pavement. Horse- 
drawn steel-tired traffic tends to destroy an oiled surface mat, while 
rubber-tired motor traffic is beneficial. 

It is good practice not to oil macadam roads upon which horse- 
drawn traffic greatly predominates, or new waterbound macadam 
which has not been under traffic at least two months, or extremely 
shady roads. 

The usual foundation defects which develop in gravel and macadam 
surfaces are ruts, due to a soft condition in the earth sub-grade, 
depressions due to settlement of fills which commonly develop at 
locations where new culverts were constructed and frost boils. 



98 TOP COURSES 

Shallow ruts and surface depressions are corrected by being filled 
in with crushed stone of as large size as the depth of depressions will 
permit, the same being well tamped into place, and more lasting 
results are obtained if a proper grade of bituminous material is used 
to firmly bind the new stone; light asphaltic oils and tars have been 
used for this, purpose with unsatisfactory results, in that patches 
made by this method do not endure, the experience being that the 
material forming the patch is pushed ahead by traffic leaving the 
original depression exaggerated by the bunch of new patching material 
at the end. Heavier binder grade material has been used; a patch 
by this method is durable but does not wear away as rapidly as the 
adjacent surface resulting in a high spot in time. To date our expe- 
rience is that an asphaltic emulsion for cold patching is most satis- 
factory, being nearly fool proof and requiring no equipment but a 
broom and shovel. This material is not recommended for use with 
stone of greater size than will pass a one and a quarter inch ring. In 
using this material the depression to be repaired should be swept 
clean, so as to be free from mud or loose material, and tamped full 
of a mixture of the emulsion and broken stone. Such a patch will 
require an hour or two to set. The proportions of the mixture re- 
quired are, where the stone used are uniform in size about three- 
quarters of a gallon per cubic foot of stone, where the stone are 
graded about a gallon per cubic foot. This mixture may be made 
in moderate quantities as stock for use as required. Ruts in gravel 
surfaces may be eliminated by the use of a hone early in the season. 
Deep ruts indicate necessity of either subdrainage or reinforcement 
of the foundation; an inspection should determine which is the proper 
remedy. On side hill roads frequently a deep drain in the upper side 
ditch to intercept the ground water will be effective; where reinforce- 
ment is decided as necessary, usually sub-base construction about 
eight feet in width will be sufficient. Field stone, quarry spalls, 
broken stone, slag or gravel are proper materials for such reinforce- 
ment. 

Frost Boils so called are caused by wet spots in the earth founda- 
tion freezing and heaving, later when the frost leaves and the foun- 
dation soil is soft the thin macadam crust tends to break through 
under loaded wheels. These spots which usually occur where the 
road construction is in a cut, should be excavated, and drained if 
practicable; any wet clayey soil or silt removed and replaced by 
gravelly material, field stone, quarry spalls or other good material, 
the macadam is then replaced. 

Ravel is the term applied to describe the condition where the 
fragments of broken stone become loosened from the body of the road, 
due to the binding agent failing to perform its function. Bare 
toothy or a pitted condition of surface are the varying degrees of a 
slightly rough surface due to the interstices between the fragments of 
stone not being filled flush with the binding material or when the 
wearing surface has innumerable extremely slight depressions. 
Dust, which is self-explanatory. 

The remedy for raveled, pitted or dusty condition is a surface 
treatment of bituminous material and cover. 



MAINTENANCE OF IMPROVED HIGHWAYS 99 

These treatments are generally made using a grade of asphaltic 
residuum oil or a refined tar product which can be applied cold, or 
which requires very little heating, and better and more uniform 
results are obtained where a pressure distributor is used. If a pressure 
machine is used not less than twenty pounds should be required. 

Asphaltic base oils, or tar products having a bituminous content 
of from 40 to 60 per cent may be applied by gravity sprinkler, but 
60 to 75 per cent asphaltic oils or tars containing 60 to 70 per cent of 
pitch are preferably applied by pressure. Uniformity in application 
is important. 

As to the relative merits of asphaltic Residuum oils, cut back 
asphalts, high carbon, or low carbon tars there is a diversity of opinion. 
Relative cost and durability will naturally be the considerations 
controlling the selection. The material which is the cheaper at 
one delivery point may not be at some other. As to durability it is 
doubtful if there is any advantage as between the asphalt and tar- 
products. When applied, the tar material appears to take a set faster 
than the asphalt, which is a decided advantage, but more criticism 
is made as to slipperiness of the tarred surfaces during freezing 
weather. It is thought that the tars have the greater adhesive 
quality, but that the exposed surface due to evaporation of volatile 
constituents becomes crumbly or dead in a shorter time than a similar 
grade of Asphalt. 

Regarding rate of application per unit area, this will vary with the 
porosity of the surface to be treated; for the cold, or light hot appli- 
cation ranging between one-sixth and one- third gallon per square yard. 
Experience is that from one fifth to one quarter gallon will produce 
good results on the average surface. 

Preliminary to the applying of the bituminous material the surface 
to be treated should be swept clean if necessary, to free it from all 
loose and organic matter; after this has been done the application can 
proceed regardless of whether the surface is wet or dry, providing 
there are no pools of standing water on the surface, a slightly damp 
surface apparently gives better penetration than an absolutely dry 
surface, the object sought being to get the material into the texture 
of the road. The surface treatment should be confined to one side 
or half wddth of the road at a time, leaving the other side available 
for traffic. Some little time should be allowed for proper penetration, 
but within one hour after the application it should be lightly covered 
with suitable material. Traffic can now use this side and the treat- 
ment continued on the opposite side. 

The materials recommended for cover are crushed stone or slag 
which will pass a half inch mesh and are free from dust, ore tail- 
ings, fine screened gravel or coarse sharp sand. The toughness of 
the mineral aggregate used for oiling cover is an element in the 
durability of the mat formed by the treatment. Relative cost will 
determine the selection of material to be used for cover. The quantity 
of cover necessary will vary with the rate of application of the bitu- 
minous material and with the porosity of the surface treated. 

Where the rate of application of oil is from one-fifth to one-quarter 
gallon per square yard the range of cover may be stated as being 



ioo TOP COURSES 

between thirty-five and seventy cubic yards per mile of road sixteen 
feet wide, and generally forty to fifty cubic yards will be ample. 

This cover should be uniformly applied either by hand or by 
mechanical spreader; however, only sufficient to cover the oil lightly 
should be applied at one time. It will require two or three separate 
spreadings from time to time as the surface becomes shiny and sticky 
to produce a perfect mat. Any excess unused material delivered 
for cover should finally be gathered up and stored in neat piles back 
of the ditch line where possible. These treatments do not require 
rolling, although rolling tends to turn any coarse sharp fragments of 
cover material onto their broader sides, reducing danger of tire cuts 
to a minimum. 

1 Thick mats formed of binder and three-quarter inch stones while 
durable are not generally satisfactory; they are expensive, costing 
from one to two thousand dollars per mile and frequently become 
rough under traffic, although they do serve at times to carry a road 
along for a few years which would otherwise be a resurfacing matter. 
This treatment also is used to restore a crown to a road worn flat. 

On gravel and new waterbound macadam and upon roads where 
there is little motor traffic, maintenance by calcium chloride is 
effective. Where this treatment is used the applications may be of 
the granulated crystals applied by hand or by a mechanical spreader, 
at the rate of one pound to one and a quarter pounds per square 
yard; preliminary sweeping is not necessary unless there is excessive 
dust, say a quarter inch depth or more upon the surface proposed to 
be treated. Should this treatment be made immediately preceding 
a rain, a considerable quantity of material would be lost. Two or 
three treatments as above should suffice for the average season, and 
the width treated may be confined to the width of the traveled way. 
This treatment has cost in New York State about one hundred fifty 
dollars a mile a year. Surfaces which have previously been oiled 
are not recommended for Calcium Chloride treatment. 

In cases where, continued surface treatments of Bituminous 
material through successive years has built up an excessive depth of 
mat, which has a tendency to be unstable and rut, it is suggested 
that such mat be removed and spread upon the shoulders, which 
will cost from fifty to one hundred fifty dollars a mile, and that sur- 
face treatments be again made upon the macadam itself. Should it 
be found that the macadam has become uneven, as to crown and 
grade, or is badly worn or has numerous holes, it is suggested that 
the road be scarified and thoroughly dragged with a heavy spike- 
tooth harrow, after which an agricultural weeder should be repeatedly 
hauled over the road, the object sought being to work all of the finer 
particles to the bottom of the scarified course, leaving fairly clean 
coarse stone at the surface; this should be shaped up by hand or 
scraper and rolled to develop any irregularities in the surface which 
should be corrected by the addition of new crushed stone. Any 
pockets of fine material should be removed and replaced by new top 
course stone, the weeder should again be used to loosen the stone, 

1 The authors wish to emphasize the danger of using thick mats for ordinary 
maintenance. 



MAINTENANCE OF IMPROVED HIGHWAYS 101 

which will then be ready for the first application of binder, 
which may be at the rate of three-quarters of a gallon per square 
yard, application being made by a pressure distributor, the surface 
then to be covered with a layer of three-quarter inch broken stone and 
thoroughly rolled. During the rolling, additional three-quarter 
inch stone shall be applied and broomed about until the voids in the 
top course are well filled; all loose stone shall then be swept from the 
surface and a sealing coat of one-half gallon of binder per square yard 
shall be applied and immediately covered with a layer of one-half 
inch stone and again rolled; surface will then be ready for traffic. 
This treatment is probably better adapted to waterbound macadam 
than to the penetration bituminous type; however, if found necessary 
to break up and reshape penetration macadam, it is suggested that 
the latter loosening by the weeder be omitted and a spread, one stone 
thick, of two-inch broken stone be applied and the first application of 
binder be increased to one gallon or one and a quarter gallons. This 
method is not applicable to an extended mileage as it is generally better 
to resurface when a road reaches this stage. 

Concrete Roads with Thin Bituminous Surfaces. 

The second-class concrete with thin bituminous wearing surface 
is a difficult type to maintain; the bituminous surface under traffic 
patches off, and as the concrete is usually not strong enough to resist 
abrasion, holes develop in the concrete, patching results in a rough 
riding surface and probably the best way to secure a smooth riding 
road is to resurface, using a two-inch bituminous mixing type top. 

Asphalt, Topeka Mix, Amiesite, etc. 

The holes which develop in the bituminous mixing method type 
wearing surfaces should be repaired as follows : — Excavate the old 
material at the defective spot the entire depth of course, so that the 
edges will present clean, vertical surfaces, these surfaces and the 
exposed foundation to be swabbed or painted with hot asphaltic 
cement or paving pitch, the hole then to be filled, with a mixture 
similar to that used in original construction, whenever practicable, 
using sufficient quantity so that after consolidation by rolling (or 
tamping in case the extent of repairs is limited) the surface of the 
new patch will be flush with the adjacent pavement. In case there 
is no local mixing plant available, or the limited extent of repairs 
do not justify expense of treatment as above, holes may be repaired 
with the mixture of crushed stone and cold patch asphaltic emulsion, 
as outlined for macadam surfaces. 

Concrete Pavements. 

The cracks which develop in concrete pavements may be the 
result of either frost action, settlement of foundation or contraction, 
and are properly treated by being poured with hot paving pitch or 
asphalt binder. If spots disintegrate, the defective material should 
be removed and replaced by new concrete. 



102 TOP COURSES 



Block Pavements. 



Block pavements of brick, stone, asphalt, etc. properly constructed 
should not require repairing for a considerable term of years; cracks 
which develop should be grouted with hot paving pitch or asphalt 
binder; areas which settle, thereby breaking the bond of the grouted 
joints resulting in crushing or cobbling the blocks, should be taken 
up, the sand cushion reformed, all sound blocks cleaned and re- 
laid, being turned over where necessary, any broken blocks to be 
replaced by new whole ones, joints then to be grouted with Portland 
cement grout preferably, if the original pavement was so constructed, 
otherwise the joints may be poured with hot paving pitch. It should 
be noted that repairs with fresh cement grout require to be protected 
by barricades for a period of about a week, so that such repairs should 
be confined to one side of the pavement in long stretches, leaving 
the other side available for traffic; where the repairs are limited in 
extent and barricades are especially undesirable, the patch may be 
covered with two inches of earth and further protected by planking 
during the time required for the grout to set. Where joints are 
poured with paving pitch, traffic need be diverted only during the 
time of actually making the repair; this is a decided advantage. 

Observation demonstrates that horse traffic on steep grades leave 
the pavement and seek the earth shoulder, so that so far as practi- 
cable these shoulders should be improved by widening,' and by 
gravelling or covering with broken stone to avoid excessive rutting, 
also that on sharp curves the tendency of motor vehicles is to cut 
close to the inner edge, making it well for this reason to stone or 
gravel the shoulders at these points. 

Along the edges of the rigid types of pavement, block and con- 
crete especially, traffic usually develops a deep rut which if neglected 
becomes dangerous, to rapidly moving traffic; this rut should be 
kept filled with gravel or broken stone. Excess material when 
removed from the shoulders should be so disposed of as to widen 
embankments and flatten slopes. 

General Organization Methods. 

There are three general plans for performing the work of general 
maintenance: the patrol system, the repair gang and by contract. 
The nature of the work renders it difficult to estimate in terms of 
labor and material with precision, so that except in the case of surface 
treatments, repair by contract is not advised. By the patrol system 
the roads patrolled are under constant supervision and the responsi- 
bility for neglect is fixed. The repair gang may be used to supple- 
ment the patrol system when it is desired to expedite extensive small 
repairs, and also to perform all necessary repairs upon any roads 
not patrolled. A patrolman living in the vicinity of his work, 
equipped with a single horse, one yard wagon and small tools, cost- 
ing three dollars a day, can make all minor repairs on a section of 
between five and seven miles of macadam. The repair gang 
should be equipped with a small motor truck, say of one and a half 
tons capacity, to be used in transporting the men and tools within 



MAINTENANCE OF IMPROVED HIGHWAYS 103 

a radius of about twenty-five miles from their headquarters base; 
this truck can also assist by hauling som^ materials required in the 
work. 

It is concluded that a combination of the patrol and repair gang 
systems is an improvement over the adoption of either plan of organ- 
ization exclusively, also that the success of either plan depends entirely 
upon the experience, good judgment and ability of the man in direct 
charge and control of this work. As nearly all of the hauling in 
connection with maintenance work is over hard-surfaced roads, 
motor equipment for delivering stone, oil, etc. would naturally be 
considered. The writers' opinion is that for short hauls teams are 
economical, also that the motor tractor and trailers system of equip- 
ment are more efficient than the complete single unit system. 

Summarized Costs for the Season of 1915 New York State, 

In order that the following figures may be more easily understood, 
it is well to outline the development of the use of the different types 
of pavement. 

From 1898 when State Highway Improvement began until 1909 
to which time 1787 miles had been constructed, practically the entire 
mileage consisted of Waterbound Macadam. Up to this time there 
had been no systematic maintenance, which resulted in a large mile- 
age of road requiring more than ordinary expenditure to bring it up 
to standard. 

Beginning in 1909, Penetration Bituminous Macadam was gen- 
erally used on the main roads with Brick near cities and villages. 

About 191 2 the department tried out Concrete roads with thin 
Bituminous Oil Tops. This type proved unsatisfactory in that the 
bituminous surface peeled in spots and the concrete used was not 
sufficiently strong to stand the traffic directly. The high cost of 
maintenance can be seen from the following table. The type has 
not been used since 19 14. The department is now designing first- 
class Concrete roads where roads of that class are economical. 

In the following tabulation of maintenance and renewal costs, 
therefore, the average per mile represents approximately a fair 
sample of both yearly maintenance and renewal for Waterbound 
Macadam, Gravel and Concrete Bituminous and represents only 
ordinary yearly maintenance for Bituminous Macadam, Concrete 
Pavements, Brick and other high-class rigid pavements; none of these 
latter classes have been down long enough to yet require renewal, 
which makes their cost as shown much less than will ultimately be 
required. 



io4 



TOP COURSES 



to 

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MAINTENANCE OF IMPROVED HIGHWAYS 105 



Of the mileage shown in the preceding table, the following table 
shows the amount of resurfacing. 

1 Table Showing Resurfacing Costs 19 15 



Type of Road Resurfaced 


No. 
Miles 


Total Cost 


Cost per 
Mile 


Gravel 


12.88 

176.29 

43-72 

24.85 

0.36 


$ 77,686.27 

997,776.66 

243,760.22 

160,321.37 

4,003.40 


$6,000 
6,000 
6,000 
6,400 

12,000 


Waterbound Macadam 

Penetration Bituminous 

Concrete Bituminous Top 

Block Pavements 




Totals 


258.10 


$1,483,547.92 







1 The type of resurfacing is not necessarily the same type as the original road as 
shown in column No. 1. 

Supplementary Explanation of Mr. Bristow's General Costs and 

Discussion 

The authors wish to call attention to two points in the general 
cost tabulation. The average cost of maintenance and renewal 
for 191 5 is given as $750 per mile for the total system. This system 
includes approximately 1,000 miles of road recently built on which 
there is practically no charge except minor repair aggregating not over 
$200 per mile per year. For a completed system of this character 
all of which is under normal maintenance and renewal, the average 
cost per mile would be approximately $900 per mile, as is evident 
by excluding the thousand miles from the tabulation of total cost. 

In the resurfacing table it is evident from the cost per mile that 
better grades of top courses were generally placed on the Waterbound 
and Gravel roads than originally constructed; this means that in 
some cases the original design was not proper for the class of traffic 
the road served. 

The most evident faults of the usual maintenance are in delaying 
the work till late in the season and in careless mending of ruts and 
depressions before the application of surface treatments. It is well 
to emphasize the necessity of using a coarse grade of stone preferably 
1^ to 2 \" size in mending noticeable depressions. The hole should 
be dug out, the edges squared up, the depression filled, bound with 
heavy binder and screened and rolled. Carelessness in this regard 
has resulted in a large amount of justifiable complaint. 

Typical Maintenance Costs of Different Types. 

From a detailed study of 600 miles of road in Western New York 
with which we are personally familiar, the following typical costs 
are derived. 



106 TOP COURSES 

It is assumed that the type used is suitable to the class of traffic 
served as indicated on page 96. 

The maintenance system is a combination of patrol, gang work 
and contract. A one-man patrol with horse and wagon is used to 
keep the shoulders in shape, the ditches clean and small holes repaired. 
Gang work with proper machinery under state control to paint guard 
rail and make more extensive surface repairs and contract work for 
oiling and surfacing. Detail oiling costs are given under cost 
data, (page 333). This system is not highly efficient as the executive 
heads are changed at short intervals for partisan reasons; the depart- 
ment is a convenient means of dispensing minor patronage and the 
maintenance money is rarely available early enough in the spring 
to be used to the best advantage, but it represents about as good a 
method as can be expected in doing public work on a large scale and 
as such is of more practical value as a guide of costs than figures 
based on maximum efficiency. 

1 6' Waterbound Macadam Class II and III Traffic. 

Life of Top Course 4 to 10 years. Say 6 years for Class II Traffic 
and 8 years Class III Traffic under the following maintenance. 

Class II Traffic. 

Yearly patrol including materials for Minor Repairs and 

Painting Guard Rail @ $200 per mile per year $1,200 

Calcium Chloride 1st and 7th year @ $125 per mile per year 250 

Cold Oiling 2nd year 250 

" 3rd " 300 

" 4 th " 300 

Hot Oiling 5th " . . - 1,000 

Cold Oiling 6th " 250 

Resurfacing with Waterbound Mac. 7th year 4,000 

7 year total $7,55° 

Cost per mile per year Maintenance and Renewal. . . .$1,000 
" " " " " for Maintenance 500 

Class III Traffic. 

Yearly Patrol $1,600 

Calcium Chloride 1st and 9th years @ $125 per year 250 

Cold Oil 2nd year 250 

" 3rd " 250 

" 4 th " 300 

" 5th " 300 

Hot Oil 6th " 1,000 

Cold Oil 8th " 250 

Resurfacing 9th " 4,000 

9 year total $8,200 

Cost per mile per year Maintenance and Renewal $900 

" " " " " for Maintenance 500 



MAINTENANCE OF IMPROVED HIGHWAYS 107 

16' Penetration Bituminous Macadam, Class II and IV Traffic. 

Life of Top course 5 to 10 years. Say 8 year average. 

Yearly patrol @ $150 per mile per year $1,200 

Cold Oil 3rd year 250 

4-tn 250 

:> tn 3°° 

Hot Oil 6th " i ? ooo 

Cold " 8th " 250 

Resurfacing 9th year Bit. Mac 6,000 

9 year total $ 9,250 

Cost maintenance and renewal per mile per year St, 000 

per mile per year 400 



a a 



16' Brick Pavement, Class I Traffic. 

Probable life based on Medium Traffic Rochester City Streets 10 to 
25 years. Say 18 year average. 

Yearly patrol and minor repairs ©$150 per mile per year .... $2 , 700 

Renewal of surface and edging 15 ,000 

18 year total $17,700 

Cost of maintenance and renewal per mile per year. . .$1,000 
" per mile per year approx 200 



.. a 



16' 1st Class Concrete Pavement, Class II A Traffic. 

None of these pavements have been down a sufficient length of 
time to give us any reliable data as to probable length of life before 
resurfacing. We will assume 10 to 15 years or an average of 12 years 
when they will be resurfaced with Asphalt, Brick, or Clay Cubes at a 
cost of $9,000 to $15,000 per mile. 

Yearly patrol $150 per mile per year $1,800 

Resurfacing and minor renewals 10,000 

13 year total $11,800 

Cost of maintenance and renewal per mile per year .... $900 
" " " per mile per year approx $200 

Maintenance Conclusion. 

The indications are that the yearly cost of maintenance and renewal 
of a well-designed road system will run about $900 per mile per year. 
The effect of bad design is evident from resurfacing costs, for if 
Waterbound Macadam is built on a Class I Traffic Road the life is 
easily halved, increasing the maintenance and renewal cost to $1,500 
per mile per year and causing continual inconvenience to the travel- 
ing public by repairs and reconstruction. 

Probably the most feasible method of reducing maintenance cost 
will be by utilizing Prison labor to manufacture and in a limited way 
apply the maintenance materials. 



io8 



TOP COURSES 











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»-i O <D --. ^ 



CHAPTER VI 

MINOR POINTS 

Under this heading are included guard-rail, bridge-rail, retaining 
walls, toe walls, curbs, guide and danger signs, cobble gutters, rip- 
rap, catch-basins, grates, and dykes. 

Guard Rail (Wooden). 

The construction generally used is shown in the following sketch; 




Ab 



This 5ign every 100 ft.(approx.) with Black Paint 



POST rsio BILlTsT 



V All Rails to be Planed on4-Sidei 



>-£-< 



8'0"- 



"»■*■ 



p-"-I "kJ Rails and Posts Painted }-\ 
lJ _* 3 Coats White Lead and Oil. l_J 




i — i 

i i 

L.J 



Iron Pin, %'Diam., 6"lonq'' 
Fig. 29 

The posts are cedar, white oak, or chestnut, and the rails are hem- 
lock, yellow pine, or white pine. Such guard-rail costs from twenty- 
five to forty cents per foot, about five cents per foot per year for 
maintenance, and needs renewal every eight to ten years: the capi- 
talized cost at 4% is approximately $1.25 as figured by the New 
York State Highway Commission, and on this basis they have decided 
that it is cheaper to use a fill slope of 1 on 4 up to a seven-foot depth, 
eliminating the guard-rail, than it is to use a 1 on 1^ fill slope with 
guard-rail. 

The wooden guard-rail as built acts as a warning only. If a machine 
or rig becomes unmanageable and hits the rail, it generally breaks 
or the posts tear out, allowing the vehicle to turn turtle on the fill 

IOQ 



no 



MINOR POINTS 



slope. So many accidents of this kind occur that there is a demand 
for a rail that actually gives protection as well as a warning. 

Concrete Guard-Rail. 

Because of this demand and the high cost of maintenance and 
renewal of the common wooden trail, concrete guard-rail is being 
adopted. The simplest and best design of this kind that the author 
has seen was tried out by the New York State Department of 
Highways on the Ridge Road, near Rochester, N.Y., in 1910. A 
sketch is given below. This construction has been specially com- 
mended by the automobile associations. 



H ---- 

J V 



~-8 



-=* 



,J 



<7i 



, I . ' » 



'Diaphragm to Prevent 

Slipping Endwise^ 



<7- 



fc? 



Mesh Rein- 
forcement 



to I 

I I 



L-J 



I I 
1 J 




Fig. 30 



The rail was invented by J. Y. McClintock, County Engineer of 
Monroe County, N.Y. It is neat in appearance, durable and strong, 
and is specially adapted for a combination bridge and approach 



- jr - 2 0%* -------- j 





Section C-D. 



End Elevation. 

Fig. 31. — Showing Raised Parapet on Skew Bridge extended over 
Straight Parapet Retaining Wall 



RETAINING WALLS 



in 



Round tol{Rad. 



Found to li'ffad. 




Weep-Holes of3"V(e\—\- 
to be Spaced 6' 




1^ CI ass Concrete 



'- 0.39 sa./n. Rods 
Spaced 18" C.toC. 



-0.-55H-H-2* 

x: 



Type W. 



"t"(ininches)=2H-7 
Type R. 



Fig. 32. — New York State Standard Retaining Walls 



Reinforcing Steel Bars of Deformed Section 



H 



n 
12 
13 
U 
15 
16 

I? 
iS 

iQ 

20 



Stem 1 



Net 


Spacing 


Area 


C-C 


O.601 


6}" 


O.601 


32 


O.601 


.s" 


O.601 


4i" 


O.601 


4" 


O.994 


6" 


0.994 


52 


0.994 


5' ; 


O.994 


42 


0.994 


4s 



Length 



12-2 " 

i3 ; -3r 

i4 r -5 " 

i6'-8 " 
i7 r -9 ' 
i8'-ioi" 
2o , -o " 

2I , -li" 
2 2 '-< " 



Heel 



Toe 



Net 
Area 


Spacing 
C-C 


Length 


Net 
Area 


Spacing 
C-C 


Length 


O.442 


1\" 


4 _II 2 


0.442 


Q§" 


3'-3*' 


O.442 


W 


5 52 


O.442 


8J" 


3-8" 


O.442 


.si" 


6'-o" 


O.442 


7i" 


4 _0? > 


O.601 


6i" 


6'-6" 


0.601 


8|* 


4 # -4*' 


O.601 


-3'/ 

5s 


7'-o" 


0.601 


~3V 

/8 


4'-0" 


O.601 


.3 if 
44 


7-6i' / 


O.601 


6i" 


s'-4' 


O.785 


52 


8'-o|* 


O.785 


~5" 
/J 


5'-6" 


O.785 


A 7 " 

4s 


8'- 7 " 


O.785 


6J" 


5'-io|" 


0.785 


4f" 


9'-i" 


0.785 


6i" 


6'-2|" 


O.785 


4 " 


9 , -7 ,/ 


0.785 


-3'/ 
54 


6'-7" 



1 In each set of 3 bars in stem, first bar which is of length given, extends to top 
of wall, second bar to height f H, third bar to height \ H. 

When Type W is used as a bank wall (that is, above the roadway), max. H= 20'; 
min. X = 2' for H of 5 to 10'; and 0.2 H for H greater than 10'. 

When Type W is used as a sustaining wall (that is, below the roadway), max. 
H = 13'; and min. X = 3', except where foundation is rock or entirely below frost. 

When Type R is used as a bank wall, max. H = 20'; min. X = 0.15 H for H 
greater than 10'. 

When Type R is used as a sustaining wall, max. H = 13'; min. X = 0.25 H for H 
greater than io'. 



112 



MINOR POINTS 



rail. The old design of an iron bridge rail connected with a wooden 
road rail has been an eyesore. § . 

The actual cost of manufacture and setting was from fifty to sixty 
cents per foot The contract price for such rail would, probably, 
run from eighty cents to one dollar, depending upon the length of 
the haul, freight rate, and difficulty of digging post holes but even 
at the high figure it is cheaper than the wooden rail and is a safe 
construction. The anchor and rod shown on the sketch is used on 
curves or even on straight stretches where new fill is encountered, 
to prevent the posts being torn out by impact from runaway machines 

The rail proper has a web and bar reinforcement; it is designed 
to stand a six-ton horizontal load at the center of the panel The 
rails and posts are molded separately and allowed to set for, at least, 
a month; they are then put together in much the same manner as 
the wooden rail. The rounded top of the post makes it possible to 

e TconsXa g bTe d mileage of this rail has been erected in New York 
and New Jersey and has prevented many serious accidents. It has 
been hit by autos, tar kettles, rollers traction-engines and 1 rigs i and 
in no case has the vehicle gone over the bank -which is the general 

cause of fatal accidents. The rails and posts 
will break when hit by a heavy machine, but 
the reinforcement merely bends (does not 
snap) and continues to exert enough resistance 
to hold the machine on the roadway. 

Guard Rail has two distinct purposes : first, 
as merely a warning, at culverts, curves, low 
embankments, etc. where the danger is not 
great, and second, as an actual protection in 
dangerous places. Concrete guard rail is not 
advocated where warning alone is sufficient. 

Bridge Rail and Raised Parapets. 

Bridge rail for small span bridges is of two 
types, iron pipe rail (see figure 29) or solid 
raised parapets (see figure 31). The solid 
parapet is to be preferred. 

Exj mansion 




Joint 



Retaining Walls. 

In unusual cases retaining walls are needed 
in road construction. Plain or reinforced 
concrete walls are generally used, the selec- 
tion depending upon the relative cost. The 
plain concrete wall is considered the best 
type for heights up to twelve feet; the re- 
inforced cantilever form from twelve feet to 
eighteen feet, and above eighteen feet the 
buttressed design. We give page 1 1 1 examples 
and rules for the plain and reinforced cantilever types only, as the 
necessity for walls higher than eighteen feet is very rare, .bor tne 



Plan. 
Key Expansion Joint. 
Fig. 32 a 



CURBS 



113 



design of buttressed walls the reader is referred to the standard works 
on reinforced concrete. 

Retaining walls are usually built in monolithic sections of 20' 
to 25' in length; expansion joints are provided between these sec- 
tions. The expansion joints may consist of simply a plane of weak- 
ness between the sections produced by allowing one section to set 
before building the adjacent wall, or it may be a key joint as shown 
in figure 3 2 a, and the plane of separation may be made more pro- 
nounced by coating the concrete with a thin layer of asphaltum or 
pitch. 



Brick Gutter., 




1)8* Tile 

Drain 



Fig. $3. — Showing Concrete Toe Wall 



Toe Walls. 



Toe walls are nothing more than low retaining walls or very sub- 
stantial curbs. They are used in cuts on the outside of the gutters 
to prevent unstable side slopes from filling the gutters or heaving 
them out of shape by sliding pressure. Figure 33 gives a section of 
Eden Valley Hill near Buffalo, N. Y., where a clay quicksand cut 
was successfully protected in this manner. 



k b *,■ Round to I "Rad. 



Cinders, 
6 ravel or 
Crushed 
Stone 




Round to I "Rad. ~ 
("Aspha/tJoinK vrfe 



Brick f\<-l2- 



Sand- 






Cinders, Oravel or Crushed 

Stvne Cinders, Grave/ 

Z" Porous OWne - or Crushed Stone- 
Tile 




Stone Curb. 




Concr.Curb and Gutter. 






2 Porous Tile- 
Concr.Curb and Gutter. 

Round to I "Rad. 
- 4 ~i "Joints Filled with Paving Pitch 



X7.it: 



- -P'fjySand 



Simple Stone Curb 
For Light Traffic Village Streets. 



k/0>i s 5' 'Concrete Base 

Simplest Form of Concrete Curb. 
(5howing also Form of Expansion Joint 
where Brick are Laid Longitudinally 
in Gutter.) 

Fig. 34 



Curbs. 

Curbs are constructed of stone and of concrete. 



H4 



MINOR POINTS 



Stone Curbs. 

The cuts given show the methods of setting; the size of curb- 
stones for first-class work range from 16" to 22" in depth, 5" to 6" 
in thickness and 3' to 5' in length. For small villages, curbstone 
of 4" width, set in the simplest manner shown, is satisfactory. The 
stones most used are granites, Milestones of New York State, and 
the tougher sandstones such as Medina, Berea, Kettle River, etc. 
The prices range widely, depending on the locality of the work. 
Mr. William Pierson Judson, in his " Roads and Pavements," gives 
the following range of costs : 



C.I.Filleh- 
Bolts 



Straplmng'thick 



Bolts. 



7 " 

8 Pine Board 



<6~> 



::::! 



30' 




Blade, Letters on 
I Red Field 

CM 



'Screws 



<22 m-HUDSONT- '.ALBANY IOnDj I^ 



<43*m- NASSAU 




! -Both Sides to be Lettered 
if Ordered. 

X.H.No.lZl lTL 



Letters to be of cm t*> 
Aluminum on a Black Field. 



1. 9" Gal v. Iron Pipe, 
(Outside Diam.) 



Cylinder of 2nd Class „ WMf'i' 
Concrete-. Diam. 6.. ".?. ■:■ ! : i-'^.' ' 

a 

I---J3 




Og 



Iron Pin 
through Pipe 



$$ 



K- 6" >i 

Cast Iron, Filler. 



<6$ 



1_ J* 




■I "Rivet 
la 



**•+- ^"Carriage Bolt 
*■ Upset Thread after Nut is in Place. 
Fig. 35 



Straight curbs set, cost about as follows, with 30 per cent to 50 per 
cent added for curves: 



GUTTERS 



115 




Granite $0.50 to $0.90, unusual case $1.25 per foot. 
Ulster and Oxford bluestone, $0.40 to $0.80, unusual case $1.00 
per foot. 

Medina and Berea sandstone, 
$0.35 to $0.90. 
Shoo/Gf er ^o^f'" Concrete usually costs from 

$.040 to $0.50 with $0.35 added 
4?Sand f° r a combined gutter, though 

Cushion combined gutter and curb have 
\ < - been built for $0.50. 

r5w^/^^^^ The s i m pi e concrete curb 

- . . . „ , ' (figure No. 34) has been built 

Cobble Gutter. - , \ • • A -cc 4. *. 

t\<A^ during 191 1 in different parts 

c, ojAif °^ Western New York at a cost 

^%g?r Jr of $0.30 to $0.40 per foot. 

vfc?^. s "5s J*^: Where stone curbs can be 

P^^^l^} built for less than $0.70 per 

K- — 3'o" H foot, it seems good policy to use 

Third Clcss Concrete ^ em &*>"& &? business sec- 

Ditch Lininq tions of small villages. Jbor the 

s residential portions or where 

\$§^ the cost of stone curbing is high, 

~~~^^^r 5$!^ a concrete curb of the simplest 

^^^^^Fr^^^E^T^ design is the best practice, as 

l^AjDrr TOC-* c ^y conditions and require- 

i'^^s^i ments are neither necessary nor 

't'(ulJ°Wd4 expected. 

Concrete orSand Foundation-, Grouted 

or Sand Joints. Guide Signs and Danger Signs. 

Brick Gutter. . 

<y$&f A good sign must be easy to 

~-~ J ££°vfaer flAfr read, pleasing in appearance 

^^^r4W'^r '' ano - P ermanen t- The drawing 

' ' P§^fg|g^|f shows one of the designs in use; 

, Q m _ 1 the posts are of galvanized iron 

1 1 and cost about $5.00 in place; 

No.4 Crushed Stone the background for the alu- 

Ditch Protection . minum is a japanned metal ; the 

Fig. 36 signs cost approximately $0.15 

per letter including the board. 

Danger signs should be used only where no doubt exists as to 

their necessity, as their indiscriminate use decreases their effectiveness. 




Vi^],^.,^^^;;^-. 



Fig. 37 



n6 



MINOR POINTS 



Cobble Gutters, Brick Gutters, Ditch Linings, etc. 

Cobble gutters are used to protect the ditches from wash on steep 
grades and at entrances to intersecting roads where there is not sufh- 




FloodElev.ofBackWafer^ 6W ^ w 

Coarse Gravel Preferred. 
Old Surf ace^ 

Fig. $8. — Method of Protection where Road can be built above 

Flood Level 




cient headroom for a culvert. Also at the entrances to private 
property where the grade line of the ditch might be badly cut by 
vehicles. 

.-Layer of Dead Water ( Prevents Wash) 
Elevation of Flood Water 




Y / ^l fJ/%%^ 



T77////////7 
^■StoneFW 

Fig. 39. — Method of Protection where Road cannot be raised above 

Flood Level 



The usual cost of such construction ranges from $0.40 to $1.00 
per square yard. 

"oj End View. 

r\1foitndBar$ 



\ 




> 




£2 










72m 










■ II 










Leaching Basin. 



Fig. 40 




Upset 
\ Ends 
of Bars 
^ and flat- 
ten to-g" 



Standard 
(jratin 



3 Diam. * ; 
Circular Opening-'' 



Catch Basin. 



REFACING OLD WALLS 



117 



Where cobblestones are not available, ordinary building brick 
may be used or No. 4 crushed stone, as shown page 115. 

"Riprap and Dykes. 

Well-constructed riprap protects stream banks and bridge ap- 
proaches from stream wash except in unusual cases where a solid 
masonry or concrete protection is required. 

The sizes of stone suitable for riprap are usually specified at a 
minimum of f cubic foot and 50 per cent or more of the material to 
be over 2 cubic feet. 

Where the road is located in bottom land and is covered with back- 
water in the Spring, it can be protected by riprap paving on both 
sides or a dyke and riprap paving on one side as shown in figures No. 
38 and No. 39. 

Grates. 

Cost of cast-iron grates about $0.05 per pound. 
Cost of wrought-iron grates about $0.08 per pound. 

Repointing Masonry and Refacing Old Walls. 

Old masonry structures can often be used complete or in part by 
repointing the joints; they should be cleaned out thoroughly with 
a chisel and filled flush with a 1 to 1 Portland Cement mortar. 

The author does not believe in facing up old masonry abutments 



2 Reinforcing Bars^J\ 
Spaced IZ'X.toC. 




Fig. 41. 



Facing for Old Masonry 



if it can be avoided; however, if it seems advisable, because of 
shortage of funds, the old joints should be well cleaned out and hook 
dowels used as shown in cut No. 41. One dowel every 6 square feet 
is good practice. 

The concrete facing should be at least 12 inches thick and reinforced 
to prevent settlement and temperature cracks. 



CHAPTER VII 

MATERIALS 

The selection of materials is an important part of the design. 
Most municipal and State Departments have well equipped labora- 
tories for testing stone, gravels, brick, bitumens, cements, etc. The 
object of these tests is to determine the physical and chemical prop- 
erties that have a particular bearing on the action of the materials 
under construction conditions. While these conditions are not 
attained they are approximated and by a comparison of the laboratory 
results with the actual performance of the different materials in 
practice a relation can be established that is useful as a basis for 
judgment : 

We are greatly indebted in this 2nd edition to Mr. H. S. Matti- 
more and Mr. J. E. Myers who have rearranged and brought up to 
date much of the material on tests and their significance. 

This chapter gives a brief statement of the desirable qualities and 
the tests for: 

1. Top course, macadam stone. 

2. Screenings. 

3. Bottom course, macadam stone. 

4. Bottom course and sub-base fillers. 

5. Brick. 

6. Bituminous binders. 

7. Concrete materials. 

1. Stone for the Surfacing of Macadam Roads 

Stone for use in the surfacing of a macadam road should be hard 
and tough to withstand the abrasive action of team traffic and the 
vibratory action of high-speed motor vehicles and should not contain 
any minerals that are likely to disintegrate rapidly under influence 
of weather conditions. 

To determine the relative hardness, toughness and power to resist 
abrasive and impact action of traffic, stones are subjected to the 
following tests: 

1. Abrasion. 

2. Hardness. 

3. Toughness. 

4. Specific Gravity. 

5. Absorption. 

6. Fracture. 

7. Geological classification. 

1 Abrasion Test. 

The machine shall consist of one or more hollow iron cylinders; 
closed at one end and furnished with a tightly fitting iron cover at 

1 American Society of Testing Materials. 
118 



DEVAL RATTLER 



119 



the other; the cylinders to be 20 cm. in diameter and 34 cm. in depth, 
inside. These cylinders are to be mounted on a shaft at an angle 
of 30 deg. with the axis of rotation of the shaft. 

At least 30 lb. of coarsely broken stone shall be available for a test. 
The rock to be tested shall be broken in pieces as nearly uniform in 
size as possible, and as nearly 50 pieces as possible shall constitute 
a test sample. The total weight of rock in a test shall be within 
10 g. of 5 kg. 

All test pieces shall be washed and thoroughly dried before weigh- 
ing. Ten thousand revolutions, at the rate of between 30 and 2>2> 
per minute, shall constitute a test. Only the percentage of materials 
worn off which will pass through a 0.16 cm. ( T V in.) mesh sieve shall 
be considered in determining the amount of wear. This may be 
expressed either as the percentage of the 5 kg. used in the test, or the 
French coefficient, which is in more general use, may be given; that 

is, coefficient of wear = 20 X — = — , where w is the weight in 

w w 

grams of the detritus under 0.16 cm. (jg in.) in size per kilogram of 
rock used. 




7P7T 



Fig. 42.Deval Rattler 



Hardness. 

Hardness is determined by a Dorry machine. A stone cylinder 
25 cm. in diameter, obtained by a diamond core drill from the material 
to be tested, is weighed and placed in the machine so that one end 
rests on a horizontal cast-iron grinding disk with a pressure of 25 
grams per sq. cm. The disk is revolved 1,000 times during which 
standard crushed quartz sand about \\ mm. in diameter is auto- 
matically fed to it. The cylinder is then removed and weighed 
and the coefficient of hardness obtained by the formula 20 — \ the 
loss in weight, expressed in grams. In order to get reliable results 
two cylinders are generally used, each one being reversed end for 
end during the test. 



1 Test for Toughness. 

1. Test pieces may be either cylinders or cubes, 25 mm. in diam- 
eter and 25 mm. in height, cut perpendicular to the cleavage of the 
rock. Cylinders are recommended as they are cheaper and more 
easily made. 

2. The testing machine shall consist of an anvil of 50 kg. weight, 
and placed on a concrete foundation. The hammer shall be of 2 kg. 

1 American Society of Testing Materials. 



120 MATERIALS 

weight, and dropped upon an intervening plunger of i kg. weight, 
which rests on the test piece. The lower or bear-surface of this 
plunger shall be of spherical shape having a radius of i cm. This 
plunger shall be made of hardened steel, and pressed firmly upon the 
test piece by suitable springs. The test piece shall be adjusted, so 
that the center of its upper surface is tangent to the spherical end of 
the plunger. 

3. The test shall consist of a 1 cm. fall of the hammer for the first 
blow, and an increased fall of 1 cm. for each succeeding blow until 
failure of the test piece occurs. The number of blows necessary to 
destroy the test piece is used to represent the toughness, or the centi- 
meter-grams of energy applied may be used. 

1 Determination of the Apparent Specific Gravity of Rock. 

The apparent specific gravity of rock shall be determined by the 
following method: First, a sample weighing between 29 and 31 g. 
and approximately cubical in shape shall be dried in a closed oven 
for 1 hour at a temperature of. no degrees C. (230 degrees F.) and 
then cooled in a desiccator for 1 hour; second, the sample shall be 
rapidly weighed in air; third, trial weighings in air and in water of 
another sample of approximately the same size shall be made in 
order to determine the approximate loss in weight on immersion; 
fourth, after the balances shall have been set at the calculated weight, 
the first sample shall be weighed as quickly as practicable in distilled 
water having a temperature of 25 degrees C. (77 degrees F.); fifth, the 
apparent specific gravity of the sample shall be calculated by the 
following formula: 

W 

Apparent specific gravity = — — Tt^ - " 1 wmcn W = tne weight 

W — MI 

in grams of the sample in air and Wi = the weight in grams of the 
sample in water just after immersion. 

Finally, the apparent specific gravity of the rock shall be the average 
of three determinations, made on three different samples according 
to the method above described. 

2 Determination of the Absorption of Water per Cubic Foot of Rock. 

The absorption of water per cubic foot of rock shall be determined 
by the following method: First, a sample weighing between 29 and 
31 g. and approximately cubical in shape shall be dried in a closed 
oven for 1 hour at a temperature of no degrees C. (230 F.) and then 
cooled in a desiccator for 1 hour; second, the sample shall be rapidly 
weighed in air; third, trial weighings in air and in water of another 
sample of approximately the same size shall be made in order to 
determine the approximate loss in weight on immersion; fourth, 
after the balances shall have been set at the calculated weight, the 
first sample shall be weighed as quickly as possible in distilled water 
having a temperature of 25 degrees C. (77 degrees F.); fifth, allow 

1 American Society of Testing Materials. 

2 American Society of Testing Materials. 



COST OF TESTS 1 21 

the sample to remain 48 hours in distilled water maintained as nearly 
as practicable at 25 degrees C. (77 degrees F.) at the termination of 
which time bring the water to exactly this temperature and weigh 
the sample while immersed in it; sixth, the number of pounds of water 
absorbed per cubic foot of the sample shall be calculated by the fol- 
lowing formula: 

W2 — Wi 
Pounds of water absorbed per cubic foot = '-= ^—x 62.24 

in which W =the weight in grams of sample in air, Wi =the weight 
in grams of sample in water just after immersion, W2 =the weight 
in grams of sample in water after 48 hours' immersion, and 62.24 — 
the weight in pounds of a cubic foot of distilled water having a tem- 
perature of 25 degrees C. (77 degrees F.). 

Finally, the absorption of water per cubic foot of the rock, in 
pounds, shall be the average of three determinations made on three 
different samples according to the method above described. 

Fracture. 

Stone suitable for road work should crush in cubical shapes rather 
than in thin, flat pieces and preferably with rough, jagged fracture 
that it may interlock firmly under action of the roller. 

Geological Classification. 

The geological classification is determined from an examination 
with a microscope or powerful hand glass, and a consideration of its 
origin. Great refinements are avoided as the general classification 
is all that is necessary to the highway engineer after the physical 
qualities are ascertained by test. 

Cost of Tests. 

The cost of collecting and testing stone as given in the 1909 Report 
of the New York State Department of Highways is $8.55 per sample. 
The following tables show tests on the more common rock: 



122 



MATERIALS 



Table 21. Taken from Bulletin No. 31, United States 
Office of Public Roads 



Rock varieties 



Granite 

Biotite-granite 

Hornblende-granite . . 

Augite-syenite 

Diorite 

Augite-diorite 

Gabbro 

Peridotite 

Rhyolite 

Andesite 

Fresh basalt 

Altered basalt 

Fresh diabase 

Altered diabase 

Limestone 

Dolomite 

Sandstone 

Feldspathic sandstone 
Calcareous sandstone 
Chert 

Granite-gneiss 

Hornblende-gneiss . . . 

Biotite-gneiss 

Mica-schist 

Biotite-schist 

Chlorite-schist 

Hornblende-schist . . . 
Amphibolite 

Slate 

Quartzite 

Feldspathic quartzite 
Pyroxene quartzite . . 

Eclogite 

Epodosite 



Per cent 


Tough- 


Hard- 


Cementing 


wear 


ness 


ness 


value 


3-5 


15 


18.I 


20 


4 


4 


IO 


16.8 


17 


2 


6 


21 


18.3 


3° 


2 


6 


IO 


18.4 


24 


2 


9 


21 


18.I 


4i 


2 


8 


19 


17.7 


55 


2 


8 


16 


17.9 


29 


4 





12 


15-2 


28 


3 


7 


20 


17.8 


48 


4 


7 


II 


137 


189 


3 


3 


23 


17. 1 


in 


5 


3 


17 


15.6 


239 


2 





30 


18.2 


49 


2 


5 


24 


17.5 


156 


5 


6 


IO 


12.7 


60 


5 


7 


IO 


14.8 


42 


6 


9 


26 


17.4 


90 


3 


3 


17 


15-3 


119 


7 


4 


15 


^•3 


60 


10 


8 


15 


19.4 


27 


3 


8 


12 


17.7 


26 


3 


7 


IO 


17.1 


30 


3 


2 


19 


17.5 


4i 


4 


4 


IO 


17.8 


30 


4 








— 


16 


4 


2 





— 


24 


3 


7 


21 


16.5 


53 


2 


9 


IO 


19.0 


29 


4 


7 


12 


"•5 


102 


2 


9 


19 


18.4 


17 


3 


2 


17 


18.3 


21 


2 


3 


27 


18.6 


17 


2 


4 


31 


17-4 


21 


3 


6 


16 


16.0 


47 



Specific 
gravity 



2.65 
2.64 
2.76 
2.80 
2.90 
2.98 
3.00 
3-40 

2.60 
2.50 
2.90 

2-75 
3.00 

2.95 

2.70 
2.70 

2-55 
2.70 
2.66 
2.50 

2.68 
3.02 
2.76 
2.80 
2.70 
2.90 
3.00 
3.00 

2.80 
2.70 
2.70 
3.00 

3-3° 
3-03 



PROPERTIES OF ROCKS 



123 



Tables 22 and 23 Combined 
From Annual Report N. Y. State Highway Comm. 1914 



County 



Number 
of com- 
plete 
tests 



Erie 

Saratoga. . . . 
Steuben .... 

Clinton 

Dutchess 

Essex 

Franklin . . . 

Fulton 

Herkimer . . . 

Monroe 

Montgomery 

Niagara 

Saratoga. . . . 
St. Lawrence 
Washington . 

Dutchess . . . 
Herkimer . . . 
Montgomery 
Niagara .... 
St. Lawrence 
Washington . 
Wayne 

Essex 

W T arren 

Clinton 

Dutchess 

Essex 

Franklin. . . . 

Fulton 

Hamilton . . . 
Jefferson. . . . 

Lewis 

Orange 

Putnam 

Saratoga. . . . 
St. Lawrence 

Warren 

Washington . 
Westchester . 

Essex 

Franklin .... 
Hamilton . . . 
Jefferson .... 

Lewis 

Oneida 

St. Lawrence 
Warren. .... 



46 
4 



Number 

of 

partial 

tests 

(no core 

piece) 



Weight 
lbs. per 
cu. ft. 



Water 

ab- 
sorbed, 
lbs. per 
cu. ft. 



French 
coeffi- 
cient of 
abrasion 



Hard- 
ness 



Tough- 
ness 



Weighted 
value 





Calcareous 


Sandstone 






5 
6 

4 


1 


167 
169 

162 


0.65 9.5 
0.31 10. 1 
1.44 9.4 


12.9 
15-9 
i5-i 


13-4 
13-8 
131 



Dolomite 



6 




175 


0.41 


11.9 


15.8 


12.7 


4 


1 


174 


0.43 


12.4 


17-3 


11.9 


4 




173 


0.42 


13-5 


16.9 


15.8 


4 




174 


0.51 


9-5 


14.9 


12. 1 


4 




176 


0.15 


11.8 


16. 1 


14.4 


17 




173 


0.67 


8.4 


I3-I 


6-7 


13 


2 


171 


1.07 


10.3 


14.8 


8.2 


8 




174 


o.39 


10.6 


14.7 


II-3 


11 




168 


1.50 


6-5 


14.0 


7.0 


8 




174 


o.33 


8.6 


15-5 


9.2 


31 




174 


0.65 


10.5 


15-7 


9.9 


6 




175 


0.29 


10.7 


i5-i 


10.5 



Dolomitic Limestone 



8 


1 


176 


0.46 


9.0 


14.9 


10.9 


4 


1 


170 


0.47 


H-3 


16.7 


8.2 


8 


1 


175 


0.41 


13.0 


15-8 


12.4 


7 




166 


2.19 


9-5 


131 


7-8 


7 




168 


0.38 


9.2 


16.8 


6.8 


4 




175 


0.36 


13-7 


16. 1 


10.8 


4 




173 


o.59 


10.2 


15.5 


8.7 



Gabbro 
176 I 0.29 

183 I 0.37 

Gneiss 



7-6 
10. 1 



17-3 
17.7 



6.9 
9.8 



5 




185 


0.27 


10.5 


17.2 


H-3 


8 


1 


172 


058 


7.0 


17. 1 


9.1 


29 


2 


176 


0.31 


8-4 


17. 1 


8.1 


8 




178 


0.50 


6.2 


16. 1 


7-8 


12 


1 


169 


0.25 


11. 1 


17.8 


11. 5 


11 




173 


o.37 


8.2 


17.0 


5-8 


26 


1 


171 


0.23 


11. 1 


17-3 


12.0 


6 




167 


0.27 


9.6 


17.9 


10.6 


7 




179 


0.38 


7-i 


17. 1 


6.4 


10 


1 


172 


0.32 


8-5 


16.6 


7-5 


7 




180 


0.20 


10.0 


17.0 


8.5 


52 




172 


0.27 


9-7 


17.5 


10.2 


30 


2 


173 


0.30 


7-5 


17-3 


6-5 


4 




170 


0.29 


8-5 


17. 1 


10.9 


37 


2 


171 


o.39 


8-3 


16.9 


7-8 







Granite 








1 5 




171 


0.38 


7-5 


18.0 


5-i 


6 




165 


0.31 


8.7 


17.9 


9-4 


5 




165 


0.36 


9.9 


18. 1 


9.0 


23 


1 


166 


0.23 


12. 1 


18.4 


10. 1 


8 




166 


0.36 


10.9 


18.4 


9.2 


6 




166 


0.13 


10.2 


18.9 


8.2 


30 




165 


0.25 


9.9 


18.3 


8.1 


5 




165 


0.45 


7-9 


17.9 


7-7 



68 

76 
72 

80 

84 
90 
70 
82 
58 
69 
73 
55 
66 
73 
73 

68 
76 
83 
63 
68 

84 
7i 

64 
75 

78 
64 
68 

59 

80 
64 

80 

75 
62 
66 
72 
74 
64 
7i 
67 

64 
7i 

75 
83 
79 
77 
74 
67 



124 



MATERIALS 



From Annual Report N. Y. State Highway Comm. 1914. — Cont. 



County 



Number 
of com- 
plete 
tests 



Number 

of 

partial 

tests 

(no core 
piece) 



Weight, 
lbs. per 
cu. ft. 



Water | French 



Hard- 
ness 



Tough- 
ness 



Albany 

Cayuga 

Clinton 

Columbia . . . 

Erie 

Fulton 

Genesee .... 

Greene 

Herkimer . . . 
Jefferson .... 

Lewis 

Madison .... 

Monroe 

Montgomery 

Niagara 

Oneida 

Onondaga . . . 

Ontario 

Otsego 

Rensselaer. . 
Saratoga .... 
Schoharie . . . 

Seneca 

Ulster 

Warren 

Washington . 



Dutchess.. 



Columbia . . . | 
Dutchess 
Rensselaer . . 
Washington . | 



Allegany. . 
Broome . . . 
Cayuga . . . 
Chenango . 
Clinton. . . 
Delaware . 

Erie 

Franklin. . 
Greene . . . 
Herkimer . 
Jefferson. . 
Livingston 
Madison . . 
Niagara. . . 
Orleans. . . 
Otsego 
Saratoga . . 



16 
8 

10 
12 



8 
n 

4 
IS 
14 
53 

8 

5 
6 

4 
8 
4 
5 
7 
8 
21 
5 



Limestone 



13 


7 


168 


0.60 


7 


9 


14-3 


6.4 


34 


6 


170 


0.49 


8 


8 


14.9 


7-8 


14 


2 


170 


0.28 


8 


2 


14.1 


5-3 


12 




170 


0.28 


9 


1 


15-3 


9.2 


9 


3 


167 


o.57 


8 


1 


16.6 


8-3 


6 


1 


168 


0.21 


7 


7 


15-5 


6-5 


6 


3 


169 


0.26 


8 





15.0 


8.2 


11 




169 


0.36 


11 


1 


16.4 


8.9 


17 


9 


169 


0.26 


8 


7 


14.8 


8.2 


105 


44 


169 


0.28 


7 


6 


I5-I 


6.4 


26 


20 


169 


0.32 


6 


9 


14.1 


6.2 


16 


1 


169 


0.23 


8 


4 


14.7 


7-7 


4 




168 


0.27 


8 


1 


14.1 


7-4 


12 


2 


169 


0.24 


8 


5 


15-3 


8.0 


11 


1 


168 


0.84 


7 


1 


12.8 


6-5 


31 


19 


169 


0.29 


7 


8 


13.8 


6.6 


25 


1 


170 


0.38 


8 


9 


15-7 


8.4 


11 




169 


o.39 


10 


2 


15-9 


10.2 


7 


2 


169 


0.32 


8 


1 


14. 1 


6-3 


4 


1 


171 


0.21 


7 


5 


15.0 


5-3 


5 




170 


0.24 


8 


7 


13-7 


7.0 


29 


2 


169 


o.34 


8 


1 


14.9 


6.7 


7 


3 


169 


0.21 


9 


4 


15-3 


7-9 


12 


3 


170 


0.25 


8 


1 


15.6 


7-4 


5 




170 


0.24 


8 


9 


15-7 


7-4 


5 


3 


169 


o.34 


7 


9 


15-5 


6.9 



Marble 
178 I 0.30 I 

QUARTZITE 



7-3 I 14.2 



Sandstone 



6.0 





168 


0.28 


16.5 


18.3 


17. 1 


2 


166 


0.36 


13.5 


18.8 


11. 8 


1 ... 


166 


0.49 


12. 1 


18.7 


14.8 


i ... 


167 


0.40 


I4.6 


18.9 


16.3 



156 


2.10 


8.4 


13.4 


9.1 


165 


1.29 


7-8 


12.9 


10.5 


167 


1.16 


7-8 


12. 1 


io.s 


164 


1.58 


8.7 


11. 2 


10.4 


163 


0.71 


11. 7 


18.5 


11.0 


167 


1-45 


7.0 


12.7 


8.5 


159 


2.10 


6.3 


s.i 


7-8 


i57 


1.06 


9-7 


17.9 


7-1 


169 


0.62 


8.6 


14-5 


8.1 


160 


2.50 


10.9 


16.4 


10.7 


156 


1.46 


8.3 


16.2 


6.3 


160 


3.02 


8.8 


9.6 


8.8 


163 


2.15 


9-9 


13-9 


8.6 


158 


1.78 


9.0 


16.4 


8.2 


155 


2.18 


n. 8 


14.4 


8.1 


162 


1-75 


8.4 


11. 9 


9.6 


163 


0.36 


10.7 


18.0 


8.7 



PROPERTIES OF ROCKS 



125' 



From Annual Report N. Y. State Highway Comm. 1914. — Coat. 



County 



Number 
of com- 
plete 
tests 



I Number 

of 

partial 

tests 

(no core 

piece) 



Weight, 

lbs. per 

cu. ft. 



Water 

ab- 
sorbed, 
lbs. per 

cu. ft. 



French 
coeffi- 
cient of 
abrasion 



Hard- 
ness 



Tough- 
ness 



Weighted 

value 



Sandstone. — Continued 



Schoharie . . . 
Schuyler .... 

Seneca 

Steuben 

St. Lawrence 
Sullivan .... 

Ulster 

Wyoming . . . 

Albany 

Columbia . . . 
Dutchess. . . . 

Greene 

Montgomery 
Rensselaer . . 
Saratoga .... 
Schenectady 
Ulster 

Essex 

Franklin .... 
Herkimer. . . 
Jefferson. . . . 



Rockland ... I 12 



6 


3 


165 


1. 21 


9-4 


15.2 


11. 7 


4 




162 


2.14 


8.1 ' 


11. 6 


10.6 


5 




165 


0.86 


IT.O 


13.9 


IS.8 


22 


3 


157 


2-79 


8-3 


9-3 


10. 


16 




159 


0.79 


IO. O 


17.8 


7.2 


30 


4 


164 


1.26 


6.5 


14.9 


8.2 


8 




166 


0.64 


8.0 


14-3 


8.1 


7 


... 


159 


2-54 


6.0 


5-1 


7-9 



5 ; ... 


167 


0.75 


7-5 


13-2 


7-2 1 


- 12 


168 


0.32 


10.7 


15.9 


11. 7 


10 2 


168 


0.57 


8.1 


16.2 


11. 5 


13 


169 


0.48 


7-1 


15.6 


9-5 


4 


166 


i-39 


10. 1 


n*3 


11. 8 


10 


169 


0.44 


9.1 


159 


9.4 


5 


168 


0.99 


11. 8 


15-2 


11.9 


4 


165 


1. 10 


9.2 


14.6 


9 5 


7 I ... 


169 


o.59 


7-5 


13.8 


10.2 



Syenite 



7 ' 




184 


0.52 


7-7 


17. 1 


6.7 


4 




171 


o.45 


10. 1 


18.3 


8.0 


13 




174 


0.16 


12.5 


18.0 


11. 6 


7 




176 


0.34 


12.4 


18.1 


14.5 



I 183 



Trap 

I Q-39 



13.2 | 17.6 I 1.64 I 



70 
58 
77 
54 
73 
58 
61 
36 

56 
76 
68 
62 
65 
69 
78 
66 
60 

64 
75 
85 
88 



_9L 



Table 24. 


L 


Geological Classification 


Class 


Type 


Family 


I Igneous 




1 Intrusive 
(plutonic) 


a Granite 
b Syenite 
c Diorite 
d Gabbro 
k e Peridotite 






2 Extrusive 
(volcanic) 
I 


a Rhyolite 
b Trachyte 
c Andesite 
d Basalt and diabase 






1 Calcareous j 


a Limestone 
b Dolomite 


II Sedimentary 




2 Siliceous 
I 


a Shale 

b Sandstone 

c Chert (flint) 




( 

1 1 Foliated 


a Gneiss 
b Schist < 
c Amphibolite 


III Metamorphic 


! 


a Slate 




2 Nonfol lilted 

1 


b Quartzite 
c Eclogite 
d Marble 



1 Bulletin No. 31, United States Department of Public Roads. 



I2 6 MATERIALS 

The following quotation from this same bulletin describes the 
characteristics of the three groups: 

Igneous Rocks. 

"All rocks of the igneous class are presumed to have solidified from 
a molten state, either upon reaching the earth's surface or at varying 
depths beneath it. The physical conditions, such as heat and pres- 
sure under which the molten rock magma consolidated, as well as 
its chemical composition and the presence of included vapors are 
the chief features influencing the structure. Thus, we find the deep- 
seated plutonic rocks coarsely crystalline with mineral constituents 
well defined, as in case of granite rocks, indicating a single, prolonged 
period of development, whereas the members of the extrusive or 
volcanic types, solidifying more rapidly at the surface, are either 
fine-grained or frequently glassy and vesicular, or show a prophyntic 
structure This structure is produced by the development of large 
crystals in a more or less dense and fine-grained ground mass, and is 
caused generally by a recurrence of mineral growth during the effusive 
period of magmatic consolidation. .1-1 

"In the arrangement of the rock families from a mineralogical 
standpoint it will be noted that the plutonic rock types, granite, 
syenite, and diorite, are represented by their equivalent extrusive 
varieties rhyolite and andesite, and that diabase has been included 
somewhat arbitrarily, with basalt, as a volcanic representative of 
gabbro. These latter rocks are of special interest, owing to their 
wide distribution and general use in road construction. They occur 
in the forms of dykes, intruded sheets, or volcanic flows and vary 
in structure from glassy-porphyritic (typical basalt) to wholly crys- 
talline and even granular (diabase). Their desirable qualities for 
road-building are caused to a large extent by a peculiar interlocking 
of the mineral components (ophitic structure), yielding a very tough 
and resistant material well qualified to sustain the wear of traffic. 

"Igneous rocks vary in color from the light gray, pink, and brown 
of the acid granites, syenites, and their volcanic equivalents (rhyolite, 
andesite, etc.) to the dark steel-gray or black of the basic gabbro, 
peridotite, diabase, and basalt. The darker varieties are commonly 
called trap. This term is in very general use and is derived from 
trappa, Swedish for stair, because rocks of this kind on cooling fre- 
quently break into large tabular mas es, as may be seen in the ex- 
posures of diabase on the west shore ol the Hudson River from Jersey 
City to Haverstraw. 

Sedimentary Rocks. 

"The sedimentary rocks as a class represent the consolidated 
products of former rock disintegration, as in the case of sandstone, 
conglomerate, shale, etc., or they have been formed from an. accumu- 
lation of organic remains chiefly of a calcareous nature, as is true of 
limestone and dolomite. These tegmental or clastic materials have 
been transported by water and 'deposited m^^^nnS °* 
the sea or lake bottoms, producing a very characteristic bedded or 
stratified structure in many of the resulting rocks. 



METAMORPHIC ROCKS 127 

"In the case of certain oolitic and travertine limestones, hydrated 
iron oxides, siliceous deposits, such as geyserite, opal, flint, chert, etc., 
the materials have been formed chiefly by chemical precipitation and 
show generally a concentric or colloidal structure. 1 Oolitic and 
pisolitic limestones consist of rounded pealike grains of calcic car- 
bonate held together by a calcareous cement. Travertine is the 
so-called 'onyx marble' of Mexico and Arizona. It is a compact 
rock, concentric in structure and formed by the precipitation of car- 
bonate of lime from the waters of springs and streams. 

"Loose or unconsolidated rock debris of a prevailing siliceous 
nature comprise the sands, gravels, finer silts, and clays (laterite, 
adobe, loess, etc.). Shell sands and marls, on the other hand, are 
mainly calcareous, and are formed by an accumulation of the marine 
shells and of lime-secreting animals. Closely associated with the 
latter deposits in point of origin are the beds of diatomaceous or 
infusorial earth composed almost entirely of the siliceous casts of 
diatoms, a low order of seaweed or algae. 

"This unconsolidated material may pass by imperceptible grada- 
tions into representative rock types through simple processes of in- 
duration. Thus clay becomes shale, and that in turn slate, without 
necessarily changing the chemical or mineralogical composition of 
the original substance. 

"Such terms as flagstone, freestone, brownstone, bluestone, gray- 
stone, etc., are generally given to sandstones of various colors and 
composition, while puddings tone, conglomerate, breccia, etc., apply 
to consolidated gravels and coarse feldspathic sands. 

"The calcareous rocks are of many colors, according to the amount 
and character of the impurities present. 

Metamorphic Rocks. 

"Rocks of this class are such as have been produced by prolonged 
action of physical and chemical forces (heat, pressure, moisture, etc.) 
on both sedimentary and igneous rocks alike. The foliated types 
(gneiss, schist, etc.) represent an advanced stage of metamorphism 
on a large scale (regional metamorphism), and the peculiar schistose 
or foliated structure is due to the more or less parallel arrangement 
of their mineral components. The non-foliated types (quartzite, 
marble, slate, etc.) have resulted from the alteration of sedimentary 
rocks without materially affecting the structure and chemical com- 
position of the original material. 

"Rocks formed by contact metamorphism and hydration, such as 
hornfels, pyroxene marble, serpentine, serpen tineous limestone, etc., 
are of great interest from a petrographical standpoint, but are rarely 
of importance as road materials. 

"The color of metamorphic rocks varies between gray and white 
of the purer marbles and quartzites to dark gray and green of the 
gneisses, schists, and amphibolites. The green varieties are com- 
monly known as greenstones, or greenstone schists." 

1 G. P. Merrill's " Rocks, Rock Weathering, and Soils," 1897, pp. 104-114. 



128 MATERIALS 

Interpretation of Tests. 

It has been found impractical to specify definite qualities of stone 
for use in macadam highways. Economy and practical engineering 
demand that all available sources be considered. Tests are made to 
determine the relative qualities of stone from these different sources 
and the results used as a guide for selection. 

In the work of the New York State Highway Commission all tests 
are tabulated geographically, using a county as a unit. Table Nos. 
22 and 23 are compiled from the records of this department. It 
will be noted that comparisons are made in different classifications 
only, as it is considered that conclusions should not be drawn from 
a comparison of tests procured from materials having different origins 
and composed of different minerals. 

For the purpose of ready comparison, there has been introduced 
a figure known as the "weighted value." (See last column Tables 
22 and 23.) This is computed by giving relative weights of three to 
the French coefficient, two to the hardness, one to the toughness 
values and adding the three together. These relative weights were 
determined from a consideration of the amount of material used in 
the different tests and the personal equation in running them. 

By consulting these tables the available rocks of different classi- 
fications in various sections throughout New York State can be 
determined readily, and as new tests are completed they are compared 
with good average material from that section. 

Conclusions. 

Trap (diabase), granite, gneiss, quartzite, sandstone and limestone 
are the most common rocks and when found in a good state of preser- 
vation make good surfacing materials. 

As generally found, trap is uniform in hardness and toughness, 
making an excellent material for use in top course. 

Granite and gneiss, where they occur with hornblende replacing 
a large percentage of the quartz, make an excellent surfacing stone. 

Quartzites when found in good state of preservation are hard and 
tough. They should not be confused with crystalline quartz which 
is hard but brittle. 

Sandstones are extremely variable and only the better varieties 
should be used. 

Limestones range from the fine grained dense products which are 
hard and tough to the coarse grained soft products which are not 
suitable for surfacing. 

Screenings. 

Screenings act as a filler and binder for waterbound macadam and 
as a partial filler for bituminous macadam. For use in waterbound 
construction the main mineral constituent is the most essential feature 
to be considered as this must be a material that will form a binder 
and "puddle" readily when subjected to the action of a road roller 
and water. 



VITRIFIED BRICK 129 

Limestone screenings have proved the most efficient as a binder in 
waterbound construction, although trap and some other igneous 
rocks can be bound with their own dust by repeated puddling. 
Screenings consisting mainly of quartz have never been used success- 
fully in waterbound construction except by the addition of some lime- 
stone screenings. The use of a percentage of clay or loam as a 
binder is not advisable except where the cost of limestone screenings 
would be prohibitive. 

Laboratory methods for testing the cementing power of rock 
powders are available but the results obtained are erratic and unde- 
pendable. 

In plain waterbound roads it is often necessary to mix some lime- 
stone screenings, fine sandy loam, or even a small percentage of 
clay loam with trap, granite, sandstone, quartzite, or gneiss screenings 
to get a good bond and prevent raveling in dry weather. 

3. Bottom Course Macadam Stone 

As the bottom stone simply spreads the wheel loads transmitted 
through the top course and is not directly subjected to the traffic 
action, almost any stone that breaks into cubical irregular shapes 
that will not air or water slake and that is hard enough to stand the 
action of the roller during construction will be satisfactory. 

Any of the materials listed above in Table No. 24 except shale and 
slate can be used, provided that they are not rotten from long ex- 
posure in the air. The different available varieties are usually tested 
in the same manner as for top stone in order to pick the best. 

4. Fillers 

Fillers are used in the bottom course to fill the voids between the 
crushed stone and to prevent rocking or sidewise movement of the 
larger pieces. 

They should be easy to manipulate in placing, should not soften 
when wet, or draw water up from the subgrade by capillary action. 
The materials most used are 
Coarse sandy loam 
Coarse sand 

Gravel with large excess of fine material 
Stone screenings 
The fitness of the material can be determined by inspection and 
by wetting a handful; if it gets sticky or works into a soft mud it 
should not be used. 

5. Vitrified Brick 

Bricks must withstand the same destructive agencies as described 
for top stone. They must be uniform in size, tough, hard, dense, 
evenly burned, and, on account of their peculiar shape, must have a 
high resistance against rupture. These properties are tested by the 
standard methods adopted by the American Brick Manufacturers' 
Association, as described in the New York State specifications on 
page 390. 



130 MATERIALS 

It should be understood that bricks suitable for paving are manu- 
factured in a different way and of different materials than ordinary 
building bricks. 

"The materials for molding any paving brick must be of a peculiar 
character which will not melt and flow when exposed to an intense 
heat for a number of days but will gradually fuse and form vitreous 
combinations throughout while still retaining its form. 

"The resulting brick must be a uniform block of dense texture in 
which the original stratification and granulation of the clay has been 
wholly lost by fusion which has stopped just short of melting the 
clay and forming glass. 

"The clay while fusing must shrink equally throughout, thus 
causing the brick to be without laminations or of any exterior vitrified ' 
crust differing from the interior." L 

The great majority of paving brick are made in Ohio, Illinois, 
Indiana, Pennsylvania, West Virginia, and New York. They are 
classed as shale or fire-clay brick. 



6. Bituminous Binders 

The subject of bitumens is an intricate one and the reader is re- 
ferred to the works of Clifford Richardson, Prevost Hubbard, and 
others, for detailed information, as a book of this character can give 
only an outline. 

There are a number of dust preventives and road binders on the 
market which depend for their effectiveness on a bituminous binding 
base. The term bitumen is applied to a great many substances. 
Hubbard arbitrarily defines bitumens as "consisting of a mixture of 
native or pyrogenetic hydrocarbons and their derivatives, which 
may be gaseous, liquid, a viscous liquid, or solid, but if solid melting 
more or less readily upon the application of heat, and soluble in 
chloroform, carbon bisulphide, and similar solvents." 2 

The bitumens may be classified as native and artificial. The 
native bituminous materials, that are used in road work, are the 
asphaltic and semi-asphaltic oils (dust layers), Malthas (the binding 
base of Rock Asphalts), Trinidad, Bermudez California, and Cuba 
asphalts, Gilsonite, and Grahamite (which, however, are too brittle 
in their natural state and require fluxing with a suitable residual oil 
before they can be used as binders). The natural asphalts are 
refined to remove water and any objectionable amount of impurities 
by heating until the gases are driven off, skimming the vegetable 
matter which rises to the surface, and removing the mineral constit- 
uents which fall to the bottom. 

The artificial bituminous materials are derived by the destructive 
distillation of coal, or by fractional distillation of crude coal tars, 
or the native petroleum oils. They comprise the crude coal and 
water gas tars, the refined tars, the residual oils and semi-solid binders 
derived from the petroleum oils. They vary greatly in consistency 
and binding power. 

1 Judson's " Roads and Pavements," page 87. 

2 "Dust Preventives and Road Binders." John Wiley & Sons. 






BITUMINOUS BINDERS 



131 



The following material is briefed from Bulletin No. 34, United 
States Office of Public Roads: The light oils and tars have a relative 
small percentage of bituminous base and are effective only so long 
as it retains its binding power; the more permanent binders contain a 
larger percentage of bitumen; these are the heavy oils and semi-solids. 

Artificial Bitumens. 

Crude Tars. — Coke ovens and gas plants produce most of the coal 
tars in use. These tars contain various complex combinations of 
carbon, hydrogen, and oxygen and small amounts of nitrogen and 
sulphur. They vary in composition according to the material from 
which they are made and the temperature at which they are distilled. 
The percentage of free carbon ranges from 5 per cent to 35 per cent, 
and the bitumen from 60 per cent to 95 per cent, depending on the 
temperature of manufacture. Tars produced at high temperatures 
contain free carbon in excess which weakens their binding power; 
they, also, contain a large amount of anthracine and naphthalene, 
two useless materials from the standpoint of road w r ork. Tars 
produced at low temperatures are to be preferred. Coke tar is low 
temperature tar; gas tar is high temperature tar. 

Refined Tars. — Much of the road tar is refined tar — that is, it 
has been subjected to fractional distillation to remove the valuable 
volatile compounds. The residuum from this process is a thick 
viscous material known as coal-tar pitch, and if the crude tar from 
which it is obtained was produced at a low temperature it is nearly 
pure bitumen; the dead oils obtained from the distillation are of 
little value and are often run back into the pitch, which makes it 
liquid when cold. The following table gives the approximate com- 
position of water-gas tar, crude coal-tar, and refined tar. 

Table 25. Specific Gravity and Composition oe Tap Products 
Table from Bulletin No. 34 United States Office of Public Roads 



Kind of Tar 


Specific 
Gravity 


Ammo- 
niacal 
Water 


Total 
Light Oils 
to 170 C. 


Total 

Dead Oils 

i7o°27o°C. 


Residue 
. (by 
Difference) 


Water-gas tar . . . 
Crude coal tar . . 
Refined coal tar . 


1. 04 1 
1. 2IO 
1. 177 


% 

2.0 
O.O 


% 

021.6 

dij.2 

612.8 


% 
652.O 
£26. 
£47-6 


% 

C24.O 

/S4-8 
/39-6 



a Distillate mostly liquid. 

b Distillate all liquid. 

c Pitch very brittle. 

d Distillate mostly solid. 



e Distillate one-half solid. 
/ Pitch hard and brittle. 
g Distillate one-third solid. 



Table 25 a gives a more up-to-date analysis of the coal tars on the 
market. 

The tests and detailed requirements for light, medium, and heavy 
bitumens are given in specifications, page 377. 

If the tar is used as a temporary dust-layer only, it should be a 
low- temperature, dehydrated tar, liquid when cold. If used as a 



13 



MATERIALS 



Table 25 a. Circular No. 97, U. S. Office of Public Roads 

Analysis of crude coke-oven tars produced in the United States and Canada. 



Serial 
No. 



5126 
5123 

5124 

5i37 

5121 

5125 

5128 
5200 

5189 

5160 

5074 

5081 

5005 
5083 

5159 

5107 
5086 
5078 
5087 

5109 

5122 
5188 
5404 

5I08 



5127 



5089 



General Information 



Company and location 



Solvay Process Co., Syracuse, N.Y 

Semet-Solvay Co., Pennsylvania Steel 

Co., Steelton, Pa 

Semet-Solvay Co. National Tube Co., 

Ben wood, W.Va 

Semet-Solvay Co., Milwaukee Coke & 

Gas Co., Milwaukee, Wis 

Semet-Solvay Co. Pennsylvania Steel 

Co., Lebanon, Pa 

By-Products Coke Corporation, South 

Chicago, 111 

Semet-Solvay Co., Detroit, Mich 

Semet-Solvay Co., Empire Coke Co., 

Geneva, N.Y. . 

Semet-Solvay Co., Dunbar Furnace Co., 

Dunbar, Pa 

Semet-Solvay Co., Central Iron & Coal 

Co., Tuscaloosa, Ala 

Philadelphia Suburban Gas & Electric 

Co., Chester, Pa 



Type of 
Oven 



Semet-Solvay 



Semet-Solvay Co., Ensley, Ala 

The X. E. Gas & Coke Co.. Everett, Mass 
Lackawanna Steel Co., Lackawanna Iron 

& Steel Co., Lebanon, Pa 

Dominion Tar & Chemical Co., Sydney. 

Xova Scotia 



Hamilton Otto Coke Co., Hamilton, Ohio. 
Carnegie Steel Co., South Sharon, Pa.. . 
Maryland Steel Co., Sparrows Point, Md. 
Citizens' Gas Co., Indianapolis, Ind 



Pittsburg Gas & Coke Co., The United 
Coke & Gas Co., Glassport, Pa 



Zenith Furnace Co., Duluth, Minn. 



Otto Hoffman 



United Otto 



Maximum 

temperature 
of firing 
retorts 



1650-1450 C. 
1050-1450 C. 
1050-1450 C. 
1050-1450° C. 
1050-1450 C. 



io5o-i45o v 
1050-1450' 



Illinois Steel Co., Joliet, 111.. 

Illinois Steel Co., Indiana 
Gary, Ind 



Steel Co. 



Camden Coke Co., Camden, N.J. 



Cambria Steel Co., Johnstown, Pa. 



Lackawanna Steel Co., Buffalo, N.Y. 



Koppers 



Otto Hoff- 
man 

United 
Otto 

Otto Hoff- 
man 

United 
Otto 

United 
Otto 

Roth berg 



1050- 1450° C. 
1050-1450° C. 

I2 5 0°C. 

1050° C. 

i25o°C. 

^icx^C. 
( 1000° C. 
hi8oo°F.) 

( 2 ) 
(iiii°C. 
( (2000° F.) 
( 1666° C. 
H30oo°F.) 
J 1333° C. 
( (2400 F.) 

( 1222° C. 

\ (2200 F.) 

{ ( 2 ) 

I I222-I277°C. 
\ 2 2OO-230O°F. 

I 1444° C. 
i( 2 6oo°F.) 

noo°C. 

I 1000 C. 
t(i8oo°F.) 

I 1222° C. 

( (2200° F.) 

(IIII°C. 

( (2000° F.) 
(iiii°C. 
( (2000° F.) 
' 1000° C. 
(1800'-' F.) 
ooo° C. 
800° F.) 






CIRCULAR ON PUBLIC ROADS 
Table 25 a — Continued 



*33 



Answers to Questions 


Examination 














Per 


Maximum 
temperature 


Specific gravity 


Per cent of 
free carbon 
in tar 


Specific 

gravity 


Per 

cent 


Per 

cent 


cent 
soluble 
in CS2, 
includ- 
ing 


to which coal 


of crude tar 


of tar, 


of free 


of 


is brought 




25 C. 


carbon 


ash 














H2O 


050-1150 C. 


1. 12-1. 21 


3-12 


1. 195 


7.76 


0.12 


92.12 


g5o-ii50° C. 


1. 12-1. 21 


3-12 


1.206 


S-77 


•07 


91.16 


050-1150 C. 


1. 12-1. 21 


3-12 


1. 176 


7-14 


.04 


92.82 


050-1150 C. 


1. 12-1. 21 


3-12 


1. 168 


6.10 


•05 


93-85 


050-1150 C. 


1. 12-1. 21 


3-12 


1. 1/3 


4-71 


.06 


95-23 


950-1150° C. 


1. 12-1. 21 


3-12 


1. 191 


7-49 


•03 


92.48 


950-1150° C. 


1. 12-1. 21 


3-12 


1. 169 


6.56 


.11 


93-33 


950-1150 C. 


1. 12-1. 21 


3-12 


I-I59 


6.07 


.08 


93-85 


950-1150 C. 


1. 12-1. 21 


3-12 


1. 181 


8.85 


.02 


9I-I3 


ii5o°C. 


1. 17 


5.72 


I-I59 


5-05 


.02 


94-93 


1000 C. 


( 1. 16 

I (20°C) 


— 


1. 141 


3-96 


•05 


95-99 


1150 c. 


{ I- 17 

I (i5° C.) 


8 


1. 175 


6.90 


.06 


93-04 


1 I200°C. 


1. 17 


8-10 


1. 160 


43-94 


.00 


86.06 


1000 C. ) 
(i8oo°F.)J 


1. 10 


16-24 


1. 214 


14-05 


• 13 


85.82 


m 


1. 170 


10-15 


1 -H3 


10.81 


•05 


89.14 ^ 


iin° c. 
(2000 F.) 


1. 14 


6 16.0 


1. 160 


8.37 


.06 


91-57 


1444° C. 
(2600° F.) 


, 2 


7. 09-10.64 


1. 191 


7.89 


•03 


92.08 


1222° C. 

, (2200 F.) 


3 1. 19 


3 8-IO 


1. 179 


8.49 


•03 


91.48 


1222° C. 

(2200 F.) 


J I. I4-I. 15 

f (50° F.) 


4-5 
1 


1. 133 


5-21 


.07 


94.72 


( 2 ) 


< 1.207 
I io° C. 


r 16.59 


1. 176 


10.53 


.04 


89.43 


( 2 ) 


( 2 ) 


(*) 


1195 


12.18 


•05 


87.77 


1388 C 

(2500 F.) 


| 1. 16-1. 20 


12-15 


1. 171 


3.89 


.06 


96.05 


( 880-950 

X c. 


4 1. 174 
1. 169 


4-35 


1. 169 


2.73 


.04 


97.23 


833° c. 


1 












(i5oo°F.) 
1055° c. 


1 1. 20-1. 30 
5 (1. 221) 


7-9 
5 (7-3) 


J 1. 182 


11.30 


.06 


88.64 


(i900°F.) 


J 












l ini°C 














(2000 F.) 


1 












l iin°C. 


} 1. 12 


1 15 


1. 211 


12.40 


.16 


87-44 


(2000 F.) 














iooo C. 


1 












(1800 F.) 
icoo° c. 


j> 1. 16 


16-24 


1. 210 


16.80 


.00 


83.20 


(1800 F.) 


i 










1 



134 



MATERIALS 

Table 25 a — Continued 



Serial 
No. 



5126 
5123 

5124 

5137 

5121 

512S 

5128 
5200 

5189 
5160 

5074 

5081 
5095 

5083 

5159 

5107 
5086 
5078 
5087 
5109 

5122 
5188 
5404 

5I08 
5127 
5089 



Company and Location 



Examination, Public Roads 



Solvay Process Co., Syracuse, N.Y. .... 
Semet-Solvay Co., Pennsylvania Steel 

Co., Steelton, Pa . . • • • • • 

Semet-Solvay Co., National Tube Co., 

Benwood, W.Va • 

Semet-Solvay Co., Milwaukee Coke & 

Gas Co., Milwaukee, Wis 

Semet-Solvay Co., Pennsylvania Steel 

Co., Lebanon, Pa • • • • 

By- Products Coke Corporation, South 

Chicago, 111 ••••:• ■■:■:•' 

Semet-Solvay Co., Detroit, Mich. 
Semet-Solvay Co., Empire Coke Co., 

Geneva, N.Y • • • ■ 

Semet-Solvay Co., Dunbar Furnace Co., 

Dunbar, Pa • • - ■ ;• • • •• 

Semet-Solvay Co., Central Iron & Coal 

Co., Tuscaloosa, Ala ... 

Philadelphia Suburban Gas & Electric 

Co., Chester, Pa 

Semet-Solvay Co., Ensley , Ala . . . 

The New England Gas & Coke Co., 

Everett, Mass • 

Lackawanna Steel Co., Lackawanna 

Iron & Steel Co., Lebanon, Pa 

Dominion Tar & Chemical Co., Sydney, 

Nova Scotia • • ••••••••• 

Hamilton Otto Coke Co., Hamilton, O.. . 
Carnegie Steel Co., South Sharon, Pa . 
Maryland Steel Co., Sparrows Point, Md. 
Citizens' Gas Co., Indianapolis, Ind.. . . . 
Pittsburg Gas & Coke Co., The United 

Coke & Gas Co., Glassport, Pa 

Zenith Furnace Co., Duluth, Minn 

Illinois Steel Co., Joliet, 111. ............ 

Illinois Steel Co., Indiana Steel Co., 

Gary,. Ind A'A'^'i 

Camden Coke Co., Camden, N.J. 

Cambria Steel Co,, Johnstown, Pa . . . 
Lackawanna Steel Co., Buffalo, N.Y 



Distillation results 



Water 



^ o 



1. a 
1.0 
1.1 
1.8 
.6 

(*) 

6.9 

4.0 

2.0 

3-2 

2.3 
3-3 

2.2 
5-4 

3-2 

3-4 
1.0 



^1 



0.8 

.8 
1.0 
1. 5 

•5 

( 7 ) 
5-9 

3-4 

1.7 

2.8 

2.0 
2.8 

2.0 

4.4 

2.8 

1.0 



1.6 


13 


1.2 


I.I 


I.I 


I.O 


3-6 


3.0 


1.9 


1.6 


3-5 


3.0 


2.2 


1.9 


IO.I 


8.3 


2.7 


2.2 



References to Table 25 a 



Light oils up 
to no° C. 



^ 



p > 



*o. 3 

• 4 
1.9 
1.4 
1.6 

• 4 

9 2.8 

2.6 
i-7 

2.4 

2.3 

8 1.4 

2-9 

9 1.4 

1.9 
3-i 

9 1.6 

1.3 

I.I 

I.I 

1.7 

9 1.7 
9 1.3 

1.8 

9 3-i 
10 c 



1 Approximately. 

2 No information. . , 

3 Varies with coal. Coal with 28 per 
cent of volatile matter used. 

4 With H2O. 

5 At present. 

6 Variable. 
i Trace. 






0.3 

.3 

1.5 

1.2 

1-3 

•3 
2-3 

2.1 

1.4 

1.9 

1.3 

1.0 

2.3 
1.4 

1-5 

2-5 
1.2 



•9 
9 
1.3 
1.2 
1.0 
1.4 
2-3 
•3 



s Trace of solids. 
9 Distillate, solid. 

10 Distillate, one-fourth solid. 

11 Distillate, nine-tenths solid. 

12 Distillate, three-fourths solid. 

13 Distillate, eight-ninths solid. 
M Distillate, one-half solid. 



CIRCULAR ON PUBLIC ROADS 



135 



Table 25 a — Continued 







Examination, 


Office of Public Roads 






Distillation results 


Middle oils, 
iio°-i7o C. 


Heavy 

i7o°-2 


oils, 
70 C. 


Heavy oils, 
2 7 o -3i5° C. 


Pitch 

1 


Serial 
No. 


i* 


&3 


• -° 


^ fcjD 




■4-1 

xi # y> 

vO°5 


-° 


Xi ,&> 


0.8 


0.7 


»I3-I 


II-5 


1 9 8.2 


7-3 


25 76.6 


79-1 


5126 


9 2.0 


1.7 


9 14.0 


12.3 


2 " 7.9 


6-9 


26 74.7 


77-6 


5123 


• 7 


.6 


14.9 


13-2 


21 11. 9 


10.6 


27 69.5 


73-1 


5124 


.8 


.6 


13 2 1. 1 


18.9 


20 5-5 


4.9 


25 69.4 


72.5 


5137 


.8 


.6 


14 17.5 


15-5 


19 9-4 


8.4 


25 70.I 


73.7 


5121 


12 1.1 

* -4 


•9 
•3 


15 23.6 
11 I4.6 


20.7 
13.0 


9 9.8 
8 6.9 


8.9 

5, 


27 65.I 
26 68.4 


68.9 
72.O 


5125 
5128 


.6 


•5 


io I7 .6 


15-5 


22 11.4 


10.4 


27 63.8 


67.7 


5200 


.2 


.2 


i° 20.0 


17.8 


21 6.5 


5-7 


25 69.6 


73-1 


5189 


•3 


•3 


18.6 


16.3 


i0 7-5 


6.8 


27 68.O 


7i. 5 


5 160 


1.2 

.2 


.8 
.2 


22.8 
17 16.5 


19-5 
14.1 


15 13.6 

14 9-3 


12.5 
8.2 


57-8 
27 69.3 


62.0 
73-2 


5074 
5081 


.6 


•5 


23.5 


20.4 


17 15.6 


14.4 


27 55-2 


59-7 


5095 


9 .1 


.1 


11 13-0 


10.9 


21 9.4 


8.1 


25 7O.7 


74-6 


5083 


.6 
• 7 

9 .6 


.6 
•4 


27.2 

27.9 

16 12. 1 


24.2 
24.4 
10.2 


19 7-3 
19 3-8 
19 11.0 


6.7 
3-5 
9-7 


27 59-8 

27 6l. I 
25 73-7 


63-5 
64.9 

77-5 


5159 

5io7 
5086 


- .6 


•4 


12 17.2 


151 


21 9.6 


8.5 


2869.7 


73-2 


5078 


1.4 
5 

•4 

9 .2 

9 -4 
.6 

p -3 
9 2.2 


i-3 

•4 
•3 
.2 

•3 
•5 
.2 

1.7 


23-9 
18 26.9 
11 18.1 
9 20.0 
9 20.6 
14 20.5 
9 7-1 
9 11. 7 


21.4 
23.6 

15-9 
18.0 
18.5 
18.2 
6.1 
9.9 


10 n.6 
I* 6.9 
19 12.5 

11 13.4 
9 7-1 

23 8.5 

12 7.4 

24 1 1.8 


10.4 

6-3 
11. 1 
12.0 

6-5 

7-5 

6.9 

10.2 


27 60.8 
27 63.5 
27 63.7 
26 62.8 
26 67.1 

2566.4 

26 72.O 

27 71. 1 


64.7 
67.6 
67.8 
66.3 
70.2 
70.1 
74-8 
75-o 


5087 
5109 
5122 
5188 
5404 
5108 
5127 
5089 



References to Table 25 a 



15 Distillate, two-thirds solid. 

16 Distillate, four-fifths solid. _ 

1 7 Distillate, seven-eighths solid. 

18 Distillate, one-ninth solid. 

1 9 Distillate, one-third solid. 

20 Distillate, one-sixth solid. 
»i Distillate, one-fifth solid. 



22 Distillate, two-fifths solid. 

23 Distillate, one-seventh solid. 

24 Distillate, three-fifths solid. 

25 Pitch, soft and sticky. 

26 Pitch, very soft and sticky. 

27 Pitch, hard and brittle. 

28 Pitch, plastic. 



136 



MATERIALS 



more permanent binder and applied hot, it should have a larger 
percentage of pitch, should contain no water, and be free from an 
excessive amount of free carbon. If used as a mastic in bituminous 
macadam, it should contain a high percentage of pitch and be free 
from the defects mentioned. 

Natural Bitumens and Artificial Residual Oils and Semi-Solids. 

Mineral oils can be classed as paraffin petroleums, mixed paraffin 
and asphaltic petroleums, and asphaltic petroleums. The relative 
value of oils as a source of supply for road materials depends on 
their percentage of asphaltic residue. The eastern oils found in 
New York, Pennsylvania, West Virginia, etc., are paraffin petro- 
leums; the western oils vary from light to heavy asphaltk petro- 
leums, and the southern oils have a mixed paraffin and asphaltic base. 

The crude petroleum is refined by fractional distillation to obtain 
its valuable products, such as kerosene, etc. The character of the 
residue depends, as for the tars, on the crude material and the method 
of manufacture; the operation known as "cracking," which is used 
to increase the yield of the inflammable oils, produces an excess of 
free carbon. 

Tlie paraffin petroleum residuums are soft and greasy and are not 
suitable for road work; they contain a large amount of the paraffin 
hydrocarbons and paraffin scale (crude paraffin) . 

The California petroleum residuums resemble asphalt, and if care- 
fully distilled without cracking should contain little or no free carbon. 
They are suited to road work. 

The Texas, or semi-asphaltic petroleums contain some paraffin 
hydrocarbons and about 1 per cent of paraffin scale. Residuums 
from these oils, if containing a relatively small amount of paraffin, 
can be successfully used. 

The tests and required properties of residuum bituminous binders 
used on the New York State roads in 19 14 are given in specifications, 
page 377. 

The following tables give a general idea of the relative character- 
istics of the crude petroleums and petroleum residuums. 

Table No. 26. Results of Tests oe Crude Petroleum 
Tables from Bulletin No. 34 United States Office of Public Roads 











4j 


+j 










9i 


oS 


a 






«3 +J 


.a 


-So 


• 5° 

&u3 


£o| 




« 

3 


Kinds of Oil 


'G > 




^° 3 

•rj offi 

^ 




*55 

<L> 






^ 


> 


> 


> 




Pennsylvania, paraffin. .. . 
Texas, semi-asphaltic .... 


0.801 
.904 


(a) 
43 


% 
47.3 


% 
58.0 


% 
68.0 


% 
632.0 


California, asphaltic ...... 


•939 


26 


20.0 


27.0 


49.0 
J42.7 


C51.0 

«57-3 







a Ordinary temperature 
b Soft 



c Quick flow 

d Volatility at 200' 



e Soft maltha; sticky 
7 hours. 



ADHESIVENESS 
RESULTS OF PETROLEUM RESIDUUM 



137 



Kinds of Oil 


"G > 


a 

'0 


Volatility at 

200° C. 

7 Hours 


u 

3 


a 

C/2 as 




Pennsylvania, paraffin. . . . 
Texas, semi-asphaltic .... 
California, asphaltic 


0.920 

•974 

1.006 


186 
214 
191 


% 
14.2 

6.2 
17-3 


<Z85.8 
093.8 

a82-7 


% 
II. O 

1-7 

O.O 


% 

3-o 
3-5 
6.0 



a Soft. 

Tests of Bitumens and their Significance. 

Bitumens for use as the cementing material in road construction 
may, according to their source and characteristics, be divided into 
the two general classes of asphalts and tars. 

The asphalts suitable for use as the cementing agent in road con- 
struction are produced either by. reducing asphaltic base petroleum 
to a suitable consistency by the distillation process or by softening 
the so-called solid asphalts to a suitable consistency by the addition 
of flux produced by the partial distillation of petroleum. 

The different grades, relative to consistency, of road oils are usually- 
produced by the partial reduction of asphaltic base petroleum. 

By the destructive distillation of bituminous coals or the " crack- 
ing" of petroleum oils during the carburetting process in the manu- 
facture of water gas, crude tars are produced. These crude tars are 
refined or reduced by distillation to a suitable consistency for use 
in road construction. 

Bitumens are used in road construction for the purpose of water- 
proofing the surface and adding to the mechanical bond of the min- 
eral aggregate by cementing together the finer particles of mineral 
matter, thus preventing their displacement under the action of traffic 
and retaining them in the road surface where they fill the inter- 
stices between the larger stone and bind them together. 

The desirable characteristics of bituminous material for road build- 
ing purposes are, first, Adhesiveness, second, Xon-SuseeptibiUty to 
changes in temperature, and third, Stability or "life." The chief 
object of bituminous material specifications is to make imperative 
these desirable qualities of the material. 

In connection with testing bituminous materials the thought 
should be kept in mind that the laboratory results obtained in the 
different tests are largely for comparative purposes. By this means 
new or but little used materials may be compared with materials 
which have proven satisfactory under service tests. Also laboratory 
results furnish an accurate means to specify the exact characteristics 
of the material desired for any given purpose. 

Adhesiveness. 

The adhesiveness of the material is provided for in specifications 
by suitable requirements of ductility and toughness. 



138 MATERIALS 

The ductility and toughness tests are made for the purpose of 
determining the adhesive and binding qualities of the material under 
different conditions of temperature. The ductility test is made by 
determining the distance a briquette of the material, having a stand- 
ard cross-section (1 sq. cm.) will draw out before breaking. Since 
temperature effects the results, a standard temperature of 77 degrees 
Fahrenheit, has been adopted generally for making this test. Expe- 
rience teaches that the greater the distance that a briquette of the 
material will stretch out before breaking the more sticky and adhesive 
the material. This test may be performed in a rough manner by 
pulling out a small roll of the material between the fingers. Material 
which will not pull out to a long thread before breaking is usually 
spoken of as "short." Such materials are not adhesive or sticky and 
it is extremely difficult to bind a road with them, even under the most 
favorable circumstances. 

As stated, the ductility test is usually made at a temperature of 77 
degrees Fahrenheit and thus measures the adhesiveness of the material 
at a rather high temperature. To obtain an indication of the char- 
acter of the material at a low temperature the Toughness test is made 
at a temperature of 32 degrees Fahrenheit. This test is performed 
by dropping a weight of 2 kilograms on a cylinder of the material 
if inches in diameter by if inches in height. The first height of the 
drop is usually from a distance of 5 cm. and is gradually increased 
until rupture of the cylinder occurs. A rough field test for toughness 
may be performed by noting whether a piece of the material will 
fracture under a sharp blow. If the temperature of the material 
is about 32 degrees Fahrenheit, the results will be more indicative 
of the character of the material. 

Bitumens which are brittle or which give a low toughness result, 
lose their binding value in cold weather and roads constructed by 
their use are apt to ravel and break up under traffic. 

Bitumens which give good ductility and toughness results under the 
methods outlined,- will give satisfactory results as the cementing 
medium when used in road construction provided the other construc- 
tion details have been properly followed out. 

In connection with the stickiness and adhesiveness of bitumens 
the fact should always be kept in mind that their purpose in road 
construction as cementing medium, is most effective when used with 
a hard, clean, dry mineral aggregate. As the departure from these 
qualities of the mineral aggregate is increased so also are increased the 
difficulties of getting a satisfactory road surface firmly bound together. 

Susceptibility to Changes in Temperature. 

The susceptibility to changes in temperature is shown by the rel- 
ative hardness as indicated by the penetration tests at different tem- 
peratures, as 32 degrees Fahrenheit, 77 degrees Fahrenheit and 115 
degrees Fahrenheit. 

The consistency of asphalts is referred to as the " penetration." 
The penetration test is made by measuring the distance in hundredths 
of a centimeter that a standard needle under a stated load, applied 



STABILITY 139 

for a stated time, will penetrate into it vertically. These variable 
factors are usually as follows: 

Needle — R. J. Roberts' Parabola " Sharps" No. 2. 
at 3 2 F. 200 gram weight, 1 minute, 
at 77 F. 100 gram weight, 5 seconds, 
at 1 1 5 F. 50 gram weight, 5 seconds. 

The material which is the most susceptible to changes in tempera- 
ture will show the greatest variation in penetration under varying 
conditions of temperature. Roads constructed by the use of mate- 
rials which are extremely susceptible to changes in temperature be- 
come soft in warm weather, mark easily, have a tendency to rut and 
become wavy. In cold weather this material becomes very hard 
and slippery and is apt to be brittle and become chipped from the 
road surface. 

In addition to the general qualities of bitumens which are shown 
by penetration tests, this test is used in specifications to define 
within narrow limits the consistency of the material. The consist- 
ency limits placed in specifications are governed by the climate and 
the type of construction to be followed, also the general size of the 
mineral aggregate to be used. When the penetration method of 
construction is followed it is necessary to use a relatively soft asphalt 
in order that it may be incorporated in the road surface. In the 
mixing types of construction a harder asphalt may be incorporated 
with the mineral aggregate. The use of a hard asphalt together with 
a graded mineral aggregate gives a dense wearing surface that does 
not readily become wavy under traffic. 

The information obtained by the penetration test is not readily 
checked in the field without the aid of laboratory apparatus, but as 
a general rule bitumens which are suitable for binders are plastic 
when "worked" in the hands. 

Stability. 

When the term "Stability" or "Life" is used in reference to bitu- 
mens it refers to the quality of the material by which it retains its 
characteristics, usually as defined by the specifications, over a long 
period of time. The laboratory tests which indicate this property 
are the evaporation test, the ratio of the penetration after evaporation 
to the original penetration, and the flash point. 

The heating or evaporation test, is made by placing 50 grams of 
the material in a flat bottomed dish 2 T 3 g inches in diameter by if 
inches in depth. This is placed in an oven maintained at a specified 
temperature, usually 325 degrees Fahrenheit for a period of 5 hours. 

This test may be considered as an accelerated test on the material. 
In a binder, the percentage lost by weight together with the resulting 
hardening as shown by the relative penetration, i. e., the ratio of the 
original penetration to the penetration after evaporation, are indica- 
tive of the "life" of the material. The less the evaporation loss and 
the less the hardening as shown by the relative penetration the greater 
will be the "life" of the material. 



140 MATERIALS 

In an oil used for surface application the evaporation test shows the 
presence and quantity of light oils. This is indicative of the time 
required for the oil to "set up" after application to the road surface; 
the evaporation from the large surface area of the oil as applied to 
the road being roughly comparable with evaporation from the smallest 
surface area of the oil exposed at the higher temperature at which the 
test is made. 

The open flash test is made by heating at the rate of about 10 
degrees Fahrenheit per minute, a small quantity of the material, 
approximately 40 grams in a dish of approximately the same size as 
the dish used for the penetration tests, 2^ inches in diameter by if 
inches in depth. A small flame from a capillary tube is passed over 
the surface of the oil at each increase of 5 degrees in temperature. 

A slight "puff" or explosion indicates the flash point has been 
reached. The presence of light oils or distillates is indicated by a low 
flash point. The flash point together with the evaporation results 
give an indication as to the methods and materials used in the man- 
ufacture of the bitumen which is being tested. 

Unless "cut-back" materials are being tested, in which an exceed- 
ingly light distillate as naphtha or benzole has been used as the "cut- 
back" agent, considerable "smoke" will be given off from the sample 
before the flash point is reached. This feature should be kept in 
mind when material is being heated for application in the held. 
Material should never be heated in the field to a point when it smokes 
profusely, for at such a temperature the material is being "burned" 
or hardened to such an extent that it loses its adhesiveness and 
becomes brittle when cold, thus failing to become a binding or cement- 
ing agent which binds the mineral aggregate of the road together. 

The same "burning" effect on the material is produced by keeping 
it at a temperature below the "smoking point" for a long period, 
(several hours) as would be produced at a higher temperature for a 
shorter period of time. This important feature should always be 
kept in mind when heating material for application in the field. 

Such tests as those for water, specific gravity, purity, paraffine, 
etc. are usually placed in specifications in addition to the tests which 
govern adhesiveness, non-susceptibility and stability for the purpose 
of identification of materials used, methods of manufacture, degree 
of refinement and care used in refining. 

The presence of water in bituminous materials causes frothing 
when heated to a temperature of about 212 degrees Fahrenheit. In 
addition to the difficulty experienced in heating material containing 
water, due to the frothing, an even application or distribution to the 
road of such material is extremely difficult, due to the presence of 
the froth which is apt to be applied rather than the liquid bitumen. 

Tests for specific gravity, purity, paraffine, etc. require laboratory 
apparatus to get results which indicate qualities of the material. The 
information obtained by these tests cannot be obtained by field tests. 

If we assume that a suitable bitumen has been specified and ob- 
tained for construction work in which a bitumen is to serve as the 
cementing material, the results obtained, relative to the bitumen, 
will depend upon: 



CEMENT 141 

1. Not over-heating (by high temperature or long time) the 
bitumen. 

2. The use of hard, clean, dry stone. 

Grading of the mineral aggregate to reduce the voids and obtain 
greater density. 

4. Thorough and uniform incorporation of the bitumen with the 
mineral aggregate. 

5. Maximum consolidation, by rolling when laid. 

When bituminous materials which may be applied cold are to be 
applied to a road surface, that surface should first be put in good 
condition. Surface application treatment is for the purpose of 
preserving a road which is in good condition and not repairing an un- 
even road. We do not repair a house by painting it; rather we repair 
the house and then paint it, in order that it may remain in good con- 
dition. An attempt to build up a road wearing surface by the use 
of bitumens which may be applied cold usually results in a surface 
which is easily marked, ruts and pushes into waves. 

Cement. 

There are five different classes of cement, Portland, Natural, 
Pozzolan, Iron Ore, and Magnesia cements. Of these the Portland 
or Natural is usually specified. 

Portland cement is the term applied to the finely pulverized product 
resulting from the calcination to incipient fusion of an intimate 
mixture of properly proportioned argillaceous and calcareous ma- 
terials, and to which no addition greater than 3 per cent has been 
made subsequent to calcination. (Amer. Soc. Testing Materials 
1915 — page 353.) 

Natural cement is the term applied to the finely pulverized product 
resulting from the calcination of an argillaceous limestone at a tem- 
perature only sufficient to drive off the carbonic acid gas. (Amer. 
Soc. Testing Materials 191 5 — p. 352.) 

Portland cements are usually heavier, stronger, slower testing, 
and more uniform than the natural cements and are generally used 
for road structures, such as culverts, retaining walls, etc.; Portland 
cement is practically the only cement used to any extent in the 
United States at the present time. The few manufacturers of natural 
cement who were retaining a hold on the market some few years back 
when the production of Portland cement was expensive, are finding 
it difficult to compete With this latter product at its present price 
and quality. 

The following is the standard specification for Portland cement 
as adopted by the American Society of Civil Engineers and the Amer- 
ican Society for Testing Materials: 

First: Specific gravity. The specific gravity of cement shall not be less than 
3.10. Should the test of cement as received fall below this requirement, a second 
test may be made upon a sample ignited at a low red heat. The loss in weight of 
the ignited cement shall not exceed 4 per cent. 

Second : Fineness. It shall leave by weight a residue of not more than 8 per 
cent on the number 100. and not more than 25 per cent on the number 200 sieve. 

Third: Time of Setting. It shall not develop initial set in less than thirty min- 
utes; and must develop hard set in not less than one hour, nor more than ten hours. 



142 MATERIALS 

Fourth: Tensile Strength. The minimum requirements for tensile strength for 
briquettes one square inch in cross section shall be as follows and the cement shall 
show no retrogression in strength within the periods specified: 

Age Neat Cement Strength 

24 hours in moist air 175 lbs. 

7 days (1 day in moist air, 6 days in water) 500 " 
28 " (1 " " " , 27 " " " ) 600 " 

One Part Cement — Three Parts Standard Ottawa Sand 
7 days (1 day in moist air, 6 days in water) 200 lbs. 
28 " (1 " " " , 27 " " " ) 275 " 

Fifth: Constancy of Volume. Pats of neat cement about three inches in di- 
ameter, one-half inch thick at the center, and tapering to a thin edge, shall be kept in 
moist air for a period of twenty -four hours. 

(a) A pat is then kept in air at normal temperature and observed at intervals 
for at least 28 days. 

(b) Another pat is kept in water maintained as near 70 degrees F. as practicable, 
and observed at intervals for at least 28 days. 

(c) A third pat is exposed in any convenient way in an atmosphere of steam, above 
boiling water, in a loosely closed vessel for five hours. 

These pats, to satisfactorily pass the requirements, shall remain firm and hard, 
and show no signs of distortion, checking, cracking or disintegrating. 

Sixth: Chemical Composition. The cement shall not contain more than 1.7.5. 
per cent of anhydrous sulphuric acid (SO3), nor more than 4 per cent of magnesia 
(MgO). 

The methods used in testing cement are standardized in detail 
and can be obtained in the "Year Book" of 1913, published by the 
American Society for Testing Materials or Committee report on 
" Uniform Tests of Cement" of the American Society of Civil 
Engineers 191 2. 

Concrete Materials 
Fine Aggregate. 

Fine aggregate for use in concrete should consist of sand free from 
any deleterious matter. Any sand which shows a coating on the 
grains should not be used until satisfactorily cleansed by washing. 

The following tests are made on sand to determine its suitability 
for use in different classes of concrete: 

1 st. Gradation. 

2nd. Percentage of voids. 

3rd. Percentage of loam or silt. 

4th. Compressive or tensile strength in cement mortar. 

In order to secure suitable qualities, minimum requirements 
determined from the above tests should be definitely specified. 

The following specifications are now being used by Highway 
Departments in several of the States: 

Sand for use in Portland cement concrete roads shall be of the 
following gradation: 100 per cent shall pass a \" screen, not more 
than 20 per cent shall pass a No. 50 sieve and not more than 6 per 
cent shall pass a No. 100 sieve. # Sand may be rejected for this class 
if it contains more than 5 per cent of loam and silt. Mortar in the 
proportion of one part of cement to three parts of the sand, shall 
develop a compressive or tensile strength at least equal to the strength 
of a similar mortar of the same are, composed of the same cement 
and standard Ottawa sand. 



COARSE AGGREGATE 143 

Sand for use in foundations, culverts, retaining walls, etc. shall 
not contain more than 8 per cent of loam and silt. Mortar in the 
proportion of one part of cement to three parts of the sand, when 
tested shall develop a compressive or tensile strength of at least 80 
per cent of the strength of a similar mortar of the same age, composed 
of the same cement and standard Ottawa sand. 

Screenings if substituted wholly or in part for the above sand, 
should meet the following requirements: 

They shall be free from dust coating or other dirt. 100 per cent 
shall pass a J" screen and not more than 6 per cent shall pass a No. 
100 sieve. Mortar in the proportions of three parts of the screenings 
or mixed screenings and sand, with one part of cement shall develop 
a strength equal to a sand for which it is to be substituted. 

The best and safest way in the selection of a concrete sand is to 
have a fair representative sample from the deposit listed. After 
this is found to meet the requirements, it is necessary to have con- 
stant and careful field inspections and tests made as the deposit is 
worked . 

The use of screenings is not advisable on any concrete work, 
except where a good grade of sand is not available. When used the 
product must be constantly inspected and tested as it is likely to 
vary to a considerable degree. Screenings from the softer limestones 
should not be used as the fine material is apt to "ball" in the mixer. 

Sand used for grout in brick and stone block pavement must be 
fine enough to ensure it getting between the joints of the block, but 
an excessively fine sand should be avoided as it weakens the grout. 
Some states and many municipalities require the grout sand to pass 
a No. 20 sieve and not more than 30 per cent pass a No. 100 sieve. 
Such sand should not contain more than 5 per cent of loam and silt. 

Coarse Aggregate. 

Coarse aggregate for use in concrete should be of hard durable stone 
or gravel, free from coating of any kind. For use in concrete pave- 
ment, stone and gravel should be hard, tough and absolutely clean. 
For use in culverts, retaining walls, etc. stone and gravel should be 
of sound, unweathered material, clean and free from coating. It 
should not contain more than 10 per cent of soft stone or shale. 
Gravel containing a large percentage of thin flat stone should not be 
used. 

For reinforced concrete the size of the stone is usually \" to 1" 
in order to facilitate the compacting of the concrete between the 
reinforcing bars or mesh. For plain concrete a mixed size is used 
ranging from \" to 3I"; a scientifically graded stone reduces the 
amount of mortar required, but the structures in road work are so 
small that it does not pay to attempt to reduce the voids in this 
manner and the size that is available is used, varying the proportions 
of mortar to get a dense product. 



PART II 

THE PRACTICE OF THE SURVEY, DESIGN, 
ESTIMATES, AND CONSTRUCTION 

CHAPTER VIII 



THE SURVEY 

As the survey furnishes the information for the design, it must 
be carefully made in regard to the essential features. These are 
alignment, levels and cross-sections, drainage, information con- 
cerning foundation soils, available stone supply, available sand, 
gravel, filler, etc.; direction and amount of traffic, railroad un- 
loading points, the location of possible new sidings, and such 
topography along the road as will have a bearing on the design. 
The survey should be made not more than a year before construc- 
tion starts and during the open season, as a snowfall of any depth 
makes the work unreliable and only fit for a rough estimate. 
When contracts based on winter surveys are awarded it is always 
necessary to take new cross sections to insure a fair estimate of 
the excavation. 

A party of five men is a well-balanced force for surveys of this 
character. 



Force 

Engineer 
Instrument man 
Three helpers 



Equipment 

Transit 
Level 

2 ioo' steel tapes 

3 50' metallic tapes 
3 pickets 

2 level rods 

Pocket compass 

Hatchet 

Sledge 

Axe 

Keel 



Stationery 

Reports 
Pencils 
Notebook 
U.S. G. S. map. 

Stakes 
For preliminary survey 
no stakes per mile 
For construction 
220 stakes per mile 



The Center Line. The placing of the center-line hubs 
(transit points) requires good judgment and should be done by 
the chief of the party. In locating them he considers the prin- 
ciples of alignment discussed on page 17. The hubs are placed at 
tangent intersections and sometimes at the P. C.'s and P. T.'s of 
curves and are referenced to at least three permanent points 

144 



LEVELS AND CROSS-SECTIONS 



145 



that will not be disturbed during construction. (See sample 
page of notes, Fig. 43.) 



P.I. Sta.d+26.4 



l s SAngle3°20'\ 
2 d - v 6°40'V 



P.I. Stu. 0+00 



Deflection 
Angle 



1 = 3°20' 



Curve V 
Data 



<y 



~o 



■o- 



I5"0ak 






-o 



Te lea raph Pole 
#4522 



°r. 



& 



0- 



^> 



y< 



i Cor. Post 
in Fen c 



tf 



'<&t6L 



Barn 



!2"MapleTree 



*£ 



4 



& 



^o 15 'Oak 



Fig. 43. — Alignment Notes 

The deflection angles at the tangent intersections are usually 
read to the nearest minute, taking a double angle to avoid mis- 
takes; the magnetic bearing of each course is recorded. For all 
deflection angles over 4 it is good practice to figure and run in 
on the ground the desired curve. Curves with central angles 
of less than 4 can be run in with the eye during construction. 

The center line is marked at intervals of either fifty or one 
hundred feet (see cross-section, page 121) in any convenient 
manner; the alignment of these points should be correct to 
within 0.2 and the distance along the line to within 0.1 per 
100 feet of the length; any attempt to get more accurate sta- 
tioning is a waste of time. The chaining may be done on the 
surface of the ground up to a grade of 5 per cent with no objec- 
tionable error; beyond that slope, however, the tape should be 
leveled and plumbed. Steel tapes should be used for chaining 
the center line and referencing the hubs. 

A convenient method of marking the actual center-line sta- 
tions is to use a nail and piece of flannel; red flannel for the ioo' 
stations and white flannel for the intermediate 50' stations, if 
needed. Where the soil is sandy, or muddy, and these nails 
would be kicked out or covered, a line of stakes can be set out- 
side of the traveled way on a specific offset from the center line. 
However, if an offset line is used the chaining of all curves should 
be done on the center line to insure a correct center-line distance 
and the stakes placed radially on the desired offset. Railroad 



146 



THE SURVEY 



spikes make good permanent transit points and are easily 
placed. 

At the same time that the line is run it is just as well to paint 
the 100' station numbers on any convenient place where they 
can be readily seen, as stations marked in this manner make it 
much easier to sketch in the topography than if marked in chalk 
on stakes. Also, if the stations are permanently marked it is 
easier for the construction engineer to pick up the transit points 
at some future time. 

A party of five men will run from two to four miles of center 
line a day, the speed depending upon the number of curves and 
length of tangents, if the hubs have been previously placed and 
referenced. If the hubs are placed at the same time the line 
is run, the work is greatly delayed. 

Two men can place and reference the transit points at the 
tangent intersections at the rate of from four to ten miles per 
day. 



Sta. 



D.M.# I 



B.M.*£ 



B.5. 

+ 



F. 5. 



7TZT 



4.ZCI 



B.IH 



-6TKT 



3-*H 



ice: 



H.I 



i n s- q -y 



4\?>.7U 



Elev. 



~v 



Tyszn*- 



wt . sP 



"Hg.KZ 



Spike in 15" Elm, Righ t o f S tq .frrfrft- 



Top qf S t one Hi t ihing Pos t , le ft . S t a. 15+ 60: 



y^ 



Fig. 44. — Bench Level Notes 



Levels and Cross-Sections. Bench levels are run in the 
usual manner; the levels will be sufficiently accurate if the rod 
is read to the nearest o.oi'; for such work any good level and a 
self-reading rod graduated to hundredths are satisfactory. 
Benches are established at intervals of 1,000-1,500 feet; they 
must be substantial, well marked, and so situated as not to be 
disturbed during construction. A small railroad spike in the 
root of a tree, a large boulder, or the water table of a building 
make good benches. 

The bench levels may be referred to some local datum in 
general use or to the U. S. levels, or the datum can be assumed. 



LEVELS AND CROSS-SECTIONS 



147 



In running bench levels it is better to use each bench as a turn- 
ing point, as side-shot benches may be wrong even if the line of 
levels is correct. 

Cross-sections are taken at either 100' or 50' intervals, at all 
culverts, possible new culvert sites, and any intermediate breaks 
not shown by the normal interval. Enough sections are taken 
to show the constantly changing shape of the road. 

The distance of the shots from the center line of the road 
is read to the nearest 1.0' where the ground has no abrupt 
change of slope and to the nearest 0.5' where there is a well- 
defined abrupt change. The elevations are read to the nearest 
o.i'. The sections should extend from fence line to fence line, 
or in villages from sidewalk to sidewalk, and the position of the 
pole lines, tree lines, curbs, etc., noted. Engineers differ as to 
whether the sections should be taken at a normal interval of 
50' or ioo'. 

Table 27 gives the difference in the computed quantity of 
earthwork using 50' and ioo' sections with intermediate sec- 
tions at well-defined breaks in the grade. 



Table 27 



Name of Road 



Scottsville 

Mumford . . 
Scottsville 

Mumford . . 
Leroy 

Caledonia . . . . 
K Leroy 
Caledonia 
Clarence 

Center 

Clarence 

Center 

Lockport 
Tonawanda . . 
"East Henrietta 
Rochester 



Length 
Figured 



mile 



Charac- Excava- 
ter of , tion 50' 
Road Section 



flat 
hilly 

rolling 
flat 

rolling 
flat 
flat 

rolling 



Cu. Ft. 

61.444 
in. 109 
57,840 
77,841 
73,727 
38,037 
59,096 
37,275 



Excava- 



tion ioo' ; 
Section 



J Appro - 
! ximate 



Cu. Ft. 

6i,995 

111,700 
60,560 
78,659 
73,048 
39-415. 
59,47o 
36,075 



Differ- 



Cu. Ft. 

55o 
600 

2700 
800 
700 

1400 
400 

1200 



Per cent 
of Differ- 
ence 



+ t 9 o% 



+ 



% 



+ 1 % 

-1 % 

+ 3iu% 
+ i 7 o% 
~2,\ % 



148 



THE SURVEY 



The following tabulation shows the variation for shorter 
sections of the starred roads. 



Name Station 

of and to 
road Station 


Quantities 
by 50' Sec- 
tions 


Quantities 
by ioo' 
Sections 


Approx- 
imate 
Difference 


Per cent of 
Difference 


Leroy 

Caledonia, 80- 90 . . . 


Cu. Ft. 
19,151 


Cu. Ft. 
19,525 


Cu. Ft. 
400 


+ 2 % 


90-100 . . . 
" 100-110 . . . 


21,915 
2i,555 


23,415 
20,689 


1500 
900 


+ 7 % 

-4 % 


" II0-I20 . . . 

Total and averages . 
East Henrietta 


15,220 

77,84i 


15,030 
78,659 


200 
800 


~~ I T0% 

+ 1 % 


Rochester, 0-19 . . . 


14,625 


14,300 


300 


-2 % 


32-49 • • • 


n,95o 


n,575 


350 


-3 % 


49-66 . . . 
Total and averages . 


10,700 

37,275 


10,200 
36,075 


500 
1200 


-s % 
-si % 



The question of quantities is not the only factor in determining 
the interval. Where it is important to fit the local conditions, 
as in a village, or to utilize an old hard foundation, the designer 
is helped by 50' sections. 



Sra. 


B.S. 


F.S. 


H.I. 


Elev. 


Left ^ 

^ ^ N U> \£> 
£ JO If) v& VC> 

£1 <M cm CM ^ 
5.0 5.3 6.0 52 5 


Right 

V) CM oo > CM 
VSJ *JS U> VSl in 
CM CM CM JV* cvj 
CD CD CD CT> CD 

/ 5.4 5.5 53 5.3 6.5 


B.M.*3 
10 tOO 


5.41 




931.73 


ezezz 


/OtSO 










40 14 12 5 C 

CM K CM ^ K N 
£> ir> JO Jo ui irj 

M CM £j £f CVj CM 

CD CD Ci ^ 0^ 

55 6.0 6.5 6.3 60 6. 


5 3/1/9 24 

M> N N ^ K 

^ ^ $"' ^ *5 

CM cm CM cm CM 

CD CD S\ CD eft 
6.3 7.0 7.0 7.6 8.0 


T.Rt65 
Rock on 

lit 00 


1.32 


2.10 


330.35 


929.63 


26 20 14 II 8 (y 

CQ *0 CJ> (VJ > Lf) 
f\i CM < Cvj t\i C\j 
CM C\J CVJ CVj C\J t\j 

O O) cd CD CSv CD 
8.2 6.7 9.1 8.8 8.6 8. 


► 8 II 12 20 23 

^ K - v> 
cvj ^- CM ^ 
fVj CM CM CM 
$) CD CD CD 
5 3.0 9.3 89 6.0 


v 








J 


30 20 13 9 5 C 


IO 14 13 30 



Fig. 45. — Cross-Section Notes 



DRAINAGE 



149 



In taking cross-sections the work becomes mechanical, and 
unless the engineer in charge is unusually alert to all the inter- 
mediate changes better results will be obtained by the use of 
the shorter interval. For these reasons the author believes that 
a 50' interval is advisable except on long uniform stretches of 
road. 

A party of three men will run from 4,000 to 7,000 feet of 50' 
cross sections per day; a party of four men from 5,000 to 9,000 
feet, depending on the country. 

DRAINAGE 

The drainage notes show the position and size of all the exist- 
ing culverts; the area of the watersheds draining to them and a 



Drainage 
Old Structures 



V^ 



Sta.lfT-f-25 Present 12" V.TP 



Bad Condition 



£l 



S+a. 24+00 Present Concrete 



To w n i n 1 211 



Culvert Built by 



Water Satisfactorily 



2'x 2 '* 3Q j C arries 



£L 



Sta . 45+5Q - 49 + 00 Fl ood 



Backwater Covers Present Rngd 



1. 5 ' i n Sp ri ng of. Y e ar y n o C urren t . 
Raise R oad 2.5 ' a nd m ak e Fil l of 



Boulder Stone or 6 ravel 



Sta. 55+10 Present 24" V.T. P does 



not C arry W ater i n F reshets 



-O- 



Notes 
New Structures 



~ 5t a J5 +25. 



Drainage Area 40 Acres 



Slope 



20' to 1000 Use l8 " C \t.P. 



?rox. 



5ta. 24+0 N o N ew \Culvert 



Needed. 



£l 



5ta. 55-t 10 Draina ge Area 300 A . 
-O Rolling Farm Land, 



Slope a bout 30' per 10 00 



Use Xx7> Cnnr.rhte Box. 



ft 



>K 



Fig. 46 



recommendation of the size culvert to be built; the location, 
drainage area, and size of desirable new culverts; the necessity 
for outlet ditches and their length, if required; the elevation of 
flood water near streams, and the condition of the abutments and 
superstructure of long-span bridges. The cross-section levels are 
supplemented to show these points fully. Where the U. S. 
geological maps are available the areas of watersheds can be 
easily determined; where no such maps have been made the 
drainage areas can be easily mapped with a small 15" plane table 



ISO 



THE SURVEY 



oriented with a magnetic needle; the distances can be paced and 
the divides determined with a hand level. One inch to 2,000 
feet is a convenient scale. 

The drainage scheme should be carefully worked out by the 
Chief of Party, as the possibilities of friction with local people 
are greater on this part of the design than any other. In the 
chapter on Drainage this fact was mentioned and designers were 
cautioned not to use new culverts unless necessary. 

TOPOGRAPHY 

The topography notes show the features of the adjacent terri- 
tory that might affect the design. These include the location 
of buildings, drives, intersecting roads, streams, railroads, poles, 
trees, sidewalks, crosswalks, and property lines. The names 
of property owners are recorded. 



+50 



-o- 



Sta.lZ 



+50 



Sta.ll 



+50 



\SfaJO 




Fig. 47 



A simple method of locating these points is to refer them di- 
rectly to the previously run center line by right-angle offsets; 
such notes are easily taken and quickly plotted. 

In taking the topography the plus stationing along the center 
line and the offset distances to all points inside of the road fences 
should be measured by tape to the nearest foot; the distances 
to and the dimensions of buildings, etc. outside of these limits, 
can be paced or estimated; the bearings of the property lines 
can be read near enough with a pocket compass, except for Right 
of Way surveys which are described on page 154. 

The instruments needed for work of this kind are a pocket 
compass reading to 2 , steel picket, and metallic tape. 



FOUNDATION SOILS 151 

Two experienced men will take from two miles to four miles 
of topography a. day except in villages, where from one half to 
a mile is average speed. 

DIRECTION AND AMOUNT OF TRAFFIC is determined 
by inspection and inquiry of the residents along the road. 

To illustrate the information required, an extract from the sur- 
vey report of the Fairport Nine Mile Point Road is given below: 

FAIRPORT NINE MILE POINT ROAD TRAFFIC REPORT 

Heavy Hauling. The direction of heavy hauling on this road 
is approximately as follows: 

1. Station No. 195 to station o towards Fairport. 
2 " " 195 " " 400 " Webster. 

3. " " 580 " "- 400 

This divides the road into three sections for the determination 
of the ruling grades. 

The ruling grade for section 1 will be determined by the hills 
at station 10 and station 48 and probably will be limited to 
5 per cent. 

The ruling grade for section 2 will be determined by the knolls 
at stations 267, 285, and 300. 

The ruling grade for section 3 will be determined by the hills 
at stations 445 and 494. 

The team traffic is medium heavy station 90 to station o; light, 
station 270 to 90; medium, station 270 to 375; heavy, station 
375 t° 386; very heavy, equivalent to city street, station 386 
to 408; medium heavy, station 408 to 450, and light, station 450 
to 580. Macadam construction will not be suitable stations 
386 to 408. 

The automobile pleasure traffic will be largely through traffic 
and probably fairly heavy. 

FOUNDATION SOILS 

The notes on soils show the character, width, and depth of 
the existing surfacing material and the kind of underlying mate- 
rial. This feature of the survey is important, as it governs the 
thickness of the bottom course, and, to a certain extent, the posi- 
tion of the grade line where an existing solid foundation can be 
utilized and the thickness of the improved road reduced to a 
minimum. 

Even with a careful soil examination it is impossible to make 
the design of the foundation definite, as mentioned on page 73, 
but the quantity of the material that will be needed can be esti- 
mated very closely. 

The subsoil can be readily examined by driving a i|" or 1" 
steel bar to the required depth, which is usually not over 4.0' 
to 5.0' even in cuts, removing the bar and replacing with a §" 
gas pipe, which is driven a few inches and withdrawn. The core 
will give a fair idea of the material to be encountered. 



152 



THE SURVEY 



Soil Notes Foundation Recommendations 


Sta.toSta. 


Surface Mat 


SubSurface 







30 


Sand &Gravel 


Sand 8c Gravel 


Total Thickness Metalling 6" 
» »? ?t 9" 


30 


3/ 


Clay & 6 ravel 


Clay I'd own 


31 


36 


Clay 


Clay 


» » v 12" 


3d 


40 


Gravel 8 "deep 


Wef Clay 


Underdrain on J?t Stone I5"deep 


40 


41 


»i 4" u 


Clay Loam 


Fill at this Point n 6 " v 














































































































































V 






s 


^ J 



Fig. 48 

Where rock is encountered the elevation of the outcrop is 
shown, and if the rock underlies the road for any distance within 
two or three feet of the surface this depth is determined by 
driving bars. Sample notes below: 



Station 


Left 


Center Line 


Right 


62 


3^ 

20 


00 


20 


63 


1*1 


1.2' 


1.0' 


25 


00 


22 



The note 3.5' means that 20' to the left of the proposed center line 

20 
of the improvement, the rock is 3.5' below the present surface; 
from these notes the rock can be readily plotted on the cross- 
sections. Its character can be determined from adjacent out- 
crops, or from test pits, if required. 

LOCATION AND CHARACTER OF MATERIALS 

The selection of materials and the estimate of the construction 
cost depend on a knowledge of the available materials and their 
location relative to the road. 



LOCATION AND CHARACTER OF MATERIALS 153 



Unloading Points for Freight. Provided U. S. geological 
maps are obtainable, the position of sidings may be marked on 
the sheets. The notes for each siding show its car capacity; 
whether or not an elevator unloading plant can be erected, and if 
hand unloading is necessary whether teams can approach from 
one side or two. They should also show any coal trestles that 
can be utilized in unloading, and the location and probable cost of 
any new sidings that will materially reduce the length of the haul. 
Canal or river unloading points are shown in the same manner. 



Stone Fs+. 



/. Oeo.Barber lOOOc.u.yds. Fence _ 
Boulders 20% Granite 40%Sanasfc 
10% Limestone 3Q% Soft Rock 



50% of the Granite must be Blasted 
or Sledged 



2. Patrick Don/In 2SOO cuyds. same 
as above 



3 Mike O' Donne. 1 1 5QO cu yd: 



Large Granite Boulders 75% must 



be Blasted 



■4-. Old Limestone Quarry 2Q 1 face ~ 

Samples taken^ looks good for Top Stone ™ 




Fig. 49 

Sand, Gravel, and Filler Material. The position of sand and 
gravel pits and filler material are noted with their cost at the 
pit; if no local material is available the cost f.o.b. at the nearest 
siding is given. 

Stone Supply. Provided imported stone is to be used the work 
is simplified to determining the rate f.o.b. to the various sidings 
for the product of the nearest commercial stone-crushing plant 
that produces a proper grade of stone. 

In case local stone is available the location of the quarries 
or outcrops is shown; the amount of stripping, if any, and the 
cost of quarry rights. If the estimate will depend upon rock 
owned by a single person an option is obtained to prevent an 
exorbitant raise in price. 

In the case of field or fence stone a careful estimate is made of 
the number of yards of boulder stone available, the owners' 



154 THE SURVEY 

names, what they will charge for it, the position of the fences or 
piles relative to the road, or side roads, and if the fences are not 
abutting on a road or lane the length of haul through fields to 
the nearest road or lane. As fer^es are usually a mixture of 
different kinds of rock, the engineer estimates the percentage of 
granite, limestone, sandstone, etc., and the percentage that will 
have to be blasted or sledged in order to be crushed by an or- 
dinary portable crusher. The amount of field stone required 
per cubic yard of macadam is given in estimates, page 274. If 
there is a large excess of stone a careful estimate need not be 
made, only enough data being collected to determine the probable 
position of the crusher set-ups and the average haul to each set- 
up. If a sufficient supply is doubtful a close estimate is made as 
outlined above and options obtained from the various owners. 
Samples of the different rocks are tested. (See materials.) 
Preliminary surveys of the above description should be made 
at a speed of from two to four miles per week at a cost of from 
$35 to $70 per mile, allowing $6 per day for the engineer; $3.50 
for the instrument man; $2 per man for three laborers; $1 per 
day board per man and $4 per day for livery. 

Right of Way and diversion line surveys are often needed but 
are usually not made at this time; if the designer believes that 
additional land must be acquired or that a diversion line is 
necessary, he indicates the information desired and the surveys 
are made. 

RIGHT OF WAY SURVEYS 

These surveys are used not only to show the amount of land 
to be acquired but, also, the damage to property from altering 
the shape of a field, cutting a farm in two, changing the position 
of a house or barn relative to the road, etc. 

The acreage to be taken is shown by an ordinary land survey 
in which the road lines, property lines, corners, etc., are located 
in relation to the proposed center line of the improvement, and 
their lengths and bearings carefully determined. It is often 
difficult to locate the road boundaries, as town records are care- 
lessly kept and there is a general tendency to encroach on the 
road. As the amount paid for new Right of Way is rarely settled 
on an acreage basis, it is customary to take the existing fence 
lines as the road line unless it is very evident that the fence has 
been moved. This produces better feeling on the part of the 
property owner and does not affect the price paid. The lines 
between adjoining properties are usually well defined. 

In cases where an orchard is damaged the position and size of 
the trees are noted; where a field or farm is cut the whole field 
is shown, with the shape and acreage of the pieces remaining after 
the land actually appropriated has been taken out. 

As is usually done in all land surveys, the parcel to be bought 
is traversed and the survey figured for closure error to insure 
the description against mistakes. 

The standard form of map and description of the N. Y. State 
Department is shown in the following illustration: 



WAY SURVEYS 




155 



"5" 



2 a >>rt 



ra -la G ~ H <" 

, fi^ -!-> ^ -^3 (J 

*T3 o „, <u o !"> G 

~ « G+ 2 ^ SiG 



en. 



o 



k" . o o o a> ^ 

^O Oh Q, C-G 0) 

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THE SURVEY 



Table 28. * Horizontal Distances and Elevations from Stadia 

Readings 



Minutes 



o 
2 

4 

6 

8 

10 

12 

14 
16 
18 
20 

22 

24 
26 
28 
30 

32 
34 
36 
38 
40 

42 
44 
46 
48 
5o 

52 
54 
56 
58 
60 



o.75 



1. 00 



1-25 



Hor. 
Dist. 



IOO.OO 
IOO.OO 
IOO.OO 
IOO.OO 
IOO.OO 
IOO.OO 

IOO.OO 
IOO.OO 
IOO.OO 
IOO.OO 
IOO.OO 

IOO.OO 

IOO.OO 

99.99 

99.99 

99.99 

99.99 
99.99 
99.99 
99.99 
99.99 

99.99 
99.98 
99.98 
99.98 
99.98 

99.98 
99.98 
99-97 
99-97 
99-97 



o.75 



1. 00 



1.25 



Diff. 
Elev. 



0.00 
0.06 
O.I2 
0.17 
O.23 
0.29 

0.35 
O.41 

O.47 
0.52 
O.58 

0.64 
O.70 
O.76 
O.81 
O.87 

0.93 
0.99 
1.05 
I. II 
1. 16 

1.22 
1.28 

1-34 
1.40 

i-45 

1. 5i 
i-57 
1.63 
1.69 
i-74 



0.01 



O.OI 



0.02 



Hor. 
Dist. 



99-97 
99-97 
99-97 
99.96 
99.96 
99.96 

99.96 
99-95 
99-95 
99-95 
99-95 

99.94 

99.94 
99.94 

99-93 
99-93 

99-93 

99-93 
99.92 
99.92 
99.92 

99.91 
99.91 
99.90 
99.90 
99.90 

99.89 
99.89 
99.89 
99.88 
99.88 



o.75 



Diff. 
Elev. 



1-74 
I.80 
1.86 
1.92 
1.98 
2.04 

2.09 

2.15 
2.21 

2.27 
2-33 

2.38 
2.44 
2.50 
2.56 
2.62 

2.67 

2.73 
2.79 
2.85 
2.91 

2.97 
3.02 
3.08 

3-!4 
3.20 

3.26 

3-3 1 
3-37 
3-43 
3-49 



0.02 



1 .00 0.03 



1.25 0.03 



Hor. 
Dist. 



99.88 
99.87 
99.87 
99.87 
99.86 
99.86 

99-85 
99-85 
99.84 
99.84 

99-83 

99-83 
99.82 
99.82 
99.81 
99.81 

99.80 
99.80 
99-79 
99-79 

99.78 

99.78 
99-77 
99-77 
99.76 
99.76 

99-75 
99-74 
99-74 
99-73 
99-73 



o.75 



1. 00 



1.25 



Diff. 

Elev. 



3-49 
3-55 
3.60 
3.66 
3-72 
3.78 

3.84 
3-9o 
3-95 
4.01 
4.07 

4-13 
4.18 
4.24 
4.30 
4.36 

4-42 
4.48 
4-53 
4-59 
4.65 

4.71 
4.76 
4.82 
4.88 
4-94 

4.99 

5-o5 
5-n 

5-i7 
5-23 



0.03 



0.04 



0.05 



Hor. 
Dist. 



99-73 
99.72 
99.71 
99.71 
99.70 
99.69 

99.69 
99.68 
99.68 
99.67 
99.66 

99.66 

99-65 
99.64 

99-63 
99-63 

99.62 
99.62 
99.61 
99.60 
99-59 

99-59 
99-58 
99-57 
99-56 
99-56 

99-55 
99-54 
99-53 
99-52 
99-51 



o.75 



1. 00 



1.25 



1 From "Theory and Practice of Surveying," by Prof. J. B. Johnson, New York: 
John Wiley & Sons. We are enabled to use this form through the courtesy of Prof. 
J. B. Johnson. 



DISTANCES AND ELEVATIONS 



157 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



6° 



Minutes 



O 
2 

4 

6 

8 

10 

12 

14 
16 
18 
20 

22 
24 
26 
28 
30 

32 
34 
36 
38 
40 

42 

44 
46 

48 

5o 

52 
54 
56 
58 



Hor. 
Dist. 



99-51 
99-51 
99-5Q 

99-49 
99.48 

99-47 

99.46 
99.46 

99-45 
99.44 

99-43 

99.42 
99.41 
99.40 

99-39 
99.38 

99.38 
99-37 
99.36 
99-35 
99-34 

99-33 
99-32 
99-31 
99.3o 
99.29 

99.28 
99.27 
99.26 
99-25 



60 99-24 



o.75 



c = 1. 00 



c = 1.25 



0.75 



1. 00 



1-25 



Diff. 
Elev. 



Hor. 
Dist. 



6.96 
7.02 

7.07 

7.13 
7.19 

7.25 

7-30 
7.36 
7.42 
7.48 
7-53 

7-59 
7.65 
7.71 
7.76 
7.82 

7.88 
7-94 
7-99 
8.05 
8.11 

8.17 
8.22 
8.28 

8-34 
8.40 

8.45 
8.51 
8.57 
8.63 
8.68 

0.06 

0.08 

0.10 



99.24 

99.23 
99.22 
99.21 
99.20 
99.19 

99.18 
99.17 
99.16 

99-15 
99.14 

99-13 
99.11 
99.10 

99.o9 
99.08 

99.07 
99.06 

99-05 
99.04 
99-03 

99.01 
99.00 
98.99 
98.98 
98.97 

98.96 
98.94 

98.93 
98.92 

98.91 
o.75 
0.99 
1.24 



Diff. 

Elev. 



Hor. 
Dist. 



8.68 

8.74 
8.80 
8.85 
8.91 
8.97 

9-o3 
9.08 
9.14 
9.20 
9.25 

9.31 
9-37 
9-43 
9.48 

9-54 

9.60 

9.65 
9.71 

9-77 
9.83 

9.88 

9-94 
10.00 
10.05 
10.11 

10.17 
10.22 
10.28 
10.34 
10.40 

0.07 

0.09 

O.II 



98.91 

98.90 

98.88 
98.87 
98.86 

98.85 
98.83 

98.82 
98.81 
98.80 
98.78 

98.77 
98.76 
98.74 

98.73 

98.72 
98.71 

9S.69 
98.68 

98.67 
98.65 

98.64 

98.63 

98.61 
98.60 

98.58 

98.57 
98.56 

98.54 
98.53 
98.51 

0.75 
0.99 

1.24 



Diff. 
Elev. 



Hor. 
Dist. 



IO.40 
IO.45 
10.51 

10.57 
IO.62 
IO.68 

IO.74 
10.79 
10.85 
IO.91 
10.96 

II.02 
11.08 
II. 13 
II. 19 
II.25 

II.30 
II.36 
II.42 
11.47 
n-53 

n-59 
11.64 
11.70 
11.76 
11.81 

11.87 

n-93 
11.98 
12.04 
12.10 

0.08 

O.II 

0.14 



98.51 
98.50 
98.48 
98.47 
98.46 
98.44 

98.43 
98.41 
98.40 
98.39 
98.37 

98.36 
98.34 
98.33 
98.31 
98.29 

98.28 
98.27 
98.25 
98.24 
98.22 

98.20 
98.19 
98.17 
98.16 
98.14 

98.13 
98.11 
98.10 
98.08 
98.06 

o.74 

o.99 
1.24 



Diff. 
Elev. 



12.10 
12.15 
12.21 
12.26 
12.32 
12.38 

12.43 
12.49 

12.55 
12.60 
12.66 

12.72 
12.77 
12.83 
12.88 
12.94 

13.00 

I3-05 
13. 11 

13-17 
13.22 

13.28 
13-33 
13-39 
13-45 
13.50 

13.56 
13.61 
13.67 

13.73 
13-78 

0.10 

0.13 
0.16 



is8 



THE SURVEY 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



Minutes 



O 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

33 

40 

42 

44 

46 

48 

5o 

52 

54 

56 

58 

60 

c = 0.75 

c = 1. 00 

c = 1.25 



Hor. 
Dist. 



98.06 
98.05 
98.03 
98.01 
98.00 
97.98 

97-97 
97-95 
97-93 
97.92 

97.90 

97.88 
97.87 
97-35 
97.83 
97.82 

97.80 
97.78 
97.76 

97-75 
97-73 

97.71 
97.69 
97-68 
97.66 
97.64 

97.62 
97.61 
97-59 
97-57 
97-55 

0.74 
0.99 
1.23 



Diff. 
Elev. 



13.78 
13.84 
13.89 

13-95 
14.01 
14.06 

14.12 
14.17 

14-23 

14.28 

14.34 

14.40 
14.45 
14.51 
14-56 
14.62 

14.67 

14.73 
14.79 
14.84 
14.90 

14.95 
15.01 
15.06 
15.12 
I5.I7 

15.23 
15.28 

15.34 
15.40 

15-45 
0.11 

0.15 
0.18 



Hor. 
Dist. 



97-55 
97-53 
97-52 
97-50 
97.48 
97.46 

97-44 
97-43 
97.41 
97-39 
97-37 

97-35 
97.33 
97.31 
97.29 

97.28 

97.26 
97.24 
97.22 
97.20 
97.18 

97.16 
97.14 
97.12 
97.10 
97.08 

97.06 
97.04 
97.02 
97.00 
96.98 

o.74 

o.99 
1.23 



Diff. 

Elev. 



15.45 
15.51 

I5-56 
15.62 

15.67 
15.73 

15.78 
15.84 
15.89 

15-95 

16.00 

16.06 
16. 1 1 
16.17 
16.22 
16.28 

16.33 
16.39 
16.44 
16.50 
16.55 

16.61 
16.66 
16.72 
16.77 
16.83 

16.88 
16.94 
16.99 

I7.05 
17.IO 

O.I2 

O.16 

O.21 



io v 



Hor. 
Dist. 



96.98 
96.96 

96.94 
96.92 
96.90 
96.88 

96.86 
96.84 
96.82 
96.80 
96.78 

96.76 
96.74 
96.72 
96.70 
96.68 

96.66 
96.64 
96.62 
96.60 
96.57 

96.55 
96.53 
96.51 
96.49 
96.47 

96.45 
96.42 
96.40 
96.38 
96.36 

O.74 

O.98 

1.23 



Diff. 

Elev. 



17.10 
17.16 
17.21 
17.26 
17.32 
17.37 

17.43 
1748 
17.54 
17-59 
17.65 

17.70 
17.76 
17.81 
17.86 
17.92 

17.97 
18.03 
18.08 
18.14 
18.19 

18.24 
18.30 

18.35 
18.41 
18.46 

18.51 

18.57 
18.62 
18.68 
18.73 

0.14 
0.18 
0.23 



II' 



Hor. 
Dist. 



96.36 

96.34 
96.32 
96.29 
96.27 
96.25 

96.23 
96.21 
96.18 
96.16 
96.14 

96.12 
96.09 
96.07 
96.05 
96.03 

96.00 
95.98 
95.96 
95-93 
95-91 

95-89 
95.86 

95.84 
95.82 

95-79 

95-77 
95-75 
95-72 
95-70 
95-68 

0-73 
0.98 
1.22 



DISTANCES AND ELEVATIONS 



159 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



Minutes 



o 
2 

4 

6 

8 

10 

12 

14 
16 
18 

20 

22 

24 
26 
28 
30 

32 
34 

36 
38 
40 

42 
44 
46 
48 
5o 

52 
54 
56 
S3 
60 



I2 V 



0.75 



C = I. OO. 



c = 1.25. 



Hor. 
Dist. 



95-68 
95-65 
95.63 
95.61 

95.58 
95.56 

95-53 
95-51 
95-49 
9546 
95-44 

95-41 
95-39 
95.36 
95-34 
95.32 

95.29 
95-27 
95-24 
95-22 

95-19 

95-17 
95-14 
95.12 

95.09 
95-07 

95.04 
95.02 
94.99 
94-97 
94-94 



0.73 



0.98 



1.22 



Diff. 
Elev. 



20.34 
20.39 

20.44 

20.50 

20.55 
20.60 

20.66 
20.71 
20.76 
20.81 
20.87 

20.92 
20.97 
21.03 
21.08 
21.13 

21.18 
21.24 
21.29 

21-34 
21.39 

21.45 
21.50 

21-55 
21.60 
21.66 

21.71 

21.76 
21.81 
21.87 
21.92 



i3 l 



Hor. 
Dist. 



0.16 



0.22 



O.27 



94.94 
94.91 
94.89 
94.86 
94.84 
94.81 

94-79 
94.76 

94-73 
94.71 
94.68 

94.66 

94.63 
94.60 
94.58 
94-55 

94-52 
94.5o 

94-47 
94.44 
94.42 

94-39 
94-36 
94-34 

94.31 
94.28 

94.26 

94-23 
94.20 

94.17 
94.15 



o.73 



0.97 



1. 21 



Diff. 
Elev. 



21.92 
21.97 

22.02 
22.08 
22.13 
22.18 

22.23 
22.28 
22.34 
22.39 
22.44 

22.49 

22.54 
22.60 
22.65 
22.70 

22.75 
22.80 
22.85 
22.91 
22.96 

23.01 
23.06 
23.11 
23.16 
23.22 

23.27 

23-32 

23.37 
23.42 

2347 



14^ 



0.17 



O.23 
0.29 



Hor. 
Dist. 



94-15 
94.12 

94.09 
94.07 

94-04 
94.OI 

93-98 
93-95 
93-93 
93.90 
93.87 

93.84 
93.81 

93.79 
93.76 
93-73 

93.70 
93.67 
93.65 
93.62 

93-59 

93.56 
93-53 
93.50 
93-47 
93-45 

93-42 
93-39 
93.36 
93-33 
93.30 



0.73 



O.97 



1. 21 



Diff. 
Elev. 



2347 
23.52 
23.58 

23.63 
23.68 

23.73 

23.78 

23.83 
23.88 

23.93 
23.99 

24.04 
24.09 
24.14 
24.19 
24.24 

24.29 
24-34 
24.39 
24.44 

24.49 

24.55 
24.60 
24.65 
24.70 
24-75 

24.80 

24.85 
24.90 

24.95 
25.OC 



O.19 



0.25 
O.31 



i5' 



Hor. 
Dist. 



93.30 
93.27 
93.24 
93.21 
93.18 
93.16 

93.13 
93.IO 

93.07 
93.04 
93.OI 

92.98 

92.95 
92.92 
92.89 
92.86 

92.83 
92.80 
92.77 

92.74 
92.71 

92.68 
92.65 
92.62 

92.59 
92.56 

92.53 
92.49 
92.46 

92.43 
92.40 



O.72 



O.96 



1.20 



Diff. 

Elev. 



25.00 

25.05 
25.10 

25.I5 
25.20 

25.25 

25.30 

25.35 
25.40 

25-45 
25.50 

25-55 
25.60 

25.65 
25.70 

25-75 

25.80 

25.85 
25.90 

25.95 
26.OO 

26.05 
26.IO 
26.15 
26.20 
26.25 

26.30 

26.35 
26.40 

26.45 
26.50 



O.20 



O.27 



0.34 



i6o 



THE SURVEY 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



16 



Minutes 



O 
2 

4 

6 

8 

10 

12 

14 
16 
18 

20 

22 
24 
26 
28 
30 

32 
34 
36 
38 
40 

42 

44 
46 
48 
5o 

52 
54 
56 
58 
60 



Hor. 
Dist. 



92.40 
92-37 
92.34 
92.31 
92.28 
92.25 

92.22 
92.19 

92.15 
92.12 

92.09 

92.06 
92.03 
92.00 
91.97 

91-93 

91.90 
91.87 
91.84 
91.81 
91.77 

91.74 
91.71 
91.68 
91.65 
91.61 

91.58 

91.55 
91.52 
91.48 
9 J -45 



c = °-75„ 0.72 



c = 1. 00 



1-25 



0.96 



1.20 



Diff. 
Elev. 



26.50 

26.55 
26.59 
26.64 
26.69 
26.74 

26.79 
26.84 
26.89 
26.94 
26.99 

27.04 
27.09 

27.I3 
27.18 

27.23 

27.28 

27.33 
27.38 

2743 
27.48 

27.52 

27-57 
27.62 
27.67 
27.72 

27-77 
27.81 
27.86 
27.91 
27.96 

0.21 1 

0.28 

o.35 



i7 ( 



Hor. 
Dist. 



91-45 
91.42 

91-39 

9 J -35 
91.32 

91.29 

91.26 
91.22 
91.19 
91.16 
91.12 

91.09 
91.06 
91.02 
90.99 
90.96 

90.92 
90.89 
90.86 
90.82 
90.79 

90.76 
90.72 
90.69 
90.66 
90.62 

90-59 
90.55 
90.52 
90.48 

90-45 
0.72 

o.9o 
1. 19 



Diff. 
Elev. 



27.96 
28.01 
28.06 
28.10 
28.15 
28.20 

28.25 
28.30 
28.34 

28.39 , 
28.44 

28.49 

28.54 
28.58 
28.63 
28.68 

28.73 
28.77 
28.82 
28.87 
28.92 

28.96 
29.01 
29.06 
29.11 
29-15 

29.20 
29.25 
29.30 
29-34 
29-39 

0.23 
0.30 
0.38 



Hor. 
Dist. 



90.45 
90.42 
90.38 

90.35 
90.31 
90.28 

90.24 
90.21 
90.18 

90.14 
90.11 

90.07 
90.04 
90.00 
89.97 
89.93 

89.90 
89.86 

89.83 
89.79 
89.76 

89.72 
89.69 

89.65 
89.61 

89.58 

89.54 
89.51 
89.47 

89.44 
89.40 

0.71 

o.95 
1. 19 



Diff. 
Elev. 



29.39 
29.44 
29.48 

29-53 
29.58 
29.62 

29.67 
29.72 
29.76 
29.81 
29.86 

29.90 

29-95 
30.00 

30.04 
30.09 

30.14 
30.19 

30.23 
30.28 

30.32 

30.37 
30.41 
30.46 
30.5I 
30.55 

30.60 
30.65 
30.69 
30.74 
30-78 

0.24 
O.32 
0.40 



19' 



Hor. 
Dist. 



89.40 
89.36 

89.33 
89.29 
89.26 
89.22 

89.18 

89.15 
89.II 
89.08 
89.04 

89.00 
88.96 

88.93 
88.89 
88.86 

88.82 
88.78 
88.75 
88.71 
88.67 

88.64 
88.60 
88.56 

88.53 
88.49 

88.45 

88.41 
88.38 

88.34 
88.30 

0.71 

0.94 

1.18 



Diff. 
Elev. 



30.78 
30.83 
30.87 
30.92 

30.97 
31.OI 

31.06 
31.10 
31.15 
31.19 
31.24 

31.28 

31-33 
31.38 
31.42 

31.47 

31.51 
3I.56 
31.60 

31.65 
31.69 

31.74 
31.78 
31.83 
31.87 
31.92 

31.96 
32.01 
32.05 
32.09 
32.14 

0.25 

o.33 
0.42 



DISTANCES AND ELEVATIONS 



161 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



20^ 



Minutes. 



O 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

4o 

42 

44 

46 

48 

5o 

52 

54 

56 

58 

60 

c = 0.75. 

c = 1. 00. 

c = 1.25. 



Hor. 
Dist. 



88.30 
88.26 
88.23 
88.19 
88.15 

88.11 

88.08 
88.04 
88.00 
87.96 
87-93 

87.89 
87.85 
87.81 
87.77 
87-74 

87.70 
87.66 
87.62 
87.58 
87.54 

87.51 
8747 
87.43 
87.39 
87.35 

87.31 
87.27 
87.24 
87.20 
87.16 

0.70 

0.94 

1.17 



Diff. 

Elev. 



32.14 
32.18 
32.23 
32.27 
32.32 
32.3 6 

32.41 

32.45 
32.49 
32.54 
32.58 

32.63 
32.67 
32.72 
32.76 
32.80 

32.85 
32.89 
32.93 
32.98 
33-02 

33.o7 
33-* 1 
33.15 
33-20 

33.24 

33.28 
33-33 
33-37 
33.41 
33-46 

0.26 

o.35 
0.44 



21' 



Hor. 
Dist. 



87.16 
87.12 
87.08 

87.04 
87.00 
86.96 

86.92 

86.88 
86.84 
86.80 
86.77 

86.73 
86.69 

86.65 
86.61 

86.57 

86.53 
86.49 

86.45 
86.41 

86.37 

86.33 
86.29 

86.25 
86.21 
86.17 

86.13 
86.09 
86.05 
86.01 
85-97 

0.70 

o.93 
1. 16 



Diff. 
Elev. 



33-46 
33-50 
33-54 
33-59 
33-63 
33.67 

33-72 
33.76 
33-8o 
33.84 
33.89 

33-93 
33-97 
34.01 
34.o6 
34.10 

34-14 
34.18 

34.23 
34.27 
34.31 

34-35 
34-40 
34-44 
3448 
34-52 

34-57 
34.61 

34.65 
34-69 
34-73 

0.27 

o.37 
0.46 



22 v 



Hor. 
Dist. 



85-97 
85.93 
85.89 
85-85 
85.80 
85.76 

85.72 
85.68 

85.64 
85.60 

85.56 

85.52 
8548 
8544 
85.40 

85.36 

85.31 
85.27 

85.23 
85.19 

85.15 

85.II 

85.07 
85.02 
84.98 
84.94 

84.90 
84.86 
84.82 
84.77 
84.73 

O.69 
O.92 
1. 15 



Diff. 
Elev. 



34-73 
34-77 
34.82 
34-86 
34.90 
34.94 

34.98 

35-02 
35-07 
35-n 
35-15 

35.19 
35-23 
35-27 
35-31 
35.36 

35.4o 
35-44 
35-48 
35.52 
35-56 

35-6o 
35.64 
35-68 
35.72 
35.76 

35.8o 
35.85 
35.89 
35-93 
35-97 

0.29 
0.38 
0.48 



23 



Hor. 
Dist. 



84.73 
84.69 

84.65 
84.61 

84.57 
84.52 

84.48 

8444 
84.40 

84.35 
84.31 

84.27 
84.23 
84.18 
84.14 
84.IO 

84.06 
84.01 
83.97 
83-93 
83.89 

83.84 
83.80 
83.76 
83.72 
83.67 

83.63 
83.59 
83.54 
83.50 
8346 

O.69 
O.92 
I- 15 



Diff. 
Elev. 



35-97 
36.01 

36.05 
36.09 

36.13 
36.17 

36.21 
36.25 
36.29 

36.33 
36.37 

36.41 
36.45 
36.49 
36.53 
36.57 

36.61 
36.65 
36.69 
36.73 
36.77 

36.80 
36.84 
36.88 
36.92 
36.96 

37.00 

37.04 
37.o8 
37-12 
37.i6 

0.30 

0.40 

0.50 



l62 



THE SURVEY 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



24^ 



Minutes 



o 

2 , 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 ....... 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

5o 

52 

54 

56 

58 

60 

c = 0.75 

c = 1. 00 

c = 1.25 



Hor. 
Dist. 



83.46 
83.41 
83.37 
83-33 
83.28 
83.24 

83.20 

83.15 
83.11 

83.07 
83.02 

82.98 
82.93 
82.89 
82.85 
82.80 

82.76 
82.72 
82.67 
82.63 
82.58 

82.54 
82.49 
82.45 
82.41 
82.36 

82.32 
82.27 
82.23 
82.18 
82.14 

O.68 

O.91 

1. 14 



Diff. 
Elev. 



37.16 
37.20 
37.23 
37.27 
37.31 
37-35 

37-39 
3743 
37-47 
37.51 
37-54 

37.58 
37.62 
37.66 
37.7o 
37^74 

37-77 
37.8i 
37-85 
37.89 
37-93 

37.96 
38.00 
38.04 
38.08 
38.11 

38.15 
38.19 
38.23 
38.26 

38.30 
0.31 

0.41 
0.52 



^5 



Hor. 
Dist. 



82.14 
82.09 
82.05 
82.01 
81.96 
81.92 

81.87 
81.83 
81.78 

81.74 
81.69 

81.65 
81.60 
81.56 
81.51 

81.47 

81.42 
81.38 

81.33 
81.28 
81.24 

81.19 

81.15 
81.10 
81.06 
81.OI 

80.97 
80.92 
80.87 
80.83 
80.78 

O.68 
O.90 
I-I3 



Diff. 

Elev. 



38.30 
38.34 
38.38 
38.41 
38.45 
38.49 

38.53 
38.56 
38.60 
38.64 
38.67 

38.71 

38.75 
38.78 
38.82 
38.86 

38.89 
38.93 
38.97 
39.00 

39-04 

39.08 
39.II 
39-15 
39.18 
39.22 

39.26 
39.29 
39-33 
39.36 
39-40 

O.32 

0.43 
0.54 



26° 



Hor. 
Dist. 



80.78 

80.74 
80.69 
80.65 
80.60 
8o.55 

80.51 
80.46 
80.41 

80.37 
80.32 

8S.28 
80.23 
80.18 
80.14 
80.09 

80.04 
80.00 

79-95 
79.9o 
79.86 

79.81 
79.76 
79.72 
79.67 
79.62 

79.58 
79-53 
79.48 
79-44 
79-39 

0.67 
0.89 
1. 12 



Diff 
Elev. 



39-40 
39-44 
39-47 
39-51 
39-54 
39.58 

39.61 
39.65 
39.69 
39.72 
3976 

39-79 
39.83 
39-86 

39.90 
39-93 

39-97 
40.00 
40.04 
40.07 
4 l o.n 

40.14 
40.18 
40.21 
40.24 
40.28 

40.31 
40.35 
40.38 
40.42 

40.45 
o.33 

_o.45 
0.56 



27' 



Hor. 
Dist. 



79-39 
79-34 
79-30 

79-25 
79.20 

79.15 

79.II 
79.06 
79.OI 
78.96 
78.92 

78.87 
78.82 

78.77 
78.73 
78.68 

78.63 
78.58 
78.54 
78.49 

78.44 

78.39 
78.34 
78.30 
78.25 
78.20 

78.15 
78.10 
78.06 
78.01 
77.96 

O.66 

O.89 

I. II 



DISTANCES AND ELEVATIONS 



163 



Table 28. Horizontal Distances and Elevations from Stadia 
Readings. — Continued 



28 



29" 



30" 



Minutes 



O 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

4o 

42 

44 

46 

48 

5o 

52 

54 

56 

58 

60 .... . 

c = 0.75 

c = 1. 00 

c = 1.25 



Hor. 
Dist. 



77.96 
77.91 
77-86 
77.81 

77-77 
77.72 

77.67 
77.62 
77-57 
77-52 
77.48 

77.42 
77.38 
77-33 
77.28 

77.23 

77-18 

77-13 
77.09 

77.04 
76.99 

76.94 
76.89 
76.84 
76.79 
76.74 

76.69 
76.64 

76.59 
76.55 
76.50 

0.66 



1. 10 



Diff. 
Elev. 



Hor. 
Dist. 



41.45 
41.48 
41.52 
41-55 
41.58 
41.61 

41.65 
41.68 
41.71 
41.74 

41-77 

41.81 
41.84 
41.87 
41.90 
41-93 

41.97 
42.00 
42.03 
42.06 
42.09 

42.12 

42.15 
42.19 

42.22 
42.25 

42.28 
42.31 
42.34 
42.37 
42.40 

0.36 

0.48 

0.60 



76.50 

76.45 
76.40 

76.35 
76.30 
76.25 

76.20 

76.15 
76.10 
76.05 
76.00 

75-95 
75-9o 
75.85 
75.80 

75-75 

75.7o 
75.65 
75.60 

75-55 
75.5o 

75-45 
75.4o 
75.35 
75-30 
75.25 

75.2o 

75.15 
75-IO 

75-05 
75.oo 

0.65 

0.87 

1.09 



Diff. 
Elev. 



Hor. 

Dist. 



42.40 

42.43 
42.46 
42.49 

42.53 
42.56 

42.59 

42.62 
42.65 
42.68 
42.71 

42.74 
42.77 

42.80 
42.83 
42.86 

42.89 
42.92 

42.95 
42.98 
43.OI 

43.04 
43.07 
43.10 

43-13 
43.16 

43.18 
43.21 

43.24 
43.27 
43-3Q 

0.37 

0.49 
0.62 



75.00 

74-95 
74.90 

74.85 
74.80 

74.75 

74-70 
74.65 
74.60 

74-55 
74-49 

74-44 
74-39 
74-34 
74.29 

74.24 

74.19 

74-14 
74-09 
74.04 

73-99 

73-93 

73 .88 

73.83 
73.78 
73-73 

73-68 
73.63 
73.58 
73-52 
73-47 

0.65 
0.86 
1.08 



Diff. 
Elev. 



43.30 
43-33 
43-36 
43-39 
43-42 
43-45 

43-47 
43.50 
43-53 
43-56 
43-59 

43.62 
43.65 
43-67 
43-7o 
43-73 

43-76 
43-79 
43.82 

43-84 
43.87 

43.90 
43-93 
43-95 

43-98 
44.01 

44.04 
44.07 
44.09 
44.12 
44-15 

0.38 

0.51 

0.64 



1 64 THE SURVEY 

Diversion Line Surveys. Where there is no doubt as to the 
grade to be adopted, or the alignment to be used, the location 
is made directly in the field and the center line is run and the 
cross sections taken in the same manner as for a preliminary 
survey. If, however, the country is badly cut up and it is diffi- 
cult to make a field location direct, a transit stadia survey is 
made covering the territory that will include all the possible 
locations and from the resulting contour map the different loca- 
tions are projected and approximate estimates figured. The 
adopted line is then run in the field, cross sections taken in the 
usual manner and an accurate estimate made. This method is 
used so seldom that the author does not feel justified in giving 
space to the theory of stadia measurements or the methods of 
stadia surveys. If the reader is not familiar with this class of 
work he is referred to the standard works on surveying. 

A convenient scale for a contour map for the projection work 
mentioned above is i" = 20' with a contour interval of i' to 5', 
depending on the country. Table 28 is useful for reducing stadia 
notes. For a small number of shots this table and a slide rule 
will answer the purpose; for any extended amount of work a 
stadia reduction diagram or Noble & Casgrain's tables are recom- 
mended. 

If the stadia work is well done very satisfactory projections 
can be made. 

ADJUSTMENT OF INSTRUMENTS 

Wye Level. To make the line of collimation parallel to the 
telescope rings. Level the instrument roughly. Loosen the Y 
clamps so the telescope can turn freely in them; clamp the hori- 
zontal motion and by means of the leveling screws and tangent 
motion bring the intersection of the cross hairs on some well- 
defined point. Then, without lifting from the Ys, turn the 
telescope over 180 watching to see if the cross wires remain on 
the point during the operation; if they do the adjustment is 
correct; if they do not, correct \ the apparent error for both 
vertical and horizontal wires by means of the cross hair ring, 
adjusting screws, and repeat until the wires remain on the point 
for a complete revolution. 

To make the longitudinal axis of the level bubble parallel to the plane 
of the line of collimation. Level the machine over either pair of level- 
ing screws; unclamp the Ys; rotate the telescope in the Ys until 
the bubble tube is on one side of the bar. If the bubble remains 
in the center the adjustment is correct. If it runs from the 
center bring it to its correct position by means of the sidewise 
adjusting screw at one end of the bubble case. 

To make the bubble parallel to the rings and line of collimation. 
Level the machine; unclamp the Ys; lift the telescope carefully 
from the Ys and reverse end for end; if the bubble runs to the 
center after the telescope has been reversed the adjustment is 
correct; if not, correct \ the error by means of the adjusting 



ADJUSTMENT OF INSTRUMENTS 165 

nuts on the bubble case and J the error with the leveling screws 
and repeat the test until the bubble remains in the center. 

To adjust the Ys so the level bubble will be at right angles to 
the axis of the instrument. Level the machine approximately over 
both sets of screws; level carefully over one set; rotate on the 
spindle 180 ; if the bubble remains in the center the adjustment 
is correct; if not, correct \ the error by means of the adjusting 
nuts on the Ys and \ by the leveling screws. Repeat until the 
bubble remains in the center when reversed over either pair of 
leveling screws. 

To test the horizontal wire. Be sure that the pin in the Y clamp 
is in the notch of the telescope ring to keep the telescope from 
rotating; level the machine and compare the horizontal wire 
with any level line; if the wire is not level loosen the cross wire 
ring and turn to the correct position. Adjust again for col- 
limation and the level adjustments are complete. 

Dumpy Level, 

To make the bubble perpendicular to the axis of the instrument. 
Level the machine roughly over both sets of leveling screws and 
carefully over one set; rotate on the pinion 180 ; if the bubble 
stays in the center the adjustment is correct; if not, correct \ 
the error by means of the bubble adjusting nut and \ by the 
leveling screws, and repeat until correct. 

To make the horizontal line of collimation parallel to the level 
bubble. Level the machine; drive a stake about 150' or 200' 
from the instrument and set the level- rod target by the hori- 
zontal wire; rotate the instrument 180 and set another stake 
at the same distance from the machine as the first one; drive it 
until a rod reading taken on it is the same as the reading on the 
first stake. These stakes will then be level even though the 
machine is out of adjustment. Then set the level up near one 
of the stakes; level carefully and take rod readings on both; if 
these readings are the same the level is in adjustment; if not, 
correct the position of the horizontal wire by means of the cross 
wire ring screws until the readings on both stakes are the same. 

Test the horizontal wire on a level line in the same manner as 
for the Y level. 

Transit. 

Plate levels. Level the machine with each plate level bubble 
parallel to one set of leveling screws; rotate on the spindle 180 ; 
if the bubbles remain in the center the adjustment is correct; 
if not, correct \ the error with the bubble adjusting screws and 
J with the leveling screws. Repeat until correct. 

Line of collimation, ordinary distances. Level the machine; 
clamp the horizontal motion; with the slow motion screw, set 
the vertical cross wire on some well-defined point 500 or 600 
feet away; transit the telescope and set a mark the same dis- 



1 66 THE SURVEY 

tance in the opposite direction; then rotate the machine on 
the spindle, set on the first mark and transit the telescope; if 
the vertical wire strikes the second point the adjustment is 
correct; if not, correct \ the error by means of cross wire ring 
adjusting screws and repeat until correct. 

To make the standards the same height. Level the machine 
carefully; set the vertical wire on some well-defined point as 
high as can be seen; bring the telescope down and set a point; 
rotate the machine 180 ; transit the telescope set on the low 
point and raise the telescope; if the wire bisects the original 
high point the adjustment is correct; if not, correct J the error 
by means of the standard adjusting screw. 

Test the vertical wire by means of a plumb line to see that it 
is vertical; if not, loosen the cross hair ring and turn to the correct 
position; test again for collimation. 

If the transit is to be used as a level make the level bubble 
parallel to the horizontal wire by the two-peg method in the same 
manner as described for the Dumpy level. 

EXPLANATION OF CURVE TABLES AND DEVELOPMENT 
OF CURVE FORMULAE 

Curves for roadwork need not be as carefully worked out as 
in railroad surveying. Except for long curves the external is 
usually measured and the curve run in by the eye, and for this 
reason many of the tables given in the railway field manuals are 
omitted and those used are tabulated in a different form. 

Table No. 29, Radii of curves. The curve radii are computed 
on a basis of 5,730 feet as the radius of a one-degree curve and 
are inversely proportional to the degree of curva- 
ture; they are tabulated to the nearest o.i'. The 
usual columns showing logarithm of radius, tangent 
offset and middle ordinate are replaced by the de- 
flection angle per foot of arc, per 25' of arc, and per 
50' of arc, which saves considerable time in the 
computation of deflections. These values are tab- 
ulated only for even degree, twenty-minute, thirty- 
minute, and forty-minute curves, as there is always 
sufficient leeway both in the external and tangent 
to select a suitable curve from this list. 

Table No. 30, Functions of i° curve. Column 1 
gives the central angle A for every 10 minutes from 
o° to 4 , every minute 4 to ioo°, and every 10 min- 
utes ioo° to 120 . 

Column 2 gives the same central angle as in col- 
umn 1 expressed in decimals of a degree. This sim- 
plifies figuring the curve length. 

Columns 3 and 4 give the tangent and external for the central 
angles of column 1 to the nearest 0.1'. By the use of the chord 
lengths recommended at the top of each page of this table no 
correction need be made for tangent length or external distance 




RADII AND DEFLECTIONS 



167 



of any desired curve, figured by dividing the value given in the 
table by the degree of curvature required. 

The error that is introduced by the use of these chords is less 
than 0.1' per ioo', which is the allowable limit of error in chain- 
ing center line. 

For the convenience of readers not familiar with the theory of 
curves and the computation of curve notes, the following brief dem- 
onstration is made: 



RADII OF CURVES AND DEGREE OF CURVATURE 

A one-degree curve is defined as a curve having such a radius that 
100 feet of arc will subtend a one-degree central angle. 

There are 360 of central angle for a complete circle. The circum- 
ference of a circle is expressed by the formula 2ir R. Therefore the 
radius of a one-degree curve is determined by the formulae 



27r R = 360 X 100 

36000 _ 36000 

27T 2(3.14159) 



R = 



5729.6 feet 



. . (1) 



Table 29. Radii and Deflections 
Figured on a basis of R = 5730' for a i° curve. 



Degree of 
Curve 


Radius of 
1 Curve 


Deflection 

per foot of 

Arc 


Deflection per 
25' of Arc 


Deflection per 50' 
of Arc 




Feet 


Minutes 


Deg. 


Minutes 


Deg. 


Minutes 


o° 30' • • 
o° 40' . . 

o° 50' . • 
i° oo' . . 

i° 20' . .; 

i° 30' . . 

i° 40' . . 

2° Oo' . . 
2° 20' . . 

2° 30' . . 

2° 40' . . 

3° 00' . . 


11,460.0 
8.595.0 
6,876.0 
5>730.o 
4,297.5 

3,820.0 
3 5 438-o 
2,865.0 

2,455-7 
2,292.0 

2,148.8 
1,910.0 


00.15 

00.2 

00.25 

00.3 

00.4 

00.45 

00.5 

00.6 

00.7 

00.75 

00.8 
00.9 


— 


— 


O 
O 
O 
O 
O 

O 
O 
O 
O 
O 

O 
O 


07-5 
10.0 

12.5 
15.0 

20.0 

22.5 
25.0 
30.0 

35-o 

37-5 

40.0 
45-o 



1 68 



THE SURVEY 



Table 29. — Continued, 



Degree of 


Radius of 


Deflection 

per foot of 

Arc 


Deflection per 


Deflection per 50' 


Curve 


Curve 


25' of Arc 


of Arc 


1 


Feet 


Minutes j 


Deg. 


Minutes ' 


Deg. 


Minutes 


3° 20' . . 


1,719.0 


01.0 


, 


1 





50.0 


3° 30' • • 


1,637-1 


01.05 


— 







52.5 


3° 40'.. 


1,562.7 


01. 1 


— 




O 


55-o 


4° 00' . . 


1,432.5 


OI.2 


— 


— 


1 


00.0 


4° 20' . . 


1,322.3 


01.3 




— 


I 


05.0 


4° 30' • • 


1,273-3 


01.35 






I 


o7-5 


4° 40;..: 


1,227.9 


01.4 


— 


— 


I 


10. 


5° 00' . . 


1,146.0 


01.5 




— 


I 


15.0 


s° 30' . . 


1,041.8 


01.65 


— 


— 


I 


22.5 


6° 00' . . 


955-o 


OI.8 


— 




I 


30.0 


6° 30' . 


881.5 


01.95 


— 




I 


37-5 


7 00' . 


818.6 


02.1 


— 


— 


I 


45-0 


7° 3o' . . 


764.0 


02.25 




— 


I 


52.5 


8° 00' . . 


716.3 


02.4 


— 


— 


2 


00.0 


8° 3°' • • 


674.1 


02.55 


— 


— 


2 


07-5 


9 00' . . 


636.6 


02.7 


— 


— 


2 


15.0 


9° 3o' . . 


603.2 


02.85 


— 


— 


2 


22.5 


io° 00' . . 


573-o 


03.0 


— 




2 


30.0 


io° 30' . . 


545-7 


03-15 


— ■ 


— 


2 


37-5 


11° 00' . . 


520.9 


03-3 


— 


— 


2 


45.o 


11° 30'.. 


498.3 


03-45 


— 


— 


2 


52.5 


12° OO' . 


477-5 


03.6 


— 


— 


3 


00.0 


12° 30' . 


458.4 


03-75 


— 


— 


3 


07.5 


13° 00' . . 


440.8 


. 03-9 


— 


— 


3 


15.0 


13° 3o' . ■ 


424.4 


04.05 


— 


— 


3 


22.5 


14 oo' . . 


409-3 


04.2 


— 


— 


3 


30.0 


14° 30' . . 


395-2 


04.35 


— 


— 


3 


37-5 


iS° 00' . . 


382.0 


04.5 


— 


— 


3 


45-o 


15° 3o' . . 


369.6 


04.65 


— 


— 


3 


52.5 


16° 00' . . 


358.1 


04.8 


2 


OO.O 


4 


00.0 


16° 30' . . 


347-3 


04.95 


2 


03.8 


4 


07.5 


17° 00' . . 


337-o 


05.1 


2 


07-5 


4 


15.0 


17° 30' . . 


3274 


05-25 


2 


II. 2 


4 


22.5 


18° 00' . . 


318.3 


05.4 


2 


15.O 


4 


30.0 


18° 30' . . 


309-7 


05.55 


2 


18.7 


4 


37-5 



RADII AND DEFLECTIONS 



169 



Table 29. — Continued 



Degree of 


Radius of 


Deflection 

per ft. of 

Arc 


Deflection per 
25' of Arc 


Deflection per 


Curve 


Curve 






50' of Arc 


Minutes 


Degree 


Minutes 


19 00' 


301.6 


05-7 


2 


22.5 




19° 3o' 


293.8 


05.85 


2 


26.2 




20° Oo' 


286.5 


06.0 


2 


30.O 




20° 30' 


279-5 


06.15 


2 


33-7 




21° OO' 


272.9 


06.30 


2 


37-5 




21° 30' 


266.5 


06.45 


2 


41.2 




2 2° Oo' 


260.5 


06.6 


2 


45-o 




22° 30' 


2547 


06.75 


2 


48.7 




23° 00' 


249.1 


06.9 


2 


52.5 




23° 3°' 


243.8 


07.05 


2 


56.2 




24° oo' 


238.8 


07.2 


3 


00.0 




24° 30' 


233-9 


07-35 


3 


03-7 




25 00' 


229.2 


07-5 


3 


07.5 




26 00' 


220.4 


07.8 


3 


15.0 




2 7 oo' 


212.2 


08.I 


3 


22.5 




28 oo' 


204.6 


08.4 


3 


30.0 




29 oo' 


197.6 


08.7 


3 


37-5 




30 00' 


191. 


09.O 


3 


45-o 


Deflection per 
10' of Arc 


31° 00' 


184.8 


09-3 


3 


52.5 




3 2° 00' 


I79-I 


09.6 


4 


00.0 


1° 


36' 


33° 00' 


173-6 


09.9 


— 


— 


1° 


39' 


34 00' 


168.5 


I0.2 


— 


— 


1° 


42' 


35° 00' 


163.7 


IO.5 


— 


— 


1° 


45' 


36 00' 


159.2 


IO.8 


— 


t — 


1° 


48' 


37° 00' 


154-9 


II. I 


— 


— 


1° 


5i' 


38 00' 


150.8 


II.4 


— 


— 


1° 


54' 


39 00' 


146.9 


11. 7 


— 


— 


1° 


57' 


40 00' 


143.2 


12.0 


— 


— 


2° 


00' 


42 00' 


136.4 


12.6 


— 


— 


2° 


06' 


44 oo' 


130.2 


13.2 




— 


2° 


12' 


46 00' 


124.6 


13.8 


— 


— 


2° 


18' 


48 00' 


119.4 


14.4 


— 


— 


2° 


24' 


5o° 00' 


114. 6 


15.0 


— 


• — 


2° 


3o' 


52° 00' 


no. 2 


15.6 


— 


— 


2° 


36' 


54° 00' 


106. 1 


16.2 


— 


— 


2° 


42' 


56° 00' 


102.3 


16.8 


— 


— 


2° 


48' 



170 



THE SURVEY 



For all practical purposes the value of 5,730 can be used. 

In the same manner a two-degree curve is one having such a 
radius that 100 feet of arc will subtend two degrees of central 
angle, and its radius is 

27T R = ^— X 100 

2 

_ 18900 

27T 

or J of the radius of a one-degree curve. 

The radius of a three-degree curve will be J of 5,730. 

The radius of a four-degree curve will be \ of 5,730. 

The formula for the radius of any degree of curve is therefore 

tt (2) 



R 



The degree of curvature for any specified radius is therefore 



D = 



5.73Q 
R. 



(3) 



In general the degree of curvature is expressed by the central 
angle subtended by 100 feet of arc, and the radius for that degree 
of curve is found by dividing 5,730 feet, the radius of a one- 
degree curve, by the degree of curve desired expressed in degrees 
and decimals of a degree. That is, if the radius of a 3 30' curve 
is wanted, divide 5730 by 3.5, which equals 1637. i'. The radii 
given in Table No. 29 are computed in this manner. 

Length of curve. For a 5 curve a central angle of 5 subtends 

100' of arc; a central angle of io°, 200' of arc; a central angle of 

12 30', 250' of arc. That is, for a specified central angle the 

length of any specified curve equals that central angle expressed 

in degrees and decimals of a degree divided by the degree of 

curve expressed in degrees and decimals multiplied by 100; 

i.e., the length of a io° 15' curve for a central angle of 20 45' = 

20. 7 ^ 

X 100' = 202.4/and is expressed by the formula 



10.2 



Table 30. Functions of a One-Degree Curve Figured on a 
Basis of R = 5730' and Tabulated to Tenths of Feet 



Use 100' chords up to 8° Curves 
Use 50' chords up to 16 Curves 



Use 25' chords up to 3 2 Curves 
Use 10' chords above 32° Curves 























5 

c 

rr 


O" 




1 






3 


g 
B 

It- 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


O 


0.0 


0.0 


0.2 


50.0 


0.9 


100.0 


2.0 


150.1 


O 


IO 


0.0 


8.3 


0.3 


S8.3 


1.0 


108.4 


2.2 


158.4 


IO 


20 


0.0 


16.7 


0.4 


66.7 


1.2 


116. 7 


2.4 


166.8 


20 


30 


O.I 


25.0 


0.5 


75.o 


1.4 


125.0 


2.7 


I75-I 


30 


40 


O.I 


33-3 


0.6 


83.3 


1.6 


133-4 


2.9 


183.4 


40 


50 


0.2 


41.7 


0.7 


91.7 


1.8 


I4I-7 


3-2 


191. 7 


So 


6O 


0.2 


50.0 


0.9 


100.0 


2.0 


150.1 


3-5 


200.1 


60 


.. .__ 


















_,... 1 



FUNCTIONS OF THE ONE-DEGREE CURVE 171 



Use ioo' chords up to 8° Curves 
Use so' chords up to i6° Curves 



Use 25' chords up to 32 ° Curves 
Use 10' chords above 32 Curves 



c 


O S 
. t-i 
O tifl 


4 





5 




6 





7 





C 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 
300.3 


Ext. 


Tan. 





.0000 


3-5 


200.1 


5-5 


250.2 


7-9 


10.7 


350.4 





I 


.0167 


3-5 


200.9 


5-5 


251.0 


7-9 


301. 1 


10.8 


351.3 


I 


2 


•0333 


3-6 


201.8 


5-5 


251.8 


8.0 


302.0 


10.8 


352.1 


2 


3 


.0500 


3-6 


202.6 


5-6 


252.7 


8.0 


302.8 


10.9 


352.9 


3 


4 


.0667 


3-6 


203.4 


5-6 


253-5 


8.0 


303.6 


10.9 


353-8 


4 


5 


•0833 


3-6 


204.3 


5-6 


254-3 


8.1 


304-5 


11. 


354-6 


5 


6 


.1000 


3-7 


205.1 


5-7 


255-2 


8.1 


305-3 


11.0 


355-5 


6 


7 


.1167 


3-7 


205.9 


5-7 


256.0 


8.2 


306.1 


11. 1 


356.3 


7 


8 


.1333 


3-7 


206.8 


5-8 


256.8 


8.2 


307.0 


11. 1 


357.1 


8 


9 


.1500 


3-8 


207.6 


5-8 


257.7 


8-3 


307.8 


11. 2 


358.o 


9 


10 


.1667 


3-8 


208.4 


5-8 


258.5 


8.3 


308.6 


11. 2 


358.8 


10 


11 


.1833 


3-8 


209.3 


5-9 


259.3 


8.4 


309.5 


11.3 


359-6 


11 


12 


.2000 


3-9 


210. 1 


5-9 


260.2 


8.4 


310.3 


11.3 


360.5 


12 


13 


.2167 


3-9 


210.9 


5-9 


261.0 


8.4 


311.1 


11.4 


361.3 


13 


14 


.2333 


3-9 


211.8 


6.0 


261.9 


8.5 


312.0 


11.4 


362.2 


14 


IS 


.2500 


3-9 


212.6 


1 6.0 


262.7 


8-5 


312.8 


H-5 


363-0 


15 


16 


.2667 


4.0 


213.4 


6.1 


263.5 


8.6 


313.7 


11. 5 


363.8 


16 


17 


.2833 


4.0 


214.3 


6.1 


264.4 


8.6 


314.5 


11.6 


364.7 


I7 a 


18 


.3000 


4.0 


215. 1 


6.1 


265.2 


8.7 


315.3 


11. 7 


365.5 


I l8 


19 


.3167 


4.1 


215.9 


6.2 


266.0 


8-7 


316.2 


11. 7 


366.3 


19 


20 


•3333 


4.1 


216.8 


6.2 


266.9 


8.8 


317.0 


11.8 


367.2 


, 20 


21 


•3500 


4.1 


217.6 


6.2 


267.7 


8.8 


317.8 


11.8 


368.0 


21 


22 


.3667 


4.2 


218.4 


6.3 


268.5 


8.9 


318.7 


11.9 


368.8 


.22 


23 


.3833 


4.2 


219.3 


6.3 


269.4 


8.9 


319-5 


11.9 


369-7 


23 


24 


.4000 


4.2 


220.1 


6.4 


270.2 


9.0 


320.3 


12.0 


37o.5 


24 


25 


.4167 


4-3 


220.9 


6.4 


271.0 


9.0 


321.2 


12.0 


371.4 


! 25 


26 


•4333 


4-3 


221.8 


6.4 


271.9 


9.0 


322.0 


12. 1 


372.2 


26 


27 


.4500 


4-3 


222.6 


6-5 


272.7 


9.1 


322.8 


12. 1 


373-0 


27 


28 


.4667 


4.4 


223.5 


6-5 


273-5 


9.1 


323-7 


12.2 


373-9 


28 


29 


•4833 


4.4 


224.3 


6-5 


274.4 


9.2 


324-5 


12.2 


374-7 


29 


30 


.5000 


4.4 


225.1 


6.6 


275-2 


9.2 


325.4 


12.3 


375-5 


30 


3i 


•5167 


4-5 


226.0 


6.6 


276.1 


9-3 


326.2 


12.4 


376.4 


31 


32 


•5333 


4-5 


226.8 


6.7 


276.9 


9-3 


327.0 


12.4 


377-2 


32 


33 


•5500 


4-5 


227.6 


6.7 


277-7 


9.4 


327-9 


12.5 


378.1 


33 


34 


.5667 


4-6 


228.5 


6.8 


278.6 


9-4 


328.7 


12.5 


378.9 


34 


35 


.5833 


4.6 


229.3 


6.8 


279-4 


9-5 


329-5 


12.6 


379-7 


35 


36 


.6000 


4-6 


230.1 


6.8 


280.2 


9-5 


330.4 


12.6 


380.6 


36 


37 


.6167 


4-7 


331.0 


6.9 


281. 1 


9.6 


331.2 


12.7 


381.4 


37 


38 


•0333 


4-7 


231-8 


6.9 


281.9 


9.6 


332.0 


12.7 


382.2 


38 


39 


.6500 


4-7 


232.6 


7.0 


282.7 


9-7 


332-9 


12.8 


383.1 


39 


40 


.6667 


4.8 


233-5 


7.0 


283.6 


9-7 


333-7 


12.9 


383.9 


|40 


41 


.6833 


4.8 


234-3 


7-i 


284.4 


9-8 


334-6 


12.9 


384.7 


41 


42 


.7000 


4.8 


235-1 


7-i 


285.2 


9.8 


335-4 


13.0 


385.6 


42 


43 


.7167 


4.9 


236.0 


7-i 


286.1 


99 


336.2 


13-0 


386.4 


43 


44 


•7333 


4.9 


236.8 


7-2 


286.9 


9.9 


337-1 


I3-I 


387.3 


44 


45 


.7500 


4.9 


237.6 


7.2 


287.7 


10. 


337-9 


I3-I 


388.1 


45 


46 


.7667 


5.o 


238.5 


7.3 


288.6 


10.0 


338.7 


13-2 


388.9 


46 


47 


•7833 


5-0 


239-3 


7-3 


289.4 


IO.I 


339-6 


13.2 


389.8 


47 


48 


.8000 


5-0 


240.1 


7-3 


290.3 


10. 1 


340.4 


13.3 


390.6 


48 


49 


.8167 


5-i 


241.0 


7-4 


291. 1 


10.2 


341.2 


13-4 


391.4 


49 


SO 


.8333 


5-1 


241.8 


7-4 


291.9 


10.2 


342-1 


13-4 


392.3 


50 


51 


.8500 


5-i 


242.6 


7-5 


292.8 


10.3 


342-9 


13.5 


393-1 


51 


52 


.8667 


5-2 


243-5 


7-5 


293-6 


10.3 


343-7 


13.5 


394-o 


52 


53 


.8833 


5-2 


244-3 


7-5 


294.4 


10.4 


344-6 


13-6 


394-8 


53 


54 


.9000 


5-2 


245-2 j 


7-6 


295-3 


10.4 


345-4 


13-7 


395-6 


|54 


55 


.9167 


5-3 


246.0 


7-6 


296.1 


10.5 


346.3 


13-7 


396.5 


|55 


56 


•9333 


5-3 


246.8 


7-7 


296.9 


10.5 


347-1 


13-8 


397-3 


56 


57 


.9500 


5-3 


247.7 i 


7-7 


297.8 


10.6 


347-9 


13-8 


398.1 


57 


58 


.9667 


5-4 


248.5 \ 


7-8 


298.6 


10.6 


348.8 


13-9 


399-0 


58 


59 


.9833 


5-4 


249-3 ! 


7-8 


299.4 


10.7 


349-6 


139 


399-8 


l» 



172 



THE SURVEY 





Use ioc 


' Chords 


up to 8 


3 Curves 


Use 


25' Chords up to 


32 Curves 




Use 50' 


Chords 


up to 16 


3 Curves 


Use 


io' Chords above 


3 2 Curves 


m 

-4-> 

3 
G 

§ 




O Z 
<i to 


8 





9° 


io° 


ii° 


m 

<u 

C 

9 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


14.0 


400.7 


17.7 


450.9 


21.9 


501.3 


26.5 


551-7 


I 


.0167 


14.0 


401.5 


17.8 


451.8 


21.9 


502.2 


26.6 


552.6 


1 


2 


•0333 


14.1 


402.4 


17.8 


452.6 


22.0 


503-0 


26.7 


553-4 


2 


3 


.0500 


14.2 


403.2 


17.9 


453-4 


22.1 


503.8 


26.7 


554-3 


3 


4 


.0667 


14.2 


404.0 


18.0 


454-3 


22.2 


504.7 


26.8 


555-1 


4 


5 


.0833 


14-3 


404.8 


18.0 


455-1 


22.3 


505.5 


26.9 


555-9 


5 


6 


.1000 


14-3 


405-7 


18.1 


456.0 


22.3 


506.4 


27.0 


556.8 


6 


7 


.1167 


14.4 


406.5 


18.2 


456.8 


22.4 


507.2 


27.1 


557-6 


7 


8 


.1333 


14.5 


407.4 


18.3 


457-7 


22.5 


508.0 


27.2 


558.5 


8 


9 


.1500 


14-5 


408.2 


18.3 


458.5 


22.6 


508.9 


27.2 


559.3 


9 


10 


.1667 


14.6 


409.0 


18.4 


459-3 


22.6 


509.7 


27.3 


560.1 


10 


11 


.1833 


14.6 


409.9 


18.4 


460.2 


22.7 


510.6 


27.4 


561.0 


11 


12 


.2000 


14.7 


410.7 


18.5 


461.0 


22.8 


511.4 


27-5 


561.8 


12 


13 


.2167 


14.8 


4H-5 


18.6 


461.8 


22.9 


512.2 


27.6 


562.7 


13 


14 


.2333 I 


14.8 


412.4 


18.7 


462.7 


22.9 


5I3-I 


27.7 


563.5 


14 


15 


.2500 


14.9 


413.2 


18.7 


463.5 


23.0 


5I3.9 


27.7 


564.3 


15 


16 


.2667 


14.9 


4I4-I 


18.8 


464.4 


23.1 


514.8 


27.8 


565.2 


16 


17 


.2833 


15-0 


414.9 


18.9 


465.2 


23.2 


515.6 


27.9 


566.0 


17 


18 


.3000 


i5-i 


415-7 


18.9 


466.0 


23.2 


516.4 


28.0 


566.9 


18 


19 


•3167 


I5-I 


416.6 


19.0 


466.9 


23.3 


517.3 


28.1 


567.7 


19 


20 


■3333 


15.2 


417.4 


19. 1 


467.7 


23-4 


518.1 


28.1 


568.5 


20 


21 


.35oo 


15-2 


418.2 


19. 1 


468.5 


23.5 


519.0 


28.2 


569.4 


21 


22 


.3667 


15.3 


4I9-I 


19.2 


469.4 


23.5 


519.8 


28.3 


57o.2 


22 


23 


•3833 ! 


15.4 


419.9 


19-3 


470.2 


23.6 


520.6 


28.4 


57i. 1 


23 


24 


.4000 


15.4 


420.8 


19-3 


471. 1 


23.7 


521.5 


28.5 


571.9 


24 


25 


.4167 


15.5 


421.6 


19.4 


471.9 


23.8 


522.3 


28.6 


572.8 


25 


26 


•4333 


15.6 


422.4 


19-5 


472.8 


23.8 


523-2 


28.6 


573-6 


26 


27 


.4500 


15.6 


423.3 


19.5 


473-6 


23-9 


524-0 


28.7 


574-4 


27 


28 


.4667 j 


15.7 


424.1 


19.6 


474-4 i 


24.0 


524-9 


28.8 


575-3 


28 


29 


•4833 j 


15.7 


424.9 


19.7 


475-3 j 


24.1 


525-7 


28.9 


576.1 


29 


30 


.5000 


15-8 


425.8 


19.8 


476.1 ! 


24.1 


526.5 


29.0 


577.o 


30 


3i 


.5167 


15-9 


426.6 


19.8 


476.9 1 


24.2 


527.4 


29.1 


577-8 


3i 


32 


•5333 ! 


15-9 


427-5 


19.9 


477-8 ; 


24-3 


528.2 


29.1 


578.6 


32 


33 


•5500 j 


16.0 


428.3 


20.0 


478.6 


24.4 


529.0 


29.2 


579-5 


33 


34 


•5667 ! 


16.0 


429.1 


20.0 


479-5 


24-5 


529-9 


29-3 


580.3 


34 


35 


.5833 ! 


16.1 


430.0 


20.1 


480.3 


24.5 


530.7 


29.4 


581.2 


35 


36 


.6000 


16.2 


430.8 


20.2 


481. 1 


24.6 


531.6 


29-5 


582.0 


36 


37 


.6167 


16.2 


431-7 


20.2 


482.0 


24.7 


532-4 


29.6 


582.8 


37 


38 


•6333 


16.3 


432.5 


20.3 


482.8 


24.8 


533-3 1 


29.7 


583.7 


38 


39 


.6500 


16.4 


433-3 


20.4 


483-6 


24.8 


534-1 . 


29.7 


584.5 


39 


40 


.6667 


16.4 


434-2 


20.5 


484.5 


24.9 


534 9' 


29.8 


585.4 


40 


41 


•6833 ! 


16.5 


435.o 


20.5 


485.3 


25.0 


535-8 


29.9 


586.2 


4i 


42 


.7000 


16.6 


435-9 


20.6 


486.2 


25.1 


536.6 


30.0 


587.1 


42 


43 


.7167 


16.6 


436.7 


20.7 


487.0 


25.1 


537-5 


30.1 


587.9 


43 


44 


.7333 


16.7 


437-5 


20.7 


487.9 


25-2 


538.3 


30.2 


588.7 


44 


45 


■7500 


16.7 


438.4 


20.8 


488.7 


25.3 


539-1 


30.3 


589.6 


45 


46 


.7667 


16.8 


439-2 


20.9 


489.6 


25.4 


540.0 


30.3 


590.4 


46 


47 


•7833 


16.9 


440.0 


21.0 


490.4 


25-5 


540.8 


30.4 


591-3 


47 


48 


.8000 


16.9 


440.9 


21.0 


491.2 


25.5 


541-7 


30.5 


592.1 


48 


49 


.8167 1 


17.0 


441.7 


21. 1 


492.0 


25.6 


542.5 


30.6 


592.9 


49 


50 


.8333 ! 


17. 1 


442.5 


21.2 


492.9 


25-7 


543-3 


30.7 


593-8 


50 


51 


.8soo 


17. 1 


443-4 


21.2 


493-7 


25.8 


544-2 


30.8 


594-6 


51 


52 


.8667 


17.2 


444.2 


21.3 


494-6 


25-9 


545-0 


30.9 


595-5 


52 


53 


.8833 


17-3 


445-1 


21.4 


495-4 


25-9 


545-9 


31.0 


596.3 


53 


54 


.9000 


17-3 


445-9 


21.5 


496.3 


26.0 


546.7 


3i.o 


597-2 


54 


55 


.9167 


17.4 


446.7 


21.5 


497-1 


26.1 


547-5 


311 


598.o 


55 


56 


•9333 


17.5 


447.6 


21.6 


498.0 


26.2 


548.4 


31.2 


598.8 


56 


57 


.95oo 


17-5 


448.4 


21.7 


498.8 


26.3 


549-2 


31.3 


599-7 


57 


58 


.9667 


17.6 


449-3 


21.8 


499-6 


26.3 


550.I 


31.4 


600.5 


58 


,59 


•9833 


17.6 


450.I 


21.S 


500.4 


26.4 


550.9 


31-5 


601.4 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 173 



Use 100' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



Use 25' Chords up to 32 Curves 
Use 10' Chords above 32° Curves 



en 

•4-J 


c u 


12° 


13° 


'*' 


15° 


en 

CD 
+J 

3 
C 

s 



Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


31.6 


602.2 


37-i 


652.9 


43.o 


703-5 


49.4 


754-4 


I 


.0167 


3i-7 


603.1 


37-2 


653-7 


43-1 


704.4 


49.6 


755-2 


I 


2 


•0333 


3i-7 


603.9 


37-3 


654.6 


43-2 


705.2 


49-7 


756.1 


2 


3 


.0500 


31-8 


604.7 


37-4 


655-4 


43-3 


706.1 


49-8 


756.9 


3 


4 


.0667 


3i-9 


605.6 


37-5 


656.3 


43-4 


706.9 


49.9 


757-7 


4 


5 


.0833 


32.0 


606.4 


37-6 


657-1 


43-5 


707.8 


50.0 


758.6 


5 


6 


.1000 


32.1 


607.3 


37-7 


657-9 


43-7 


708.6 


50.1 


759-4 


6 


7 


.1167 


32.2 


608.1 


37-7 


658.8 


43-8 


709.5 


50.2 


760.3 


7 


8 


•1333 


32.3 


609.0 


37.8 


659-6 


43-9 


710.3 


50.3 


761. 1 


8 


9 


.1500 


32.4 


609.8 


37-9 


660.5 


44.0 


711. 2 


50.5 


762.0 


9 


10 


.1667 


32.5 


610.7 


38.0 


661.3 


44.1 


712.0 


50.6 


762.8 


10 


11 


•1833 


32.5 


611. 5 


38.1 


662.2 


44.2 


712.9 


50.7 


763.7 


! 11 


12 


.2000 


32.6 


612.4 


38.2 


663.0 


44-3 


713-7 


50.8 


764-5 


12 


13 


.2167 


32.7 


613.2 


38.3 


663.8 


44.4 


714-6 


50.9 


765-4 


13 


14 


•2333 


32.8 


614.0 


38.4 


664.7 


44-5 


715.4 


5I.O 


766.2 14 


IS 


.2500 


32.9 


614.9 


38.5 


665.5 


44-6 


716.3 


5I.I 


767.1 


15 


16 


.2667 


33-0 


6i5-7 


38.6 


666.4 


44-7 


717-1 


51.2 


767.9 


16 


17 


.2833 


33-t 


616.6; 


38.7 


667.2 


44.8 


718.0 


51.3 


768.8 


17 


18 


.3000 


33-2 


617.4! 


38.8 


668.1 


44-9 


718.8 


51-5 


769.6 


18 


19 


.3167 


33-3 


618.3 ! 


38.9 


668.9 


45-o 


719.6 


51-6 


770.5 19 


20 


.3333 


33-4 


619.1 


39-o 


669.8 


45-i 


720.5 


51.7 


771.3 


20 


21 


•3500 


33-4 


619.9 


39-i 


670.6 


45-2 


721.3 


51.8 


772.2 


21 


22 


.3667 


33-5 


620.8 j 


39-2 


671.4 


45-3 


722.2 


51-9 


773.o 


22 


23 


•3833 


33-6 


621.6 j 


39-3 


672.3 


45-4 


723.1 


52.0 


773-9 


23 


24 


.4000 


33-7 


622.5 


39-4 


673.1 


45-5 


723.9 


52.1 


774-7 


24 


25 


.4167 


33-8 


623.3 


39-5 


674-0 


45-6 


724.7 1 


52 3 


775-6 


25 


26 


.4333 


33-9 


624.2 


39-6 


674-8 


45-8 


725-6, 


52.4 


776.4 


26 


27 


.4500 


34-o 


625.0 


39-7 


675-7 


45-9 


726.5 


52.5 


777-3 


27 


28 


.4667 


34-1 


625.9 


39-8 


676.5 


46.0 


727.3 


52.6 


778.1 


28 


29 


.4833 


34-2 


626.7 


39-9 


677.4 


46.1 


728.1 


52.7 


778.9 29 


30 


.5000 


34-3 


627.6 


40.0 


678.2 


46.2 


729.0 


52.8 


779-8 30 


3i 


•5167 


34-4 


628.4 


40.1 


679.0 


46.3 


729.8 


52.9 


780.6 31 


32 


•5333 


34-5 


629.2 


40.2 


679-9 


46.4 


730.7 


53-i 


781.5 32 


33 


•5500 


34-5 


630.1 


40-3 


680.7 


46.5 


731.5 


53-2 


782.3 33 


34 


.5667 


34-6 


630.9 


40.4 


681.6 


46.6 


732.4 


53-3 


783-2 34 


35 


.5833 


34-7 


631.8 


40.5 


682.4 


46.7 


733-2 


53-4 


784.0 35 


36 


.6000 


34-8 


632.6 


40.6 


683.3 


46.8 


734-o 


53-5 


784.9 


36 


37 


.6167 


34-9 


633-5 


40.7 


684.1 


46.9 


7349 '< 


53-6 


785.7 


37 


38 


•6333 


35-o 


634-3 


40.8 


685.0 


47.0 


735-7 | 


53-7 


786.6 


38 


39 


.6500 


35-1 


635.1 


40.9 


685.8 


47.2 


736.6 


53-9 


787.4 


39 


40 


.6667 


35-2 


636.0 


41.0 


686.6 


47-3 


737-4 


54-o 


788.3 


40 


41 


.6833 


35-3 


636.8 


41. 1 


687.5 


47-4 


738.3 


54-i 


7S9.1 


41 


42 


.7000 


35-4 


637-7 


41.2 


688.3 


47-5 


739-1 


54-2 


790.0 


42 


43 


.7167 


35-5 


638.5 


4i-3 


689.2 


47.6 


740.0 


54-3 


790.8 


43 


44 


.7333 


35-6 


639-4 


41.4 


690.0 


47-7 


740.8 


54-4 


791.7 


44 


45 


.7500 


35-7 


640.2 


4i-5 


690.9 


47-8 


741.7 


54-6 


792.5 


45 


46 


.7667 


35-8 


641. 1 


41.6 


691.7 


47-9 


742.5 


54-7 


793-4 


46 


47 


.7833 


35-8 


641.9 


41.7 


692.5 


48.0 


743-4 


54-8 


794-2 


47 


48 


.8000 


35-9 


642.7 


41.8 


693.4 


48.1 


744.2 


54-9 


795-1 


48 


49 


.8167 


36.0 


643.6 


41.9 


694.2 


48.2 


745-1 


55-o 


795-9 


49 


5o 


.8333 


36.1 


644.4 


42.0 


695-1 


48.3 


745-9 


55-i 


796.8 


50 


51 


.8500 


36.2 


645-3 


42.1 


695-9 


48.5 


746.7 


55-3 


797-6 


51 


52 


.8667 


36.3 


646.1 


42.2 


696.8 


48.6 


747.6 


55-4 


798.5 


52 


53 


.8833 


36.4 


647.0 


42-3 


697.6 


48.7 


748.4 


55-5 


799-3 


53 


54 


.9000 


36.5 


647.8 


42.4 


698.5 


48.8 


749-3 


55-6 


800.2 


54 


55 


.9167 


36.6 


648.6 


42-5 


699-3 


48.9 


750.I 


55-7 


8ot.o 


55 


56 


•9333 


36 A 


649-5 


42.6 


700.1 


49.0 


75i -o 


55-8 


801.9 


56 


57 


.9500 


36.8 


650.3 


42.7 


701.0 


49-1 


751-8 


56.0 


802.7 


57 


58 


.9667 


36.9 


651.2 


42.8 


701.8 


49.2 


752.7 


56.1 


803.6 


58 


59 


.9833 


37-° 


652.0 


42.9 


702.7 


49-3 


753-5 


56.2 


804.4 


59 j 



174 

Use ioo' ^fiords u 
Use 50' Chords up 



THE SURVEY 



Curves 





u to 

1) 


1 


6° 


17° 


. 


8° 


1 


f 


tn 

<u 

+5 

C 


















§ 


QQ 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


O 


O 


.0000 


56.3 


805.3 


63.6 


856.4 


71.4 


907.5 


79-7 


958.9 


I 


.0167 


56.4 


806.2 


63.8 


857.2 


71.6 


908.4 


79-8 


959-7 


I 


2 


•0333 


56.5 


807.0 


63-9 


858.1 


71.7 


909.2 


79-9 


960.6 


2 


3 


.0500 


56.7 


807.8 


64.0 


858.9 


71.8 


910. 1 


80.1 


961.4 


3 


4 


.0667 


56.8 


808.6 


64.2 


859.8 


72.0 


910.9 


80.2 


962.3 


4 


5 


•0833 


56.9 


809.5 


64.3 


860.6 


72.1 


911.8 


80.4 


963.2 


5 


6 


.1000 


57-o 


810.4 


64.4 


861.5 


72.2 


912.7 


80. < 


964.0 


6 


7 


.1167 


57-1 


811. 2 


64.5 


862.3 


72.4 


913-5' 


80.7 


964.9 


7 


8 


.1333 


57-3 


812. 1 


64.7 


863.2 


72.5 


914-4 


80.8 


965.7 


8 


9 


.1500 


57-4 


812.9 


64.8 


864.0 


72.6 


915.2 


80.9 


966.6 


9 


IO 


.1667 


57-5 


813.8 


64.9 


864.9 


72.8 


916. 1 


81. 1 


967.4 


10 


ii 


•1833 


57-6 


814.6 


65.0 


865.7 


72.9 


916.9 


81.2 


968.3 


11 


12 


.2000 


57-7 


815.5 


65.2 


866.6 


73.o 


917.8 


81.4 


969.2 


12 


13 


.2167 


57-9 


816.3 


65-3 


867.4 


73-2 


918.6 


81.5 


970.0 


13 


14 


.2333 


58.0 


817.2 


65.4 


868.3 


73-3 


919.5 


81.7 


970.9 


14 


15 


.2500 


58.1 


818.0 


65.6 


869.1 


73-4 


920.3 


81.8 


971.7 


15 


16 


.2667 


58.2 


818.9 


65-7 


870.0 


73 -6 


921.2 


81.9 


972.6 


16 


17 


.2833 


58.3 


819.7 


65.8 


870.8 


73.7 


922.0 


82.1 


973-4 


i 17 


18 


.3000 


58.5 


820.6 


65-9 


871.7 


73-9 


922.9 


82.2 


974-3 


18 


19 


.3167 


S8.6 


821.4 


66.1 


872.5 


74.0 


923-8 


82.4 


975-1 


19 


20 


•3333 


58.7 


822.3 


66.2 


873.4 


74.1 


924.6 


82.5 


976.0 


20 


21 


.3500 


58.8 


823.1 


66.3 


874.2 


74-3 


925.5 


82.7 


976.9 


21 


22 


.3667 


58.9 


824.0 


66.4 


875.1 


74-4 


926.3 


82.8 


977-7 


'22 


23 


.3833 


59-1 


824.8 


66.6 


875.9 


74-5 


927.2 


82.9 


978.6 


23 


24 


.4000 


59-2 


825.7 


66.7 


876.8 


74-7 


928.1 


83.1 


979-4 


i 24 


25 


.4167 


59*3 


826.5 


66.8 


877.6 


74-8 


928.9 


83.2 


980.3 


25 


26 


•4333 


59-4 


827.4 


67.0 


878.5 


74-9 


929.8 


83.4 


981.2 


26 


27 


.4500 


59-6 


828.2 


67.1 


879.3 


75-i 


930.6 


83.5 


982.0 


27 


28 


.4667 


59-7 


829.1 


67.2 


880.2 


75-2 


931-5 


83.7 


982.9 


28 


29 


.4833 


59-8 


829.9 


67.3 


881.0 


75-4 


932.3 


83.8 


983.7 


29 


30 


.5000 


59-9 


830.8 


67.5 


881.9 


75-5 


933-2 


84.0 


984.6 


30 


31 


.5167 


60.0 


831.6 


67.6 


882.7 


75-6 


934-0 


84.1 


985.4 


31 


32 


•5333 


60.2 


832.5 


67.7 


883.6 


75-8 


934-9 


84-3 


986.3 


32 


33 


.5500 < 


60.3 


833-3 


67.9 


884.5 


75-9 


935-7 


84.4 


987.2 : 


33 


34 


.5667 


60.4 


834.2 


68.0 


885.3 


76.1 


936.6 


84.6 


988.0 


34 


35 


.5833 


60.5 


835.1 


68.1 


886.2 


76.2 


937-5 


84.7 


988.9 


35 


36 


.6000 


60.7 


835.9 


68.2 


887.0 


76.3 


938.3 


84.8 


989-7 


36 


37 


.6167 


60.8 


836.8 


68.4 


887.9 


76.5 


939.2 


85.0 


990.6 


i 3 Z 


38 


•6333 


60.9 


837.6 


68.5 


888.7 


76.6 


940.0 


85.1 


991-5 


38 


39 


.6500 


61.0 


838.5 


68.6 


889.6 


76.7 


940.9 


85.3 


992.3 


39 


40 


.6667 


61. 1 


839.3 


68.8 


890.4 


76.9 


941.7 


85.4 


993-2 


40 


4i 


•6833 


61.3 


840.2 


68.9 


891.3 


77.o 


942.6 


85.6 


994.0 


41 


42 


.7000 


61.4 


841.0 


69.0 


892.2 


77.1 


943-5 


85.7 


994.9 


42 


43 


.7167 


61.5 


841.9 


69.2 


893-0 


77-3 


944-3 


85.9 


995-8 


43 


44 


•7333 


61.6 


842.7 


69-3 


893-9 


77-4 


945-2 


86.0 


996.6 


44 


45 


.7500 


61.8 


843-6 


69.4 


894-7 


77.6 


946.0 


86.2 


997-5 


45 


46 


.7667 


61.9 


844.4 


69.6 


895.6 


77-7 


946.9 


86.3 


998-3 


46 


47 


.7833 


62.0 


845-3 


69.7 


896.4 


77-8 


947-7 


86.5 


999-2 


4 l 


48 


.8000 


62.1 


846.1 


69.8 


897.3 


78.0 


948.6 


86.6 


1000. 


48 


49 


.8167 


62.3 


847-0 


70.0 


898.1 


78.1 


949-4 


86.8 


1000.9 


49 


5o 


•8333 


62.4 


847.8 


70.1 


899.0 


78.3 


950.3 


86.9 


1001.8 


50 


5i 


.8500 


62. <5 


848.7 


70.2 


899-8 


78.4 


95i-i 


87.1 


1002.6 


51 


52 


.8667 


62.6 


849-5 


70.4 


900.7 


78.5 


952.o 


87.2 


1003.5 


52 


53 


•8833 


62.8 


850.4 


70.5 


901.5 


78.7 


952.9 


87.4 


1004.3 


53 


54 


.9000 


62.9 


851.2 


70.6 


902.4 


78.8 


953-7 


87.5 


1005.2 


54 


55 


.9167 


63.0 


852.1 


70.8 


903-3 


79.0 


954-6 


87.7 


1006.0 


55 


56 


•9333 


63.1 


852.9 


70.9 


904.1 


79.1 


955-4 


87.8 


1006.9 


56 


57 


.9500 


63.3 


853-8 


71.0 


905.0 


79.2 


956.3 


•88.0 


1007.7 


5 l 


58 


.9667 


63-4 


854.7 


71.2 


905-8 


79-4 


957-2 


88.1 


1008.6 


58 


59 


.9833 


63-5 


855.5 


7i.3 


906.7 


79-5 


958.o 


88.2 


1009.5 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 175 



Use ioo' Chords up to 8' 
Use 50' Chords up to 16 



Curves 
Curves 



Use 25' Chords up to 32 
Use 10' Chords above 32 



<u 

+■> 

a 

3 




O 0) 


20° 


21° 


22° 


23° 


3 

-fi 

3 
C 

S 
O 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


88.4 


1010.4 


97.6 


1062.0 


IO7.2 


1113.8 


117.4 


1165.8 


1 


.0167 


88.5 


1011.2 


97-7 


1062.8 


IO7.4 


1114.6 


117. 6 


1166.6 


I 


2 


.0333 


88.7 


1012.1 


97-9 


1063.7 


IO7.6 


1115.5 


117. 7 


1167-5 


2 


3 


.0500 


88.8 


1012.9 


98.1 


1064.5 


IO7.7 


1116.4 


117.9 


1 168.3 


3 


4 


.0667 


89.0 


1013.8 


98.2 


1065.4 


IO7.9 


1117.3 


118. 1 


1169.2 


4 


5 


•0833 


89.1 


1014.6 


98.4 


1066.3 


I08.0 


1118.1 


118.3 


1170.1 


5 


6 


.1000 


89.3 


1015-5 


98.5 


1067.2 


I08.2 


1119.0 


118.4 


117 1. 


6 


7 


.1167 


89.4 


1016.3 


98.7 


1068.0 


I08.4 


1119.8 


118.6 


1171.8 


7 


8 


•1333 


89.6 


1017.2 


98.8 


1068.9 


IO8.6 


1120.7 


118.8 


1172.7 


8 


9 


.1500 


89.7 


1018.1 


99.0 


1069.7 


I08.7 


1121.5 


118.9 


H73-5 


9 


10 


.1667 


89.9 


1019.0 


99.2 


1070.6 


I08.9 


1122.4 


119. 1 


H74-4 


10 


11 


.1833 


90.0 


1019.8 


99-3 


1071.5 


IO9.O 


1123.3 


H9-3 


H75-3 


11 


12 


.2000 


90.2 


•1020.7 


99-5 


1072.4 


IO9.2 


1124.2 


II95 


1176.2 


12 


13 


.2167 


90.3 


1021.5 


99.6 


1073.2 


IO9.4 


1125.0 


II9-7 


1177.0 


13 


14 


•2333 


90.5 


1022.4 


99-8 


1074.1 


IO9.6 


1125.9 


119.8 


1177.9 


14 


15 


.2500 


90.6 


1023.2 


99-9 


1074.9 


IO9.7 


1126.7 


120.0 


1178.8 


15 


16 


.2667 


90.8 


1024. 1 


100. 1 


1075.8 


IO9.9 


1127.6 


120.2 


1179.7 


16 


17 


•2833 


90.9 


1024.9 


100.2 


1076.6 


IIO.O 


1128.5 


120.4 


1180.5 


17 


18 


.3000 


91. 1 


1025.8 j 


100.4 


1077.5 


HO.2 


1129.4 


120.5 


1181.4 


18 


19 


.3167 


91.2 


1026.7 


100.5 


1078.4 


IIO.4 


1130.2 


120.7 


1182.2 


19 


20 


■3333 


91.4 


1027.6 


100.7 


1079-3 


I IO.6 


1131.1 


120.9 


1183.I 


20 


21 


•3500 


91.6 


1028.4 


100.9 


1080. 1 


HO.7 


1131.9 


1 21.0 


1184.0 


21 


22 


.3667 


91.7 


1029.3 


IOI.I 


1081.0 


no. 9 


1132.8 


121. 2 


1184.9 


22 


23 


•3833 


91.9 


1 030. 1 | 


IOI.2 


1081.8 


III.O 


II33.7 


121. 4 


1185.7 


23 


24 


.4000 


92.0 


103 1. 


IOI.4 


1082.7 


in. 2 


1134.6 


121.6 


1186.6 


24 


25 


.4167 


92.2 


1031.8 


IOI.5 


1083.5 


111.4 


"35.4 


121. 7 


1187.5 


25 


26 


•4333 


92.3 


1032.7 


IOI.7 


1084.4 


111.6 


1136.3 


121.9 


1188.4 


26 


27 


•4500 


92.5 


IQ33-5 


101.8 


1085.3 


in. 7 


1137.1 


122. 1 


1189.2 


27 


28 


.4667 


92.6 


1034.4 


102.0 


1086.2 


111.9 


1138.0 


122.3 


1190.1 


28 


29 


•4833 


92.8 


1035.2 


102. 1 


1087.0 


112. 1 


1138.8 


122.4 


1190.9 


29 


30 


.5000 


92.9 


1036.1 


102.3 


1087.9 


112. 3 


H39-7 


1 2 2.6 


1191.8 


30 


31 


•5167 


93-1 


1037.0 


102.5 


1088.7 


112.4 


1140.6 


122.8 


1192.7 


3i 


32 


•5333 


93-2 


1037.9 


102.7 


1089.6 


112. 6 


1141.5 


123.0 


1 193.6 


32 


33 


•55oo 


93-4 


1038.7 


102.8 


1090.4 


112.7 


1142.3 


123.2 


1194.4 


33 


34 


•5667 


93-5 


1039.6 


103.0 


1 09 1. 3 


112. 9 


H43-2 


123.3 


"95-3 


34 


35 

36 


.5833 


93-7 


1040.4 


103. 1 


1092.2 


113. 1 


1 144.0 


123.5 


1196.2 


35 


.6000 


93-9 


1041-3 


103.3 


1093. 1 


II3-3 


1144.9 


123.7 


1197.1 


36 


37 


.6167 


94.0 


1042. 1 


103.4 


1093.9 


H3-4 


H45-8 


123.9 


H97-9 


37 


38 


•6333 


94.2 


1043.0 


103.6 


1094.8 


113-6 


1146.7 


124. 1 


1198.8 


38 


39 


.6500 


94-3 


1043.9 


103.8 


1095.6 


H3-7 


II47.5 


124.3 


1199.6 


39 


40 


.6667 


94-5 


1044.8 


104.0 


1096.5 


II3-9 


1 148.4 


124.4 


1200.5 


40 


41 


.6833 ! 


94.6 


1045.6 


104. 1 


1097.4 


114.1 


1149.2 


124.6 


1201.4 


4i 


42 


.7000 j 


94-8 


1046.5 


104.3 


1098.3 


H4-3 


1150.1 


124.8 


1202.3 


42 


43 


.7167 


94.9 


1047.3 


104.4 


1099. 1 


114.4 


1151-0 


124.9 


1203. 1 


43 


44 


•7333 


95-1 


1048.2 


104.6 .1100.0 


II4.6 


1151.9 


125. 1 


1204.0 


44 


45 


•750O 


95-2 


1049.0 


104.7 


1 100.8 


II4.8 


1152.7 


125.3 


1204.9 


45 


46 


.7667 


95-4 


1049-9 


104.9 


1101.7 


115.0 


H53-6 


125-5 


1205.8 


46 


47 


.7833 


95-6 


1050.8 


105. 1 


1102.5 


II5- 2 


II54.5 


125-7 


1206.7 


47 


48 


.8000 


95-7 


1051.7 


105.3 


1103.4 


II5.3 


II55.4 


125.8 


1207. 5 


48 


49 


.8167 


95-9 


1052.5 


105.4 


1 104.3 


H5-5 


1156.2 


126.0 


1208.3 


49 


50 


•8333 

.8500 


96.0 


1053-4 


105.6 


1105.2 


H5-7 


1157.1 


126.2 


1209.2 


50 


51 


96.2 


1054.2 


105.7 


1106.0 


115.8 


H57-9 


126.4 


1210.1 


51 


52 


.8667 


96.3 


1055. 1 


105.9 


1 106.9 


116. 


1158.8 


126.6 


1211.0 


52 


53 


•8833 


96.5 


IQ55-9 


106. 1 


1107.8 


116. 1 


H59-7 


126.7 


1211.8 


53 


54 


.9000 


96.7 


1056.8 


106.3 


1108.6 


116.3 


1160.6 


126.9 


1212.7 


54 


55 


.9167 


96.8 


IQ57-7 


106.4 


1 109.4 


116.5 


1161.4 


127. 1 


1213.6 


55 


56 


•9333 


97-o 


1058.6 


106.6 


1110.3 


116.7 


1162.3 


127.3 


1214-5 


56 


57 


.9500 


97.1 


1059.4 


106.7 


IIII. 2 


116.8 


1163.1 


127.5 


1215.3 


57 


58 


.9667 


97-3 


1060.3 


106.9 


1112.1 


117. 


1 164.0 


127.6 


1216.2 


58 


59 


•9833 


97-4 


1061.1 


107.0 


1112.9 


117. 2 


1164..9 


127.8 


1217.1 


59 



176 



THE SURVEY 





Use 50 


' Chords 


up to it 


Curves Use 10' Chords above 32 Curves 




(A 
+-> 

O 


QQ 


24° 


25° 


26 


27° 


w 

<L> 

c 

9 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 
1375-6 


.0000 


128.0 


1218.0 


139.1 


1270.3 


150.7 


1322.9 


162.8 


I 


.0167 


128.2 


1218.8 


139.3 


1271.1 


150.9 


1323.7 


163.0 


1376.5 


I 


2 


.0333 


128.4 


1219.7 


139.5 


1272.0 


151. 1 


1324.6 


163.2 


1377-4 


2 


3 


.0500 


128.5 


1220.5 


139-7 


1272.9 


151.3 


1325.5 


163.5 


1378.3 


3 


4 


.0667 


128.7 


1221.4 


139-9 


1273-8 


I5I-5 


1326.4 


163.7 


1379.2 


4 


5 


■0833 


128.9 


1222.3 


1 40. 1 


1274.6 


151.7 


1327.3 


163.9 


1380.0 


5 


6 


.1000 


129. 1 


1223.2 


140.3 


1275-5 


151.9 


1328. 1 


164. 1 


1380.9 


6 


7 


.1167 


129.3 


1224.0 


140.4 


1276.4 


152. 1 


1329 


164.3 


1381.8 


7 


8 


•1333 


1295 


1224.9 


140.6 


1277.3 


152.3 


1329.9 


164.5 


1382.7 


8 


9 


.1500 


129.7 


1225.8 


140.8 


1278.2 


152.5 


1330.7 


164.7 


1383.6 


9 


IO 


.1667 


129.8 


1226.7 


141.0 


1279. 1 


152.7 


1331.6 


164.9 


1384.5 


10 


ii 


.1833 


130.0 


1227.5 


141. 2 


1279.9 


152.9 


1332.5 


165. 1 


1385.3 


11 


12 


.2000 


130.2 


1228.4 


141.4 


1280.8 


I53-I 


1333.4 


165.3 


1386.2 


12 


13 


.2167 


130.4 


1229.3 


141. 6 


1281.6 


153-3 


1334-3 


165.5 


J387.1 


13 


14 


•2333 


130.6 


1230.2 


141.8 


1282.5 


153.5 


1335.2 


165.7 


1388.0 


14 


15 


.2500 


130.7 


1231.0 


142.0 


1283.4 


153-7 


1336.0 


165.9 


1388.9 


15 


16 


.2667 


130.9 


1231.9 


142.2 


1284.3 


153-9 


1336.9 


166. 1 


1389.8 


16 


17 


.2833 


131-1 


1232.7 


142.3 


1285.2 


I54-I 


1337-8 


166.3 


1390.6 


17 


18 


.3000 


131-3 


1233.6 


142.5 


1286. 1 


154-3 


1338.7 


166.5 


I39I.5 


18 


19 


.3167 


I3I-5 


1234-5 


142.7 


1286.9 


154-5 


1339.5 


166.7 


1392.4 


19 


20 


•3333 


131.7 


1235-4 


142.9 


1287.8 


154-7 


1340.4 


167.0 


1393.3 


CO 


21 


•35oo 


i3i-9 


1236.2 


143. 1 


1288.7 


154-9 


I34I-3 


167.2 


1394.1 


21 


22 


.3667 


132.0 


1237. 1 


143-3 


1289.6 


155. 1 


1342.2 


167.4 


I395-0 


22 


23 


.3833 


132.2 


1238.0 


143-5 


1290.4 


155-3 


I343-Q 


167.6 


1395-9 


23 


24 


.4000 


132.4 


1238.9 


143-7 


1291.3 


155.5 


1343.9 


167.8 


1396.8 


24 


25 


.4167 


132.6 


1239.7 


143-9 


1292.2 


155-7 


1344.8 


168.0 


1397-7 


25 


26 


•4333 


132.8 


1240.6 


144.1 


1293-1 


155-9 


1345.7 


168.2 


1398.6 


26 


27 


.4500 


i33-o 


1241-5 


144-3 


1293.9 


156.1 


1346.5 


168.4 


I3Q9-4 


27 


28 


.4667 


133. 1 


1242.4 


144-5 


1294.8 


156.3 


1347.4 


168.6 


1400.3 


28 


29 


.4833 


133-3 


1243.2 


144.7 


1295-7 


156.5 


1348.3 


168.9 


1401.2 


29 


30 


.5000 


133-5 


1244-1 


144.9 


1296.6 


156.7 


1349.2 


169. 1 


1402. 1 


30 


31 


.5167 


133-7 


1244.9 


I45-I 


1297.4 


156.9 


I350.I 


169.3 


1403.0 


31 


32 


•5333 


133-9 


1245.8 


145-3 


1298.3 


157. 1 


I35I.O 


169.5 


1403.9 


32 


33 


.55oo 


134.0 


1246.7 


145-5 


1299.2 


157-3 


I35I-8 


169.7 


1404.7 


33 


34 


.5667 


134.2 


1247.6 


145.6 


1300.1 


157-5 


1352.7 


169.9 


1405.6 


34 


35 


•5833 


134-4 


1248.4 


145-8 


1300.9 


157.7 


1353.6 


170.1 


1406.5 


35 


36 


.6000 


134-6 


1249.3 


146.0 


1301.8 


157.9 


1354-5 


170.3 


1407.4 


36 


37 


.6167 


134-9 


1250.2 


146.2 


1302.7 


158.1 


1355-3 


170.5 


1408.3 


3 l 


38 


•6333 


I35-0 


1251.I 


146.4 


1303.6 


158.3 


1356.2 


170.8 


1409.2 


38 


39 


.6500 


135.2 


1251.9 


146.6 


1304.4 


158.5 


1357. 1 


171.0 


1410.0 


39 


40 


.6667 


135-4 


1252.8 


146.8 


1305.3 


158.7 


1358.0 


171. 2 


1410.9 


40 


41 


•6833 


135-6 


1253-7 


147.0 


1306.2 


158.9 


1358.9 


I7I-4 


1411.8 


41 


42 


.7000 


135-7 


1254.6 


147.2 1307. 1 


I59.I 


1359-8 


171.6 


1412.7 


42 


43 


.7167 


135-9 


1255-4 


147.4 


1307.9 


159-3 


1360.6 


171.8 


1413-6 


43 


44 


•7333 


136.1 


1256.3 


147.6 


1308.8 


159-5 


1361.5 


172.0 


I4I4.5 


44 


45 


•75oo 


136.3 


1257.2 


147-8 


1309.7 


159-7 


1362.4 


172.2 


I4I5.4 


45 


46 


.7667 


136. 5 


1258.1 


148.0 


1310.6 


160.0 


1363-3 


172.5 


1416.3 


46 


47 


•7833 I 


136.7 


1258.9 


148.2 


1311-5 


160.2 


1364.2 


172.7 


1417.1 


47 


48 


.8000 


136.9 


1259.8 


148.4 


1312.4 


160.4 


1365-1 


172.9 


1418.0 


48 


49 


.8167 


I37-I 


1260.7 


148.6 


1313.2 


160.6 


1365-9 


I73-I 


1418.9 


49 


50 


•8333 


137.2 


1261.5 


148.8 


1314.1 


160.8 


1366.8 


173-3 


1419-8 


50 


51 


.8500 ! 


137-4 


1262.4 


149:0 


1315-0 


161. 


1367.7 j 


173-5 


1420.7 51 


52 


.8667 


137-6 


1263.3 


149.2 


I3I5-9 


161. 2 


I368.6 ; 


173-7 


1421.6 52 


53 


.8833 


137-8 


1264. 1 


149.4 


1316.7 


161. 4 


1369-5 ! 


173-9 


1422.4 53 


54 


.9000 


138.0 


1265.0 


149-5 


1317-6 


161.6 


1370.4 


174.1 


1423.3 


54 


55 


.9167 


138.2 


1265.9 


149.7 


1318.5 


161.8 


I37I-2 


174-4 


1424.2 


55 


56 


•9333 


138.4 


1266.8 


149.9 


1319-4 


162.0 


1372. 1 


174-6 


1425. 1 


56 


57 


.9500 


138.6 


1267.6 


150.1 


1320.3 


162.2 


1373-0 j 


174.8 


1426.0 


57 


58 


.9667 


138.7 


1268.5 


150.3 


1321.1 j 


162.4 


1373-9 


i75.o 


1426.9 


58 


[59 


.9833 


138.9 


1269.4 


150.5 


1322.0 


162.6 


1374-7 


175-2 


1427.7 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 



177 



Use 100' Chords up to 8° 
Use 50' Chords up to 16 



Curves Use 25' Chords up to 32 Curves 
Curves Use 10 ' Chords above 32 Curves 



en 



a 

3 




O <u 

. 1-1 


28° 


,9° 


! 30° 


! 31° 


a 

a 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


175-4 


1428.6 


188.5 


1481.9 


202.1 


1535-3 


216.3 


1589.0 


\o 


1 


.0167 


175-6 


1429-5 


188.7 


1482.8 


202.3 


1536.2 


216.5 


1589.9 


1 


2 


.0333 


175-8 


1430.4 


189.0 


1483-7 


202.6 


1537. 1 


216.8 


1590.8 


2 


3 


.0500 


176.0 


I43I-3 


189.2 


1484-5 


202.8 


1538.0 


217.0 


i59i-7 


3 


4 


.0667 


176.3 


1432.2 


189.4 


1485.4 


203.1 


1538.9 


217.2 


1592.6 


4 


5 


.0833 


176.5 


I433- 1 


189.6 


1486.3 


203.3 


1539.8 


217.4 


1593-5 


5 


6 


.IOOO 


■ 176.7 


1434.0 


189.9 


1487.2 


203.5 


1540.7 


217.7 


1594-4 


6 


7 


.1167 


176.9 


1434-8 


190. 1 


1488. 1 


203.7 


1541-6 


217.9 


1595-3 


7 


8 


.1333 


I77-I 


1435.7 


190.3 


1489.0 


204.0 


1542.5 


218.2 


1596.2 


8 


9 


.1500 


177.3 


1436.6 


190.5 


1489.9 


204.2 


1543-4 


218.4 


I597- 1 


9 


10 


.1667 


177.6 


1437-5 


190.8 


1490.8 


204.5 


1544.3 


218.7 


1598.0 


10 


11 


.1833 


177-8 


1438.4 


191. 


1491.7 


204.7 


1545.2 


218.9 


1598.9 


11 


12 


.2000 


178.0 


1439-3 


191. 2 


1492.6 


204.9 


1546.0 


219.2 


1599-8 


1X2 


13 


.2167 


178.2 


1440.2 


191. 5 


1493-4 


205.1 


1546.9 


219.4 


1600.7 


13 


14 


•2333 


178.4 


1441.1 


191.7 


1494-3 


205.4 


1547-8 


219.6 


1601.6 


14 


15 


.2500 


178.6 


1441.9 


I9I-9 


1495-2 


205.6 


1548.7 


219.8 


1602.5 


15 


16 


.2667 


178.9 


1442.8 1 


192. 1 


1496. 1 


205.9 


1549.6 


220.1 


1603.4 


16 


17 


.2833 


179. 1 


1443-7 ! 


192.3 


1497.0 


% 2C6.I 


I550.5 


220.3 


1604.3 


17 


18 


.3000 


179-3 


1444.6 


192.5 


1497.9 


'206.3 


I55I-4 


220.6 


1605.2 


18 


19 


.3167 


179-5 


1445-5 


192.7 


1498.8 


206.5 


1552.3 


220.8 


1606. 1 


19 


20 


•3333 


179-7 


1446.4 


193-0 


1499-7 


206.8 


1553-2 


221. 1 


1607.0 


20 


21 


.3500 


179-9 


1447.3 


193.2 


1500.6 


207.0 


I554-I 


221.3 


1607.9 


21 


22 


.3667 


180.2 


1448.2 


193.5 


1501.5 


207.3 


I555-0 


221.6 


1608.8 


'22 


23 


•3833 


180.4 


1449-0 


193.7 


1502.3 


207.5 


1555.9 


221.8 


1609.7 


23 


24 


.4000 


180.6 


1449.9 


193-9 


1503.2 


207.7 


1556.8 


222.1 


1610.6 


24 


25 


.4167 


180.8 


1450.8 


194-1 


1504.I 


207.9 


1557.7 


222.3 


1611.5 


25 


26 


•4333 ; 


181.0 


I45I-7 


194-4 


1505-0 


208.2 


1558.6 


222.6 


1612.4 


26 


27 


.4500 


181. 2 


1452.6 


194.6 


I505-9 


208.4 


1559-5 


222.8 


1613.3 


27 


28 


.4667 


181.5 


1453-5 1 


194-8 


1506.8 


208.7 


1560.4 


223.0 


1614.2 


28 


29 


.4833 


181.7 


1454-3 j 


195.O 


1507.7 


208.9 


1561.3 


223.2 


1615.1 


29 


30 


.5000 


181.9 


1455-2 ! 


195.3 


1508.6 


209.1 


1562.2 


223.5 


1616.0 


30 


31 


.5167 j 


182. 1 


1456.1 i 


195.5 


1509-5 


209.3 


.1563-1 


223.7 


1616.9 


31 


32 


•5333 


182.3 


i457.o i 


195-7 


1510.4 


209.6 


1564.0 


224.0 


1617.8 


32 


33 


.5500 


182.5 


1457-9 


195-9 


1511-2 


209.8 


1564.9 


224.2 


1618.7 


33 


34 


•5667 


182.8 


1458.8 


196.2 


1512.1 


210. 1 


1565.7 


224.5 


1619.6 


34 


35 


.5833 


183.0 


1459.7 


196.4 


1513-0 


210.3 


1566.6 


224.7 


1620.5 


35 


36 


.6000 


183.2 


1460.6 


196.7 


I5I3.9 


210.5 


1567.5 


225.0 


1621.4 


36 


37 


.6167 


183.4 


1461.4 


196.9 


1514-8 


210.7 


1568.4 


225.2 


1622.3 


37 


38 


•6333 


183.6 


1462.3 


197. 1 


I5I5.7 


211.0 


1569-3 


225.5 


1623.2 


38 


39 


.6500 : 


183.8 


1463.2 


197-3 


1516.6 


211. 2 


1570.2 


225.7 


1624. 1 


39 


40 


.6667 ' 


184.1 


1464. 1 


197.6 


I5I7-5 


211.5 


I57I.I 


226.0 


1625.0 


40 


41 


.6833 


184.3 


1465.0 


197.8 


1518.4 


211. 7 


1572.0 


226=2 


1625.9 


4i 


42 


.7000 


184-5 ; 


1465-9 


198.0 


I5I9.3 


212.0 


1572.9 


226.5 


1626.8 


42 


43 


.7167 


184.7 


1466.8 


198.2 


1520. 1 


212.2 


1573.8 


226.7 


1627.7 


43 


44 


•7333 , 


185.0 


1467.7 | 


198.5 


1521.0 


212.4 


1574-7 


227.0 


1628.6 


44 


45 


.75oo 


185.2 


1468.6 ' 


198.7 


1521.9 


212.6 


1575-6 


227.2 


1629.5 


45 


46 


.7667 


185.4 


1469.5 


198.9 


1522.8 


212.9 


1576.5 


227.5 


1630.5 


46 


47 


.7833 


185.6 


1470.3 


I99-I 


I523.7 


213-1 


1577-4 


227.7 


1631.4 


47 


48 


.8000 


185.9 


1471.2 


199.4 


1524-6 


213.4 


1578.3 


228.0 


1632.3 


48 


49 


.8167 


186. 1 


1472. 1 


199.6 


I525.5 


213.6 


1579-2 


228.2 


1633.2 


49 


50 


.8333 ' 


186.3 


I473-0 ; 


199.8 


1526.4 


213-9 


1580.1 


228.4 


1634.1 


50 


51 


.8500 


186.5 


1473-9 


200.0 


1527.3 


214. 1 


1581.0 


228.6 


1635.0 


51 


52 


.8667 


186.8 


1474-8 


200.3 


1528.2 


214.4 


1581.9 


228.9 


I635-9 


52 


53 


•8833 


187.0 


1475-7 


200.5 


1529. 1 


214.6 


1582.8 


229.1 


1636.8 


53 


54 


.9000 


187.2 


1476.6 


200.8 


1530.0 


214.8 


1583.7 


229.4 


I637-7 


54 


55 


.9167 ! 


187.4 


1477.4 


201.0 


1530.9 


215.0 


1584.6 


229.6 


1638.6 


55 


56 


•9333 


187.6 


1478.3 


201.2 


I53I-7 


215-3 


1585.5 


229.9 


1639-5 


56 


57 


.9500 


187.8 


1479.2 


201.4 


1532.6 


215-5 


1586.3 


230.1 


1640.4 


57 


58 


.9667 


188. 1 


1480.1 


201.7 


1533-5 


215-8 


1587.2 


230.4 


1641.3 


58 


59 


•9833 


188.3 


1481.0 


201.9 


1534-4 


216.0 


1588.1 


, 230.6 


1642.2 


59 



178 THE SURVEY 

Use 100'* Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16° Curves Use io' Chords above 32° Curves 



-t-> 




. 1-1 

CJ bC 


32° 


33 ° 


34° 


35° 


i 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


230.9 


1643. 1 | 


246.1 


1697.3 


261.8 


I75I.8 


278.1 


1806.7 





I 


.0167 


231-1 


1644.0 | 


246.3 


1698.2 


262.0 


1752.7 


278.4 


1807.6 


1 


2 


•0333 


231.4 


1644.9 


246.6 


1699. 1 


262.3 


1753.7 


278.6 


1808.5 


2 


3 


.0500 


231.6 


1645.8 


246.8 


1700.0 


262.6 


1754.6 


278.9 


1809.4 


3 


4 


.0667 


231.9 


1646.7 


247.1 


1700.9 


262.9 


1755.5 


279.2 


1810.3 


4 


5 


.0833 


232.1 


1647.6 


247.4 


1701.8 


263.1 


1756.4 


279-4 


1811.2 


5 


6 


.1000 


232.4 


1648.5 


247.7 


1702.7 


263.4 


1757-3 


279.7 


1812.2 


6 


7 


.1167 


232.6 


1649.4 


247.9 


1703.6 


263.7 


1758.2 


280.0 


1813.1 


7 


8 


• 1333 


232.9 


1650.3 


248.2 


1704-5 


264.0 


1759- 1 


280.3 


1814 


8 


9 


.1500 


233-1 


1651.2 


248.4 


1705.4 


264.2 


1760.0 


280.6 


1814.9 


9 


10 


.1667 


233-4 


1652. 1 


248.7 


1706.4 


264.5 


1761.0 


280.8 


1815.8 


10 


11 


•1833 


233-6 


1653-0; 


248.9 


1707.3 


264.7 


1761.9 


281. 1 


1816.7 


11 


12 


.2000 


233-9 


1653-9 ! 


249.2 


1708.2 


265.0 


1762.8 


281.4 


1817.7 


12 


13 


.2167 


234.1 


1654.8 ; 


249.4 


1709. 1 


265.3 


1763.7 


281.6 


1818.6 


13 


14 


.2333 


234-4 


1655.7 


249.7 


1710.0 


265.6 


1764.6 


281.9 


1819.5 


14 


15 


.2500 


234-6 


1656.6 


249.9 


1710.9 


265.9 


1765.5 


282.2 


1820.4 


15 


16 


.2667 


234-9 


1657.5 


250.2 


1711.8 


266.1 


1766.4 


282.5 


1821.3 


16 


17 


.2833 


235-1 


1658.4 


250.5 


1712.7 


266.4 


1767.3 


282.7 


1822.2 


17 


18 


.3000 


235-4 


1659-3 


250.8 


1713-6 


266.7 


1768.3 


283.0 


1823.? 


18 


19 


.3167 


235-6 


1660.2 


251.0 


I7I4-5 


266.9 


1769.2 


283.3 


1824.1 


19 


20 


•3333 


235-9 


1661.1 


251-3 


I7I5-5 


267.2 


1770.1 


283.6 


1825.0 


20 


21 


•3500 


236.1 


1662.0 


251.5 


1716.4 


267.4 


1771.0 


283.9 


1825.9 


21 


22 


.3667 


236.4 


1662.9 


251.8 


1717.3 


267.7 


1771.9 


284.2 


1826.8 


22 


23 


.3833 


236.6 


1663.8 


252.0 


1718.2 


268.0 


1772.8 


284.4 


1827.7 


23 


24 


.4000 


236.9 


1664.7 


252.3 


1719.1 


268.3 


1773-7 


284.7 


1828.7 


24 


25 


.4167 


237.1 


1665.6 


252.6 


1720.0 


268.6 


1774-6 


285.0 


1829.6 


25 


26 


•4333 


237-4 


1666.5 


252.9 


1720.9 


268.8 


1775.6 


285.3 


1830.5 


26 


27 


.4500 


237-6 


1667.4 


253-1 


1721.8 


269.1 


1776.5 


285.6 


1831.4 


27 


28 


.4667 


237-9 


1668.3 


253-4 


1722.7 


269.3 


1777-4 


285.9 


1832.3 


28 


29 


.4833 


238.1 


1669.2 


253-6 


1723.6 


269.6 


1778.3 


286.1 


1833.2 


29 


30 


.5000 


238.4 


1670. 1 


253-9 


1724.6 


269.9 


1779.2 


286.4 


1834.2 


30 


31 


.5167 


238.7 


1671.0 


254.1 


1725.5 


270.1 


1780.1 


286.7 


1835. 1 


3i 


32 


•5333 


239.0 


1671.9 l 


254-4 


1726.4 


270.4 


1781.0 


287.0 


1836.0 


32 


33 


.5500 


239.2 


1672.8 


254-7 


1727.3 


270.7 


1781.9 


287.2 


1836.9 


33 


34 


.5667 


239.5 


1673.7 


255.o 


1728.2 


271.0 


1782.9 


287.5 


1837.8 


34 


35 


.5833 


239-7 


1674.6 1 


255-2 


1729. 1 


271.2 


1783.8 


287.8 


1838.7 


35 


36 


.6000 


240.0 


1675-5, 


255-5 


1730.0 


271-5 


1784.7 


288.1 


1839.7 


36 


37 


.6167 


240.2 


1676.4 ) 


255-7 


1730.9 


271.7 


1785.6 


288.4 


1840.6 


37 


38 


•6333 


240.5 


1677.4 


256.0 


1731.8 


272.0 


1786.5 


288.7 


1841.5 


38 


39 


.6500 


240.7 


1678.3 


256.2 


1732.7 


272.3 


1787.4 


289.0 


1842.4 


39 


40 


.6667 


241.0 


1679.2 


256.5 


1733-6 


272.6 


1788.4 


289.2 


1843.4 


40 


41 


.6833 


241.2 


1680.1 


256.8 


1734-5 


272.9 


1789.3 


289.5 


1844-3 


41 


42 


.7000 


241.5 


1681.0 


257-1 


1735-5 


273-1 


1790.2 


289.8 


1845.2 


42 


43 


.7167 


241.7 


1681.9 


257.3 


1736.4 


273-4 


1791-1 


290.1 


1846. 1 


43 


44 


•7333 


242.0 


1682.8 


257-6 


1737-3 


273-7 


1792.0 


290.4 


1847. 1 


44 


45 


.7500 


242.2 


1683.7 


257-8 


1738.2 


274-0 


1792.9 


290.6 


1848.0 


45 


*6 


.7667 


242.5 


1684.6 


258.1 


I739-I 


274-2 


1793-9 


290.9 


1848.9 


46 


47 


.7833 


242.7 


1685.5 


258.3 


1740.0 


274-5 


1794-8 


291.2 


1849.8 


47 


48 


.8000 


243 -o 


1686.4 


258.6 


1740.9 


274.8 


1795-7 


291.5 


1850.7 


48 


49 


.8167 


243-2 


1687.3 


258.9 


1741.8 


275.o 


1796.6 


291.8 


1851.6 


49 


50 


.8333 


243-5 


1688.2 


259-2 


1742.7 


275-3 


1797-5 


292.0 


1852.6 


50 


51 


.8500 


243-8 


1689. 1 


259-4 


1743-6 


275-6 


1798.4 


292.3 


1853.5 


51 


52 


.8667 


244.1 


1690.0 


259-7 


1744.6 


* 275-9 


1799.3 


292.6 


1854.4 


|52 


53 


.8833 


244-3 


1690.9 


259-9 


1745-5 


276.1 


1800.2 


292.9 


1855-3 


53 


54 


.9000 


244.6 


1691.8 


260.2 


1746.4 


276.4 


1801.2 


293-2 


1856.3 


54 


55 


.9167 


244-8 


1692.7 


260.5 


1747-3 


276.7 


1802. 1 


293-4 


1857.2 


55 


56 


•9333 


245-1 


1693.7 


260.8 


1748.2 


277.o 


1803.0 


293-7 


1858.1 


56 


57 


.9500 


245-3 


1694.6 


261.0 


I749-I 


277-3 


1803.9 


294.0 


1859-0 


,57 


58 


.9667 


245-6 


1695-5 


261.3 


1750.0 


277-5 


1804.8 


294-3 


18599 


58 


59 


•9833 


245-8 


1696.4 


261.5 


1750.9 


277-8 


1805.7 


294.6 


1860.8 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 



179 



Use 100' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



Use 25' Chords up to 32° Curves 
Use 10' Chords above 32° Curves 



en 
<u 
■*-> 

a 

9 



"SB 

u to 

CD CD 

QP 


36° 


37° 


38° 


39° 


I en 

a 



Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


294.9 


1861.8 


312.3 


I9I7-3 


330.2 


1973.0 


348.7 


2029.1 


1 


.0167 


295.2 


1862.7 


312.5 


1918.2 


330.5 


1973-9 


349-Q 


2030.0 


1 


2 


•0333 


295.4 


1863.6 


312.8 


1919.1 


330.8 


1974.9 


349-3 


2031.0 


2 


3 


.0500 


295-7 


1864.5 


3I3-I 


1920.0 


33i. 1 


1975-8 


349-6 


2031.9 


3 


4 


.0667 


296.0 


1865.5 


313-4 


1921.0 


331.4 


1976.7 


349-9 


2032.9 


4 


5 


•0833 


296.3 


1866.4 


313-7 


1921.9 


331-7 


1977.6 


350.3 


2033.8 


5 


6 


.1000 


296.6 


1867.3 


314.0 


1922.8 


332-0 


1978.6 


350.6 


2034.7 


6 


7 


.1167 


296.9 


1868.2 


314.3 


1923-7 


332.3 


1979-5 


350.9 


2035.6 


7 


8 


•1333 


297.2 


1869.2 1 


314-6 


1924.7 


332.6 


1980.5 


351-2 


2036.6 


8 


9 


.1500 


297.5 


1870.1 


314-9 


1925.6 


332.9 


1981.4 


351.5 


2037-5 


9 


10 


.1667 


297-7 


1871.0 


315-2 


1926.5 


333-2 


1982.3 


351-8 


2038.5 


10 


11 


.1833 


298.0 


1871.9 


315.5 


1927.4 


333-5 


1983-2 


352-1 


2039.4 


11 


12 


.2000 


298.3 


1872.9 


315.8 


1928.4 


333-8 


1984.2 


352.4 


2040.4 


12 


13 


.2167 


298.6 


1873.8 


316. 1 


1929.3 


334-2 


1985. 1 


352.8 


2041.3 


13 


14 


-2335 


298.9 


1874-7 


316.4 


1930.2 


334-5 


1986.1 


353-1 


2042.3 


14 


15 


.2500 


299.2 


1875.6 


316.7 


1931-1 


334-8 


1987.0 


353.4 


2043.2 


15 


16 


.2667 


299-5 


1876.5 ! 


317.0 


1932. 1 | 


335-1 


1987.9 


353-7 


2044.1 


16 


17 


.2833 


299.7 


1877.4! 


317-2 


19330 


335-4 


1988.8 


354-o 


2045.0 


17 


18 


.3000 


300.0 


1878.4 


317.5 


1933-9 | 


335-7 


1989.8 


354-3 


2046.0 


18 


19 


.3167 


300.3 


1879-3 


317.8 


1934-8 


336.0 


1990.7 


354-6 


2046.9 


19 


20 


•3333 


300.6 


1880.2 ! 


318.1 


1935-8 


336.3 


1991.7 


354-9 


2047.9 


20 


21 


•35oo 


300.9 


1881.1 


318.4 


1936.7 ! 


336.6 


1992.6 


355-3 


2048.8 


21 


22 


.3667 


301-2 


1882.1 


318.7 


1937.6 ! 


336.9 


1993-6 


355-6 


2049.8 


22 


23 


.3833 


301.5 


1883.0 


319.0 


I938.S 


337-2 


1994-5 


355-9 


2050.7 


23 


24 


.4000 


301.8 


1883.9 


319-3 


1939-5 


337-5 


1995-4 


356.2 


2051.7 


24 


25 


.4167 


302.0 


1884.8 


319.6 


1940.4 


337-8 


1996.3 


356.6 


2052.6 


25 


26 


•4333 


302.3 


1885.8 


319-9 


I94I-3 


338.1 


1997.3 


356.9 


2053-5 


26 


27 


.4500 


302.6 


1886.7 


320.2 


1942.2 


338.4 


1998.2 


357-2 


2054.4 


|27 


28 


.4667 


302.9 


1887.6 


320.5 


1943-2 


338.7 


1999.2 


357-5 


2055-4 


28 


29 


.4833 


303.2 


1888.5 


320.8 


I944-I 


339-1 


2000.1 


357-8 


2056.3 


29 


30 


.5000 


303.5 


1889.5 


321. 1 


1945.0 


339-4 


2001.0 


358.1 


2057.3 


30 


3i 


•5167 


303.8 


1890.4 


321.4 


1945.9 


339-7 


2001.9 


358.4 


2058.2 


I 31 


32 


•5333 


304.1 


1891.3 


321.7 


1946.9 


340.0 


2002.9 


358.8 


2059.2 


132 


33 


•5500 


304-3 


1892.2 


322.0 


1947.8 


340.3 


2003.8 


359-1 


2060.1 


33 


34 


.5667 


304.6 


1893.2 


322.3 


1948.8 


340.6 


2004.8 


359-4 


2061. 1 


34 


35 


.5833 


304-9 


1894-1 


322.6 


1949.7 


340.9 


2005.7 


359-8 


2062.0 


35 


36 


.6000 


305-2 


1895.0 


322.9 


1950.6 


341.2 


2006.6 


360.1 


2063.0 


36 


37 


.6167 


305.5 


1895.9 


323.2 


I95I-5 


341-5 


2007.5 


360.4 


2063.9 


37 


38 


.6333 


305.8 


1896.9 


323.5 


1952.5 , 
1953.4 


341.8 


2008.5 


360.7 


2064.8 


38 


39 


.6500 


306.1 


1897.8 


323.8 


342-1 


2009.4 


361.0 


2065.7 


39 


40 


.6667 


306.4 


1898.7 


324.2 


1954.4 


342.4 


2010.4 


361.3 


2066.7 


[40 


41 


•6833 


306.7 


1899.6 


324-5 


1955.3 


342.8 


2011.3 


361.6 


2067.6 


41 


42 


.7000 


307.0 


1900.6 


324-8 


1956.2 J 


343-1 


2012.3 


362.0 


2068.6 


42 


43 


.7167 


307.2 


1901.5 


325.1 


I957-I 1 


343-4 


2013.2 


362.3 


2069.5 


43 


44 


•7333 


307-5 


1902.4 


325-4 


1958.1 ; 


343-7 


2014. 1 


362.6 


2070.5 


44 


45 


.7500 


307.8 


1903.3 


325-7 


1959.0 


344-0 


2015.0 


363.0 


2071.4 


45 


46 


.7667 


308.1 


1904.3 


326.0 


1960.0 


344-3 


2016.0 


363-3 


2072.4 


46 


47 


.7833 


308.4 


1905.2 


326.3 


1960.9 


344-6 


2016.9 


363-6 


2073.3 


47 


48 


.8000 


308.7 


1906. 1 


326.6 


1961.8 


344-9 


2017.9 


363.9 


2074.2 


48 


49 


.8167 : 


309.0 


1907.0 


326.9 


1962.7 


345-3 


2018.8 


364-2 


2075.1 


49 


50 


•8333 


309.3 


1908.0 


327.2 


1963-7 


345-6 


2019.7 


364-5 


2076.1 


50 


51 


.8500 


309-6 


1908.9 


327.5 


1964.6 


345-9 


2020.6 


364-9 


2077.0 


51 


52 


.8667 


309.9 


1909.8 ] 


327.8 


1965-5 


346.2 


2021.6 


365-2 


2078.0 


52 


53 


.8833 


3^0.2 


1910.7 


328.1 


1966.4 


346.5 


2022.5 


365-5 


2078.9 


53 


54 


.gooo 


310.5 


1911.7 


328.4 


1967.4 


346.8 


2023.5 


365.8 


2079-9 


54 


55 


.9167 


310.8 


1912.6 


328.7 


1968.3 


347-1 


2024.4 


366.2 


2080.8 


55 


56 


•9333 


311. 1 


1913-5 


329-0 


1969.3 


347-4 


2025.4 


366.5 


208I.8 '; 


56 


57 


.9500 


3H-4 


1914-4 


329-3 


1970.2 


347-8 


2026.3 


366.8 


2082.7 


57 


58 


•9667 


3II-7 


1915-4 


329-6 


1971-1 


348.1 


2027.2 


367.1 


2083.7 


I 58 


59 


.9833 


312.0 


1916.3 


329-9 


1972.0 


348.4 


2028.1 


367.4 


2084.6 1 


! 59j 



i8o 



Use ioo' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



THE SURVEY 



Use 25' Chords up to 3 2° Curves 
Use 10' Chords above 32 Curves 



en 

<u 
+•* 
S3 

a 

§ 






40° 


41° 


42° 


43° 


L 

a 

s 






Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 




.0000 


367.7 


2085.5 


387.4 


2142.3 


407.7 


2199.5 


428.6 


2257.1 




I 


.0167 


368.0 


2086.4 


387.8 


2143.2 


408.0 


2200.4 


429.0 


2258.0 


I 




2 


•0333 


368.4 


2087.4 


388.1 


2144.2 


408.3 


2201.4 


429-3 


2259.0 


2 




3 


.0500 


368.7 


2088.3 


388.5 


2145-1 


408.7 


2202.3 


429-7 


2260.0 


3 




4 


.0667 


3690 


2089.3 


388.8 


2146. 1 


409.0 


2203.3 


430.0 


2261.0 


4 




5 


.0833 


369-4 


2090.2 


389.1 


2147.0 


409.4 


2204.3 


430.4 


2261.9 


5 




6 


.1000 


369-7 


2091.2 


389.4 


2148.0 


409.7 


2205.3 


430.7 


2262.9 


6 




7 


.1167 


370.0 


2092.1 


389.8 


2148.9 


410. 1 


2206.2 


43i. 1 


2263.8 


7 




8 


•1333 


370.3 


2093.1 


390.1 


2149.9 


410.4 


2207.2 


431-4 


2264.8 


8 




9 


.1500 


370.7 


2094.0 


390.4 


2150.9 


410.8 


2208.1 


431.8 


2265.7 


9 




10 


.1667 


37i.o 


2095.0 


390.7 


2151.9 


411.1 


2209.1 


432.1 


2266.7 


10 




11 


.1833 


371.3 


2095.9 


39I-I 


2152.8 


411. 5 


2210. c 


432.4 


2267.7 


11 




12 


.2000 


371.6 


2096.9 


391-4 


2153.8 


411.8 


2211.0 


432.8 


2268.7 


12 




13 


.2167 


372.0 


2097.8 


391-8 


2154.7 


412.2 


2211.9 


433-2 


2269.6 


13 




14 


•2333 


372.3 


2098.8 


392.1 


2155.7 


412.5 


2212.9 


433-5 


2270.6 


14 




15 


.2500 


372.6 


2099.7 


392.4 


2156.6 


412.9 


2213.9 


433-9 


2271.5 


15 




16 


.2667 


372.9 


2100.7 


j 392.7 


2157-6 


413-2 


2214.9 


434.2 


2272.5 


16 




17 


•2833 


373-3 


2101.6 


! 393.1 


2158.5 


413.6 


2215.8 


434-6 


2273-5 


17 




18 


.3000 


373-6 


2102.6 


393-4 


2159-5 


413-9 


2216.8 


434-9 


2274.5 


18 




19 


.3167 


374-o 


2103.5 


393-7 


2160.4 


414-3 


2217.7 


435-3 


2275-4 


19 




20 


•3333 


374-3 


2104.5 


394-1 


2161.4 


414-6 


2218.7 


435-6 


2276.4 


20 




21 


•35oo 


374-6 


2105.4 


! 394-4 


2162.3 


415.0 


2219.6 


436.0 


2277.3 


21 




22 


.3667 


374-9 


2106.3 


394-7 


2163.3 


415.3 


2220.6 


436.3 


2278.3 


22 




23 


•3833 


375-3 


2107.2 


| 395-1 


2164.2 


415-7 


2221.5 


436.7 


2279.2 


23 




24 


.4000 


375-6 


2108.2 


395-4 


2165.2 


416.0 


2222.5 


437.o 


2280.2 


24 




25 


.4167 


375-9 


2109. 1 


395-8 


2166. 1 


416.3 


2223.4 


437-4 


2281.2 


25 




26 


•4333 


376.2 


2110.1 


396.1 


2167. 1 


416.6 


2224.4 


437-8 


2282.2 


26 




27 


.4500 


376.6 


2111.0 


396.5 


2168.0 


417.0 


2225 4 


438.2 


2283.1 


27 




28 


.4667 


376.9 


21 1 2.0 


396.8 


2169.0 


417.3 


2226.4 


438.5 


2284.1 


28 




20 


.4833 


377-2 


2112.9 


397-2 


2169.9 


417-7 


2227.3 


438.9 


2285.0 


29 




30 


.5000 


377-5 


2113.9 


397-5 


2170.9 


418.0 


2228.3 


439-2 


2286.0 


30 




31 


•5167 


377-9 


2114.8 


397.8 


2171.8 


418.4 


2229.2 


439-6 


2287.0 


3i 




32 


•5333 


378.2 


2115.8 


398.1 


2172.8 


418.7 


2230.2 


439-9 


2288.0 


32 




33 


•55oo 


378.5 


2116.7 


398.5 


2173-7 


4I9-I 


2231. 1 


440.3 


2288.9 


33 




34 


•5667 


378.8 


2117.7 


398.8 


2174.7 


419.4 


2232.1 


440.6 


2289.9 


34 




35 


.5833 


379.2 


2118.6 


399-2 


2175-6 


419-8 


2233.0 


441.0 


2290.8 


35 




36 


.6000 


379-5 


2119.6 


399-5 


2176.6 


420.1 


2234.0 


441.4 


2291.8 


36 




37 


.6167 


379-8 


2120.5 


399-9 


2177.5 


420.5 


2235.0 


441-8 


2292.8 


37 




38 


•6333 


380.1 


2121.5 


400.2 


2178.5 


420.8 


2236.0 


442.1 


2293.8 


38 




39 


.6500 


380.5 


2122.4 


400.6 


2179.4 


421.2 


2236.9 


442.5 


2294.7 


39 




40 


.6667 


380.8 


2123.4 


400.9 


2180.4 


421.5 


2237.9 


442.8 


2295.7 


40 




4i 


•6833 


381. 1 


2124.3 


401.2 


2181.4 


421.9 


2238.8 


443-2 


2296.7 


41 




42 


.7000 


381.4 


2125.3 


401.5 


2182.4 


422.2 


2239.8 


443-5 


2297.7 


42 




43 


.7167 


381.8 


2126.2 


401.9 


2183.3 


422.6 


2240.7 


443-9 


2298.6 


43 




44 


•7333 


382.1 


2127.2 ; 


402.2 


2184.3 


422.9 


2241.7 


444-2 


2299.6 


44 




45 


.7500 


382.5 


2128. 1 J 


402.6 


2185.2 


423-3 


2242.6 


444.6 


2300.5 ! 


45 




46 


.7667 


382.8 


2129. 1 


402.9 


2186.2 


423-6 


2243.6 


445-0 


2301.5 


46 




47 


•7833 


383.1 


2130.0 


403.3 


2187. 1 


424.0 


2244.6 


445-4 


2302.5 


47 




48 


.8000 


383.4 


2131.0 


403-6 


2188. 1 


424-3 


2245.6 


445-7 


2303.5 


48 




49 


.8167 


383.8 


2131-9 


404.0 


2189.0 


424.7 


2246.5 


446.1 


2304.4 


49 




50 


•8333 


384.1 


2132.9 


404.3 


2190.0 


425.0 


2247.5 


446.4 


2305.4 


SO 




51 


.8500 


384.5 


2133.8 


404.6 


2190.9 


425-4 


2248.4 


446.8 


2306.3 


51 




52 


.8667 


384.8 


2134-7 


404.9 


2191.9 


425-7 


2249.4 


447.1 


2307.3 


52 




53 


.8833 


385-1 


2135-6 


405.3 


2192.8 


426.1 


2250.3 


447-5 


2308.3 


53 




54 


.9000 


385.4 


2136.6 


405.6 


2193.8 


426.4 


2251.3 


447-8 


2309-3 


54 




55 


.9167 


385.8 


2137-5 


406.0 


2194.7 


426.8 


2252.3 


448.2 


2310.2 


55 




56 


•9333 


386.1 


2138.5 


406.3 


2195.7 


427.1 


2253-3 


448.6 


2311.2 


56 




57 


.9500 


386.5 


2139-4 


406.7 


2196.6 


427.5 


2254.2 


449.0 


2312. 1 


57 




58 


.9667 


386.8 


2140.4 


407.0 


2197.6 


427.8 


2255.2 


449-3 


23I3.I 


58 




59 


•9833 


387.1 


2141-3 


407.4 


2198.5 


428.2 


2256.1 


449-7 


23I4.I 


59 





FUNCTIONS OF THE ONE-DEGREE CURVE 181 



Use ioo' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



Use 25' Chords up to 32 Curves 
Use 10' Chords above 32 Curves 



G 
O 


y 
u to 

pp 


44° 


45° 


46° 


!| «■ 


en 

<u 

— ' 
3 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


C 

s 


.0000 


450.0 


2315-1 


472.1 


2373-4 


494.8 


2432.2 


518.3 


2491-5 





I 


.0167 


450.4 


2316.0 


472.5 


2374-4 


495-2 


2433-2 


518.7 


2492.4 


I 


2 


•0333 


450.7 


2317.0 


472.9 


2375-4 


495-6 


2434.2 


519.0 


2493.4 


2 


3 


.0500 


45I-I 


2318.0 


473-3 


2376.3 


496.0 


2435.1 


519.4 


2494.4 


3 


4 


.0667 


451.5 


2319.0 


473-6 


2377-3 


496.4 


2436.1 


; 519.8 


2495.4 


4 


5 


.0833 


451-9 


2319.9 


474-0 


2378.3 


496.7 


2437.1 


520.2 


2496.4 


5 


6 


.1000 


452.2 


2320.9 


474-4 


2379-3 


497.2 


2438.1 


520.6 


2497.4 


6 


■ 7 


.1167 


452.6 


2321.8 


474-8 


2380.2 


497-6 


2439.1 


52I.O 


2498.4 


7 


8 


•1333 


452.9 


2322.8 


. 475-1 


2381.2 


497-9 


2440.1 


521.4 


2499.4 


8 


9 


.1500 


453-3 


2323.8 


475-5 


2382.2 


498.3 


2441. 1 


j 521.8 


2500.4 


9 


10 


.1667 


453-7 


2324.8 


475-9 


2383.2 


498.7 


2442.1 


522.2 


2501.4 


10 


11 


.1833 


454-1 


2325-7 


476.3 


2384-2 


499.1 


2443-Q 


522.6 


2502.4 


11 


12 


.2000 


454-4 


2326.7 


476.6 


2385.2 


499-5 


2444.0 


523.0 


2503-4 


12 


13 


.2167 


454-8 


2327.7 


477-0 


2386.1 


499.9 


2445-Q 


523-4 


2504.4 


13 


14 


•2333 ; 


455-1 


2328.7 


477-4 


2387.1 


500.3 


2446.0 


523-8 


2505.4 


14 


15 


.2500 


455-5 


2329.6 


477-8 


2388.1 


500.7 


2447.0 


524-2 


2506.3 


15 


16 


.2667 ' 


455-9 


2330.6 ' 


478.1 


2389-1 


501.0 


2448.0 


i 524-6 


2507-3 


16 


17 


.2833 \ 


456.3 


2331-6 


478.5 


2390.0 


501.4 


2449.0 


525.0 


2508.3 


17 


18 


.3000 


456.6 


2332.6 


478.9 


2391.0 


501.8 


2449.9 


1 525-4 


2509-3 


18 


19 


.3167 


457-0 


2333.5 


479-3. 


2392.0 


502.2 


2450.9 


| 525.8 


2510.3 


19 


20 


■3333 


457-3 


2334-5 


479-6 


2393-0 


502.6 


2451.9 


526.2 


25H-3 


20 


21 


•35oo 


457-7. 


2335.4 


480.0 


2393-9 


503-0 


2452.9 


526.6 


2512.3 


21 


22 


.3667 


458.1 


2336.4 


480.4 


2394-9 


503-4 


2453-9 


527.O 


2513-3 


22 


23 


•3833 


458.5 


2337-4 


480.8 


2395-9 


503.8 


2454-9 


527-4 


25I4-3 


23 


24 


.4000 


458.8 


2338.4 


481. 1 


2396.9 i 


504-1 


2455-9 


527.8 


25I5-3 


24 


25 


.4167 


459-2 


2339-3 


481.5 


2397.8 ! 


504.5 


2456.8 


528.2 


2516.3 


25 


26 


•4333 


459-5 


2340.3 i 


481.9 


2398.8 ; 


504-9 


2457.8 


528.6 


2517.3 


26 


27 


.4500 


459-9 


2341-3 


482.3 


2399.8 j 


505.3 


2458.8 


529-0 


2518.3 


27 


28 


.4667 


460.3 


2342.3 ! 


482.6 


2400.8 


505-7 


2459-8 


529.4 


2519-3 


28 


29 


.4833 


460.7 


2343-2 l 


483.0 


2401.8 | 


506.1 


2460. S 


529.8 


2520.2 


29 


30 


.5000 


461.0 


2344.2 ! 


483-4 


2402.8 


506.5 


2461.8 


530.2 


2521.2 


30 


31 


•5167 


461.4 


2345-1 ! 


483.8 


2403.7 


506.9 


2462.8 


530.6 


2522.2 


31 


32 


•5333 


461.7 


2346.1 I 


4S4.2 


2404.7 


507-3 


2463-8 


53I.O 


2523.2 


32 


33 


•55oo 


462.1 


2347-1 


484.6 


2405-7 


507-7 


2464.7 


531-4 


2524.2 


33 


34 


.5667 


462.5 


2348.1 ! 


484.9 


2406.7 


508.0 


2465.7 


531-8 


2525-2 


34 


35 


•5833 


462.9 


2349-0 


485.3 


2407.6 


508.4 


2466.7 


532.2 


2526.2 


35 


36 


.6000 : 


463.2 


2350.0 


485.7 


2408.6 


508.8 


2467.7 


532.6 


2527.2 


36 


37 


.6167 ' 


463.6 


2351-0 


486.1 


2409.6 [ 


509.2 


2468.7 


533-0 


2528.2 


37 


38 


•6333 


463-9 


2352.0, 


486.5 


2410.6 


509.6 


2469.7 


533-4 


2529.2 


38 


39 


.6500 


464-3 


2352.9 , 


486.9 


2411.6 


510.0 


2470.7 


-533-8 


2530.2 


39 


40 


.6667 


464-7 


2353.9 i 


487.2 


2412.6 


510.4 


2471.7 


534-2 


2531-2 


40 


41 


6833 * 


465-0 ! 


2354-9 


487.6 


24I3-5 


510.8 


2472.6 


534-6 


2532.2 


41 


42 


.7000 : 


465-4 


2355-9 


488.0 


24I4-5 


5H.I 


2473-6 


535-o 


2533-2 


42 


43 


.7167 


465-8 


2356.8 


488.4 


24I5-5 i 


5H-5 


2474.6 


535-4 


2534-2 


43 


44 


•7333 : 


466.2 


2357-8 


488.7 


2416.5 


5H-9 


2475.6 


535-8 


2535-2 


44 


45 


.7500 : 


466.5 ! 


2358.8 


489.1 


2417.5 


512.3 


2476.6 


536.2 


2536.2 


45 


46 


.7667 ; 


466.9 


2359-8 


4890 


2418.5 


512.7 


2477-6 


536.6 


2537-2 


46 


47 


•7833 i 


467-3 


2360.7 


489.9 


2419.4 


5I3-I 


2478.6 


537-0 


2538.2 


47 


48 


.8000 i 


467.7 


2361.7 


490.3 


2420.4 


513-5 


2479-6 


537-4 


2539-2 


48 


49 


.8167 


468.0 


2362.7 


490.7 


2421.4 


513-9 


2480.6 


537-8 


2540.2 


49 


50 


.8333 


468.4 


2363-7 


491 


2422.4 


514-3 


2481.6 


538.2 


2541.2 


50 


51 


.8500 


468.8 


2364.6 


491-4 


2423.4 


514-7 


2482.5 


538.6 


2542.2 


51 


52 


.8667 


469.1 


2365.6 


491-8 


2424.4 


5i5-i 


2483.5 


539-0 


2543-2 


52 


53 


.8833 


469-5 


2366.6 


492.2 


2425-3 


515-5 


2484.5 


539-4 


2544.2 


53 


54 


.9000 


469.9 


2367.6 


492.5 


2426.3 


515-9 


2485-5 


539-8 


2545.2 


54 


55 


.9167 


470.3 


2368.5 ! 


492.9 


2427.3 


516.3 


2486.5 


540.2 


2546.2 


5 £ 


56 


•9333 


470.6 


23695 


493-3 


2428.3 


516.7 


2487.5 


540.6 


2547-2 


56 


57 


.9500 


471.0 


2370.5 


493-7 


2429.2 


517. 1 


2488.5 


541.0 


2548.2 


57 


58 


.9667 


471-4 


2371-5 i 


494-1 


2430.2 


517.5 


2489.5 


541-4 


2549.2 


58 


59 


.9833 


471.8 


2372.4 ; 


494-5 


2431.2 


517-9 


2490.5 


541-9 


2550.1 


59 



182 



THE SURVEY 





Use 50 


' Chords 


up to 1 6° Curves Use 


10' Chords above 32 Curves 






8 

be 


48° 


49° 


5o° 


5i° 


en 

C 
9 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


o 


.0000 


542.3 


2551. 1 


567.0 


2611.3 


592.4 


2671.9 


618.5 


2733-Q 


O 


I 


.0167 


542.7 


2552.1 


567-4 


2612.3 


592.8 


2672.9 


618.9 


2734-1 


I 


2 


•0333 


543-1 


2553.1 


567.8 


2613.3 


593-2 


2673.9 


619.3 


2735-1 


2 


3 


.0500 


543-5 


2554-1 


568.3 


2614.3 


593-7 


2675.0 


619.8 


2736.1 


3 


4 


0667 


543-9 


2555-1 


568.7 


2615.3 


594-1 


2676.0 


620.2 


2737.1 


4 


5 


•0833 


544-3 


2556.1 


569.1 


2616.3 


594-5 


2677.0 


620.7 


2738.2 


5 


6 


.1000 


544-7 


2557.1 


569.5 


2617.3 


594-9 


2678.0 


621. 1 


2739.2 


6 


7 


.1167 


545-1 


2558.1 


5699 


2618.3 


595-4 


2679.0 


621.6 


2740.2 


7 


8 


• 1333 


545-5 


2559-1 


570.3 


2619.3 


595-8 


2680.0 


622.0 


2741.2 


8 


9 


.1500 


546.o 


2560.1 


57o.8 


2620.4 


596.2 


2681. 1 


622.5 


2742.3 


9 


IO 


.1667 


546.4 


2561. 1 


571.2 


2621.4 


596.7 


2682.1 


622.9 


2743-3 


10 


ii 


.1833 


546.8 


2562.1 


571-6 


2622.4 


597-1 


2683.1 


623.3 


2744-3 


11 


12 


.2000 


547-2 


2563.1 


572.o 


2623.4 


597-5 


2684.1 


623.7 


2745-3 


12 


13 


.2167 


547-6 


2564.1 


572.4 


2624.4 


598.o 


2685.1 


624.2 


2746.4 


13 


14 


•2333 


548.0 


2565.1 


572.8 


2625.4 


598.4 


2686.1 


624.6 


2747-4 


14 


15 


.2500 


548.4 


2566.1 


573-3 


2626.4 


598.9 


2687.2 


625.1 


2748.4 


15 


16 


.2667 


548.8 


2567.1 


573-7 


2627.4 


599-3 


2688.2 


625.5 


2749.4 


16 


17 


• 2833 


549-2 


2568.1 


574-1 


2628.4 


599-7 


2689.2 


626.0 


2750.5 


17 


18 


.3000 


549-6 


2569.1 


574-5 


2629.4 


600.1 


2690.2 


626.4 


275L5 


18 


19 


.3167 


550.I 


2570.1 


574-9 


2630.4 


600.6 


2691.3 


626.9 


2752.5 


19 


20 


•3333 


55o.5 


2571. 1 


575-3 


2631.4 


601.0 


2692.3 


627.3 


2753-5 


20 


21 


.3500 


55o.9 


2572.1 


575-8 


2632.5 


601.5 


2693.3 


627.8 


2754.6 


21 


22 


.3667 


551.3 


2573.1 


576.2 


2633-5 


601.9 


2694.3 


628.2 


2755.6 


22 


23 


.3833 


551.7 


2574-1 


576.6 


2634.5 


602.3 


2695.3 


628.7 


2756.7 


23 


24 


.4000 


552.1 


2575-1 


577-o 


2635.5 


602.7 


2696.3 


629.1 


2757.7 


24 


25 


.4167 


552.5 


2576.1 


577-5 


2636.5 


603.2 


2697.4 


629.6 


2758.7 


25 


26 


•4333 


552.9 


2577.1 


577-9 


2637.5 


603.6 


2698.4 


630.0 


2759-7 


26 


27 


.4500 


553.3 


2578.1 


578.3 


2638.5 


604.1 


2699.4 


630.5 


2760.8 


27 


28 


.4667 


553-7 


2579-1 


578.7 


2639-5 


604.5 


2700.4 


630.9 


2761.8 


28 


2Q 


.4833 


554-2 


2580.1 


579-2 


2640.5 


604.9 


2701.4 


631.4 


2762.8 


29 


30 


.5000 


554-6 


2581. 1 


579-6 


2641.5 1 


605.3 


2702.4 


631.8 


2763.8 


30 


31 


.5167 


555-o 


2582.1 


580.0 


2642.5 


605.8 


2703.5 


632.3 


2764.9 


3i 


32 


•5333 


555-4 


2583-1 


580.4 


2643.5 


606.2 


2704.5 


632.7 


2765.9 


32 


33 


5500 


555-8 


2584-1 


580.9 


2644.6 


606.6 


2705.5 


633-2 


2766.9 


33 


34 


•5667 


556.2 


2585.1 


581.3 


2645.6 


607.0 


2706.5 


633-6 


2767.9 


34 


35 


.5833 


556.6 


2586.2 


581.7 


2646.6 


607.5 


2707.6 


634.1 


2769.0 


35 


36 


.6000 


557-o 


2587.2 


582.1 


2647.6 


607.9 


2708.6 


634-5 


2770.0 


36 


37 


.6167 


557-4 


2588.2 


582.6 


2648.6 


608.4 


2709.6 


634-9 


2771.0 


37 


38 


•6333 


557-8 


2589.2 


583.0 


2649.6 


608.8 


2710.6 


635-3 


2772.0 


38 


39 


.6500 


558.3 


2590.2 


583.4 


2650.6 


609.3 


2711.6 


635.8 


2773-1 


39 


40 


.6667 


558.7 


2591.2 


583.8 


2651.6 


609.7 


2712.6 


636.2 


2774-1 


40 


4i 


•6833 


559-1 


2592.2 


584.3 


2652.7 


610. 1 


2713.7 


636.7 


2775.2 


41 


42 


.7000 


559-5 


2593-2 


584.7 


2653.7 


610.5 


2714.7 


637.1 


2776.2 


42 


43 


.7167 


559-9 


2594.2 


585-1 


2654.7 


611. 


2715.7 


637.5 


2777-2 


43 


44 


• 7333 


560.3 


2595-2 


585.5 


2655.7 


611.4 


2716.7 


638.0 


2778.2 


44 


45 


.7500 


560.8 


2596.2 


586.0 


2656.7 


611. 9 


2717.8 


638.5 


2779.3 


45 


46 


.7667 


561.2 


2597.2 


586.4 


2657.7 


612.3 


2718.8 


638.9 


2780.3 


46 


47 


.7833 


561.6 


2598.2 


S86.8 


2658.7 


612.8 


2719.8 


639-4 


2781.3 


47 


48 


.8000 


562.0 


2599.2 


587.2 


2659.7 


613.2 


2720.8 


639.8 


2782.3 


48 


49 


.8167 


562.4 


2600.2 


587.7 


2660.8 


613.7 


2721.8 


640.3 


2783.4 


49 


50 


.8333 


562.8 


2601.2 


588.1 


2661.8 


614. 1 


2722.8 


640.7 


2784.4 


SO 


51 


.8500 


563-3 


2602.2 


588.5 


2662.8 


614.5 


2723.9 


641.2 


2785.4 


51 


52 


.8667 


563-7 


2603.2 


588.9 


2663.8 


614.9 


2724.9 


641.6 


2786.4 


52 


53 


.8833 


564.1 


2604.2 


589-4 


2664.8 ! 


615.4 


2725.9 


642.1 


2787.5 


53 


54 


.9000 


564-5 


2605.2 


589.8 


2665.8 ; 


615.8 


2726.9 


642.5 


2788.5 


54 


55 


.9167 


564-9 


2606.2 


590.2 


2666.8 1 


616.3 


2728.0 


643-0 


2789.6 


55 


56 


•9333 


565-3 


2607.2 


590.6 


2667.8 


616.7 


2729.0 


643-4 


2790.6 


56 


57 


.9500 


565.8 


2608.3 


5911 


2668.9 : 


617.2 


2730.0 


643-9 


2791.6 


57 


58 


.Q667 


566.2 


2600.3 


591.5 


2669.9 


617.6 


2731-0 


644-3 


2792.6 


58 


59 


.9833 


566.6 


2610.3 


592.0 


2670.9 j 


618. 1 


2732.0 


644.8 


2793-7 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 183 



Use 100' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



Use 25' Chords up to 32 Curves 
Use 10' Chords above 32 Curves 



tn 

"5 




O a, 


52° 


53° 


54° 


. 55° 


1! 




Ext. 


Tan. 


Ext. 

t 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


645.2 


2794.7 


1 , 
672.7 


2856.9 


700.9 


2919-5 


729.9 


2982.8 


I 


.0167 


; 645.7 


2795-8 


I 673.2 


2857-9 


701.4 


2920.6 


730.4 


2983.9 


1 


2 


.0333 


' 646.I 


2796.8 


i 673-7 


2858.9 


701.9 


2921.6 


730.9 


2984.9 


1 2 


3 


.0500 


646.6 


2797-8 


1 674.2 


2860.0 


702.4 


2922.7 


731-4 


2986.0 


3 


4 


.0667 


| 647.O 


2798.8 


■ 674.6 


2861.0 


702.8 


2923.8 


731-9 


2987.1 


1 4 


5 


.0833 


1 647.5 


2799-9 


! 675.1 


2862.1 


703.3 


2924.9 


732.4 


2988.2 


5 


6 


.1000 


647.9 


2800.9 


j 675.5 


2863.1 


703.8 


2925.9 


732.9 


2989.2 


6 


7 


.1167 


648.4 


2802.0 


: 676.0 


2864.2 


704-3 


2927.0 


733-4 


2990.3 


1 7 


8 


•1333 


648.9 


2803.0 


676.4 


2865.2 


704.8 


2928.0 


733-8 


2991.3 


8 


9 


.1500 


649.4 


2804.0 


! 676.9 


2866.3 


705.3 


2929.1 


734-3 


2992.4 


9 


10 


.1667 


649.8 


2805.0 


677-4 


2867.3 


705.7 


2930.1 


734-8 


2993-4 


' 10 


11 


.1833 


650.3 


2806.1 


i 677.9 


2868.4 


706.2 


2931.2 


735-3 


2994-5 


11 


12 


.2000 


650.7 


2807.1 


678.3 


2869.4 


706.7 


2932.2 


735-8 


2995-5 


12 


13 


.2167 


651.2 


2808.2 


678.8 


2870.5 


707.2 


2933-3 


736.3 


2996.6 


13 


14 


.2333 


651.6 


2809.2 


679.2 


2871.5 


707.7 


2934-3 


736.8 


2997-7 


14 


15 


.2500 


652.1 


2810.2 


679.7 


2872.5 


708.2 


2935.4 


737-3 


2998.8 


15 


16 


.2667 


652.5 


2811.2 


680.2 


2873-5 


708.6 


2936.4 


737-8 


2999.8 


16 


17 


.2833 


653.0 


2812.3 


: 680.7 


2874.6 


709.1 


2937-5 


738.2 


3000.9 


17 


18 


.3000 


653.4 


2813.3 


! 68l. I 


2875.6 


709.6 


2938.5 


738.7 


3001.9 


18 


19 


•3167 


653.9 


2814.4 


681.6 


2876.7 


710. 1 


2939-6 


739-2 


3003.0 


19 


20 


•3333 


654.3 


2815.4 


682.0 


2877.7 


710.5 


2940.6 


739-7 


3004.0 


20 


21 


•35oo 


654-8 


2816.4 


682.5 


2878.8 


711. 


2941.7 


740.2 


3005.1 


21 


22 


.3667 


655-2 


2817.4 


683.O 


2879-8 


7ii. 5 


2942.7 


740.7 


3006.2 


[ 22 


23 


.3833 


655-7 


2818.5 


683.5 


2880.9 


712.0 


2943.8 


741-2 


3007.3 


23 


24 


.4000 


656.2 


2819.5 


683.9 


2881.9 


712.5 


2944.8 


741-7 


3008.3 


24 


25 


.4167 


656.7 


2820.6 


684.4 


2883.0 


713-0 


2945.9 


742.2 


3009.4 


25 


26 


•4333 


6571 


2821.6 


684.9 


2884.0 


713-4 


2946.9 


742.7 


3010.4 


26 


27 


.4500 


657.6 


2822.6 


685.4 


2885.1 


713.9 


2948.0 


743-2 


3011.5 


27 


28 


.4667 


658.O 


2823.6 


685.8 


2886.1 


714-4 


2949.0 


743-7 


3012.5 


28 


29 


•4833 


658.5 


2824.7 


686.3 


2887.1 


714-9 


2950.1 


744-2 


3013.6 


29 


30 


.5000 


658.9 


2825.7 


686.7 


2888.1 


715-3 


2951-1 


744-7 


30I4-7 


30 


3i 


•5167 


659-4 


2826.8 


687.2 


2889.2 


715.8 


2952.2 


745-2 


3015-8 


31 


32 


•5333 


659-8 


2827.8 


687.7 


2890.2 


716.3 


2953-2 


745-7 


3016.8 


32 


33 


•5500 


660.3 


2828.8 


688.2 


2891.3 


716.8 


2954-3 


746.2 


30I7-9 


33 


34 


.5667 


660.7 


2829.8 


688.6 


2892.3 


717-3 


2955-3 


746.7 


3018.9 


34 


35 


•5833 


66l.2 


2830.9 


689.1 


2893.4 


717.8 


2956.4 


747-2 


3020.0 


35 


36 


.6000 


661 6 


2831.9 


689.6 


2894.4 


718.2 


2Q57-5 


747-7 


3021. 1 


36 


37 


.6167 


662.1 


2833.0 


690.1 


2895-5 


718.7 


2958.6 


748.2 


3022.1 


37 


38 


•6333 


662.5 


2834.0 


690.5 


2896.5 


719-2 


2959-6 


748.7 


3023.2 


38 


39 


.6500 


663.0 


2835.1 


691.0 


2897.6 


719-7 


2960.7 


749-2 


3024.3 


39 


40 


.6667 


663.5 


2836.1 


691.5 


2898.6 


720.2 


2961.7 


749-7 


3025.3 


40 


4i 


.6833 


664.0 


2837.2 


692.0 


2899.7 


720.7 


2962.8 


75o.2 


3026.4 


41 


42 


.7000 


664.4 


2838.2 


692.4 


2900.7 


721. 1 


2963.8 


750.7 


3027.5 


42 


43 


.7167 


664.9 


2839.2 


692.9 


2901.8 


721.6 


2964.9 


751-2 


3028.6 


43 


44 


•7333 


665.3 


2840.2 


693.4 


2902.8 


722.1 


2965.9 


751-7 


3029.6 


44 


45 1 


•7500 


665.8 


2841.3 


693-9 


2903.9 


722.6 


2967.0 


752.2 


3030.7 


45 


46 


.7667 


666.2 


2842.3 


694-3 


2904.9 | 


723.1 


2968.0 


752.6 


3031-7 


46 


47 .7833 


666.7 


2843.4 


694.8 


2906.0 


723.6 


2969.1 


753-1 


3032.8 


47 


48 


.8000 


667.2 


2844.4 


695-3 


2907.0 


724.1 


2970.1 


753-6 


3033.8 


48 


49 


.8167 


667.7 


2845.5 


695.8 


2908.1 


724.6 


2971.2 


754-1 


3035-0 


49 


50 


.8333 


668.1 


2846.5 


696.2 


2909.1 


725.0 


2972.2 


754-6 


3036.0 


50 


51 


.8500 


668.6 


2847.5 


696.7 


2910.2 ! 


725-5 


2973-3 


755-1 


3037-I 


51 


52 


.8667 


669.0 


2848.5 


697.1 


2911.2 ; 


726.0 


2974-4 


755-6 


3038.1 


52 


53 


.8833 


669.5 


2849.6 


697.6 


2912.3 


726.5 


2975-5 


756.1 


3039.2 


53 


54 


.9000 


669.9 


2850.6 


698.1 


2913-3 


727.0 


2976.5 


756.6 


3040.2 


54 


55 


•9167 


670.4 


2851.7 


698.6 


2914.4 


727-5 


2977.6 


757-1 


3041.3 


55 


56 


•9333 


670.9 


2852.7 ! 


699.0 


2915-4 


728.0 


2978.6 


757-6 


3042.4 


56 


57 


•9500 


671.4 


2853.8 


699-5 


2916.5 


728.5 


2979-7 


758.1 


3043-5 


57 


58 


.9667 


671.8 


2854.8 s 


700.0 


29I7-5 I 


729.0 


2980.7 


758.6 


3044-5 


58 


59 


.9833 


: 672.3 


2855.9 


| 700.5 


2918.5 


729-5 


2981.8 


759-1 


3045-6 


59 



1 84 THE SURVEY 

Use ioo' Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16 Curves Use 10' Chords above 32 Curves 



n 

s 




8 Dec. of 
8 Degree 


56° 


0/ 


58° 


59° • 


en 

V 

s 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 
3241.9 


759-6 


3046.6 j 


790.2 


1 
3111.1 


821.4 


3176.1 


853.5 


I 


.0167 ; 


760.1 


3047-7 


790.7 


3112.2 | 


821.9 


3177.2 


8540 


3243-0 


I 


2 


.0333 ■ 


760.6 


3048.8 


: 791.2 


3II3-3 ! 


822.5 


3178.3 j 


854.6 


32441 ; 


2 


3 


.0500 


761. 1 


3049.9 


; 791.7 


3"4-4 j 


823.0 


3179-4; 


855.1 


3245-2 


3 


4 


.0667 | 


7*61.6 


3050.9 


792.2 


3U5-4 ; 


823.5 


3180.5 


855.7 


3246.3 


4 


5 


.0833 ! 


762.2 


3052.0 


792.8 


3116.5 1 


824.1 


3181.6 


856.2 


3247.4 


5 


6 


.1000 


762.7 


3053-1 


793-3 


3117.6 i 


824.6 


3182.7 ; 


856.8 


3248.5 


6 


7 


.1167 1 


763.2 


3054.2 


793-8 


3118.7I 


825.2 


3183.8 


857.3 


3249^6 


7 


8 


•1333 


763.7 


3055-2 


794-3 


3119-7 ! 


825.7 


3184.9 


857.9 


3250.7 


8 


9 


.1500 


764.2 


3056.3 


794-8 


3I20.8 : 


826.2 


3186.0 1 


858.5 


3251.8 


9 


10 


.1667 


764.7 


3057.4 


795-3 


3I2I.9 \ 


826.7 


3187.1 


859.0 


3252.9 


10 


11 


.1833 


765.2 


3058.5 


i 795-8 


3I23.0 , 


827.3 


3188.2 : 


859.5 


3254-0 


11 


12 


.2000 ; 


765-7 


3059-5 


796.3 


3124.1 ; 


827.8 


3189.2 


860.0 


3255-1 


12 


13 


.2167 


766.2 


3060.6 


796.9 


3125.2 i 


828.4 


3190.3 


860.6 


3256.2 


13 


14 


•2333 


766.7 


3061.6 


797.4 


3126.2 j 


828.9 


3191-4, 


861.1 


3257.3 


14 


15 


.2500 ! 


767.2 


3062.7 


797-9 


3127.3 


829.4 


3192.5 


861.7 


3258.4 


15 


16 


.2667 ! 


767.7 


3063.8 


798.4 


3128.4; 


829.9 


3193-6 


862.2 


3259-5 


16 


17 


.2833 1 


768.2 


3064.9 


798.9 


3129-5 1 


830.5 


3194-7 


862.8 


3260.6 


17 


18 


.3000 I 


768.7 


3065.9 


799-4 


3130.6 | 


; 831.0 


3195.8, 


863.3 


3261.7 


18 


19 


.3167 


769.2 


3067.0 


799.9 


3I3I.7 j 


1 831.5 


3196.9 


863.8 


3262.8 


19 


20 


.3333 


769.7 


3068.1 


800.5 


3132.7 ! 


832.1 


3198.0 


864.4 


3263.9 


20 


21 


.3500 


770.3 


3069.2 


801.0 


3133-8 ; 


i 832.5 


3199-1 


864.9 


3265.0 


21 


22 


.3667 


770.8 


3070.2 


801.5 


3134-9 


! 833.1 


3200.2 


865.5 


3266.1 


22 


23 


.3833 


771-3 


3071.3 


802.0 


3136.0 


833.6 


3201.3 


866.0 


3267.2 


23 


24 


.4000 


771.8 


3072.4 


802.5 


3I37.0 


834-2 


3202.4 


866.6 


3268.3 


24 


25 


.4167 


772-3 


3073-5 


803.1 


3138.1 j 


834.7 


3203.5 


867.1 


3269.4 


25 


26 


•4333 


772.8 


3074.5 


803.6 


3139-2 


835.3 


3204.5 


867.7 


3270.5 


26 


27 


.4500 


773-3 


3075.6 


804.2 


3140.3 : 


835.8 


3205.6 


868.2 


3271.6 


27 


28 


.4667 


773-8 


3076.6 


804.7 


3141-4 ! 


836.3 


320.6.7 


868.8 


3272.7 


28 


29 


.4833 


774-3 


3077-7 


805.2 


3142.5 


836.8 


3207.8 


869.3 


3273-8, 


29 


30 


.5000 


774-8 


3078.8 


805.7 


3143.5 : 


837.4 


3208.9 


869.9 


3274-9 


30 


31 


.5167 


775.3 


3079-9 


806.3 


3144-6 


837.8 


3210.0 


870.5 


3276.0 


3i 


32 


•5333 


775-8 


3080.9 


806.8 


3145-7 : 


838.4 


3211.1 


871.0 


3277.1 


32 


33 


•5500 


776.3 


3082.0 


807.3 


3146.8 , 


838.9 


3212.2 


871.6 


3278.2 


33 


34 


.5667 


776.8 


3083.1 


807.8 


3147-9 j 


839-5 

! 840.0 


3213.3 


872.1 


3279-4 


34 


35 


.5833 


777-3 


3084.2 


808.3 


3149.0 


3214.4 


872.7 


3280.5 


35 


36 


.6000 j 


777-8 


3085.2 


808.8 


3150.0 


! 840.6 


3215.5 


873.2 


3281.6 


36 


37 


.6167 


778.4 


3086.3 


j 809.4 


3151.1 


841. 1 


3216.6 


873-8 


3282.7 


37 


38 


•6333 


778.9 


3087.4 , 


809.9 


3152.2 ' 


. 841.6 


3217.7 


874.3 


3283.8 


38 


39 


.6500 


779-4 


3088.5 


810.4 


3153.3 


842.1 


3218.8 


874-9 


3284.9 


39 


40 


.6667 


779-9 


3089.6 


810.9 


3154.4 


842.7 


3219.9 


875.4 


3286.0 


40 


41 


.6833 


780.4 


3090.7 


811.5 


3155.5 


843-1 


3221.0 


876.0 


3287.1 


41 


42 


.7000 


780.9 


3091.7 


812.0 


3156.6 


843-8 


3222.1 


876.5 


3288.2 


42 


43 


.7167 


781.4 


3092.8 


812.5 


3157.7 


844.2 


3223.2 


877.0 


3289.3 


43 


44 


•7333 


781.9 


3093-9 


813.0 


3158.7 


844.9 


3224.3 


877.6 


3290.5 


44 


45 


.7500 


782.5 


3095.0 


813.6 


31598 


845.5 


3225.4 


878.1 


3291.6 


45 


46 


.7667 


783.0 


3096.0 


814.1 


3160.9 


846.0 


3226.5 


878.7 


3292.7 


46 


47 


.7833 


783.5 


3097.1 


814.6 


3162.0 


846.5 


3227.6 


879.2 


3293-8 


47 


48 


.8000 


784.0 


3098.2 


815. 1 


3163 I 


847.0 


3228.7 


879-8 


3294.9 


48 


49 


.8167 


784.5 


3099-3 


815.7 


3164.2 


847.6 


3229.8 


880.3 


3296.0 


49 


50 


•8333 


785.0 


3100.3 


816.2 


3165.3 


848.1 


3230.9 


880.9 


3297.1 


50 


51 


.8500 


785.5 


3101.4 


816.7 


3166.4 


848.7 


3232.0 


881.5 


3298.2 


5i 


52 


.8667 


786.0 


3102.5 


817.2 


3167.4 


849.2 


3233-1 


882.0 


3299.3 


52 


53 


.8833 


786.6 


3103.6 


817.8 


3168.5 


849.8 


3234.2 


882.6 


3300.4 


53 


54 


.9000 


787.1 


3104.6 


818.3 


3169.6 


850.3 


3235-3 


883.1 


3301.5 


54 


55 


.9167 


787.6 


3105.7 


818.8 


3170.7 


850.9 


3236.4 


883.7 


3302.6 


55 


56 


•9333 


788.1 


3106.8 


8i9-3 


3171.8 


851.4 


3237-5 


884.2 


3303.S 


56 


57 


•95oo 


788.6 


3107.9 


819.9 


3172.9 


852.0 


3238.6 


884.8 


3304-9 


57 


58 


.9667 


789.1 


3108.9 


820.4 


3174-0 


852.5 


3239-7 


885.3 


3306.0 


58 


59 


•9833 


789.7 


3110.0 


820.9 


3175.1 i 


853.0 


3240.8 


885.9 


3307.1 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 185 



Use 100' Chords up to 8 C 
Use 50' Chords up to 16° 



Curves 
Curves 



Use 25' Chords up to 32 Curves 
Use io' Chords above 32 Curves 



Q 

a 


Dec. of 
Degree 


60° 


6i° 


62° 


63° 


.5 



Ext. 


Tan. 


Ext 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


886.4 


3308.2 


920.2 


3375-2 


954-8 


3442.9 


990.3 


35H-3 


1 


.0167 


886.9 


3309-3 1 


920.8 


3376.3 


955-4 


3444-1 


990.9 


3512.4 


1 


2 


•0333 


887.5 


3310.4 


921.4 


3377-4 


956.o 


3445-2 


991-5 


3513-6 


2 


3 


.0500 


888.1 


33H-5 


922.0 


3378.5 


956.6 


3446.3 


992.1 


3514-8 


3 


4 


.0667 


888.7 


3312.7 


922.5 


3379-7 


957-2 


3447-5 


992.7 


3515-9 


4 


5 


•0833 


889.3 


3313-8 


923.0 


3380.8 


957-7 


3448.6 


993-3 


35I7-I 


5 


6 


.1000 ' 


889.8 


3314-9 


923-6 


3381.9 


958.3 


3449-7 


993-9 


35i8.2 


6 


7 


.1167 | 


890.3 


3316.0 


924.2 


3383.1 


958.9 


3450.9 


994-5 


3519-3 


7 


8 


•1333 ' 


890.9 


3317. 1 


924.8 


3384-2 


959-5 


3452.o 


995-1 


3520.5 


8 


9 


.1500 


891.5 


3318.2 


925-3 


3385.3 


960.1 


3453-2 


995-7 


3521.6 


9 


10 


.1667 1 


892.0 


3319-3 


92 5-9 


3386.4 


960.7 


3454-3 


996.3 


3522.8 


10 


11 


•1833 1 


892.6 


3320.5 


926.5 


3387.5 


961.3 


3455-4 


996.9 


3524-0 


11 


12 


.2000 ' 


893-1 


3321.6 


927.1 


3388.7 


961.9 


3456.6 


997-5 


3525-1 


12 


13 


.2167 ; 


893-7 


3322.7 


927.6 


3389.8 


962.4 


3457-7 


998.1 


3526.2 


13 


14 


•2333 I 


894-3 


3323-8 


928.2 


3390.9 


963.0 


3458.8 


998.7 


3527.4 


14 


IS 


.2500 


894.8 


3324-9 


928.7 


3392.1 


963-6 


3460.0 


999-3 


3528.6 j 


15 


16 


.2667 


895-4 


3326.0 


929-3 


3393-2 


964.2 


346i. 1 


999.9 


3529-7 j 


16 


17 


.2833 


8959 


3327-1 


929.9 


3394-3 


964.8 


3462.3 


1000.5 


3530.9 ; 


17 


18 


.3000 


896.5 


3328.3 


930.5 


3395-4 


965.4 


3463-4 


IOOI.I 


3532.0 


18 


19 


•3167 


897.0 


3329-4 


931.0 


3396.6 


966.0 


3464.6 


1001.7 


3533-1 


19 


20 


■3333 


897.6 


3330.5 


931.6 


3397-7 


966.6 


3465.7 


1002.3 


3534-3 


20 


21 


•35oo 


898.2 


3331-6 


932.2 


3398.8 


967.2 


3466.8 


1002.9 


3535-4 


21 


22 


.3667 


898.8 


3332.7 


932.8 


3399-9 


967.8 


3467.9 


1003.5 


3536.6 


22 


23 


.3833 


899-3 


3333-8 


933-3 


340I. 1 


968.3 


3469.0 


1004. 1 


3537-8 


23 


24 


.4000 


899-9 


3334-9 


933-9 


3402.2 


968.9 


3470.2 


1004.7 


3538.9 


24 


25 


.4167 


900.5 


3336.1 


934.5 


3403.3 


969-5 


3471-3 


1005.3 


3540.0 


25 


26 


•4333 


901.0 


3337-2 


935-1 


3404.4 


970.I 


3472.5 


1005.9 


3541-2 


26 


27 


.4500 


901.6 


3338.3 


935-7 


3405.6 


970.7 


3473-6 


1006.5 


3542.3 


27 


28 


.4667 


902.1 


3339-4 


936.3 


3406.7 


971-3 


3474-7 


1007. 1 


3543-5 


28 


29 


.4833 


902.7 


3340.5 


936.8 


3407.8 


971.9 


3475-9 


1007.8 


3544-6 


29 


30 


.5000 


903-2 


3341-6 


937-4 


3408.9 


972.5 


3477-Q 


1008.4 


3545-8 


30 


3i 


•5167 


903-8 


3342.7 


: 938.0 


3410.1 


973-o 


3478.1 


1009.0 


3546.9 


31 


32 


•5333 


904.4 


3343-9 


; 938.6 


3411.2 


973-6 


3479-3 


1009.6 


3548.1 


32 


33 


•5500 


904.9 


3345-0 


939-1 


3412.3 


974-2 


3480.5 


1010.2 


3549-2 


33 


34 


.5667 


905-5 


3346.1 


939-7 


3413-5 


974-8 


3481.6 


1010.8 


3550.4 


34 


35 


.5833 


906.1 


3347-2 


940.4 


3414.6. 


975-4 


3482.7 


1011.4 


3551-6 


35 


36 


.6000 


906.6 


3348.3 


940.9 


3415-7 


976.0 


3483-9 


1012.0 


3552.7 


36 


37 


.6167 


907.2 


3349-5 


; 941-5 


3416.8 


976.6 


3485-o 


1012.6 


3553-8 


37 


38 


.6333 


907.7 


3350.6 


942.1 


3418.0 


977-2 


3486.2 


1013.2 


3555-Q 


38 


39 


.6500 


908.2 


335L7 


942.6 


3419-2 


977-8 


3487.4 


1013.9 


3556.2 


39 


40 


.6667 


908.8 


3352.8 


943-2 


3420.3 


978.4 


3488.5 


1014.5 


3557-3 


40 


41 


.6833 


909.4 


3353-9 


1 943-8 


3421-4 


979.0 


3489.6 


1015.1 


3558.4 


41 


42 


.7000 


910.0 


3355-0 


944-4 


3422.5 


979-6 


3490.7 


1015.7 


3559-6 


42 


43 


.7167 


910.6 


3356.1 


! 944-9 


3423-6 


980.2 


3491-9 


1016.3 


356o.8 


43 


44 


•7333 


911. 1 


3357-3 


! 945-5 


3424.8 


980.8 


3493 .0 


1016.9 


3562.0 


44 


45 


.7500 


911.7 


3358.4 


946.1 


3426.0 


981.4 


3494.2 


1017.5 


3563-2 


45 


46 


.7667 


912.3 


3359-5 


946.7 


3427-1 


982.0 


3495-3 


1018.1 


3564.3 


46 


47 


.7833 


912.8 


3360.6 


947-2 


3428.2 


982.6 


3496.4 


1018.7 


3565.5 


47 


48 


.8000 


913-4 


3361.8 


'i 947.8 


3429-3 


983.2 


3497-6 


1019.3 


35O6. 6 


48 


49 


.8167 


913-9 


3362.9 


94S.4 


3430.4 


983.8 


3498.7 


1020.0 


3567.7 


49 


5o 


•8333 


914-5 


3364-0 


949.0 


3431-6 


984.4 


3499-9 


1020.6 


3568.9 


50 


5i 


.8500 


9i5-i 


3365-I 


949.6 


3432.8 


' 984.0 


350I.O 


1021.2 


357o.o 


51 


52 


.8667 


915-7 


3366.2 


: 950.2 


3433-° 


985.5 


3502.2 


1021.8 


3571.2 


52 


53 


.8833 


916.2 


3367-3 


950.7 


3434-0 


1 986.1 


3503.3 


1022.4 


3572.3 


53 


54 


.9000 


916.8 


3368.5 


Q5X.3 
\ 951-9 


3436.1 


i 986.7 


3504-5 


1023.0 


3573-5 


54 


55 


.9167 


917.4 


3369-6 


3437-2 


; 987.3 


3505.6 


1023.6 


3574-6 


55 


56 


•9333 


918.0 


3370.7 


952.5 


3438.4 


987.9 


35o6.8 


1024.2 


3575-8 


56 


57 


.9500 


918.6 


3371-9 


953-o 


; 3439-6 


1 988.5 


3507.9 


1024.8 


3576.9 


57 


58 


.9667 


9i9-i 


S 3373-Q 


! 953-6 


3440.7 


1 989-1 


3509-0 


1025.4 


3578.1 


58 


59 


•9833 


i 919-6 


! 3374-1 


954-2 


! 3441-8 


i 989.7 


35IO.I 


1026. 1 


3579-3 


59 



i86 



Use ioo' Chords up to 8 C 
Use 50' Chords up to i6 c 



THE SURVEY 

Curves Use 25' Chords up to 32 Curves 
Curves Use 10' Chords above 32 Curves 



m 
<u 
■i-i 

3 

d 



Dec. of 
Degree 


6 4 ° 


65° 


66° 


67° 


<u 

3 

C 

3 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan 


Ext. 


Tan. 


.0000 


1026.7 


3580.4 


1064.0 


3650.4 


1102.2 


3721. 1 


1141.5 


3792.6 ' 


O 


I 


.0167 


1027.3 


3581.6 


1064.6 


3651.6 


1102.9 


3722.3 


1142.2 


3793.8'! 


I ' 


2 


•0333 


1027.9 


3582.8 


1065.2 


3652.8 


1103.5 


3723.4 


1142.8 


3795.o 


2 


3 


.0500 


1028.6 


3583.9 ! 


1065.9 


3654-0 


1104.2 


3724.6 


1 143-5 


3796.2 


3 


4 


.0667 


1029.2 


3585.1 


1066.5 


3655.1 


1 104.8 


3725.8 


1144.1 


3797.4 


4 


5 


•0833 


1029.8 


3586.3 


1067. 1 


3656.3 


1105.5 


3727.0 


1144-8 


3798.6 


5 


6 


.1000 


1030.4 


3587.4 


1067.7 


3657.5 


1106.1 


3728.2 


1 145.4 


3799-8 


6 


7 


.1167 


1031.1 


3588.6 


1068.4 


3658.6 


1106.8 


3729.4 


1146.1 


3801.0 


7 


8 


•1333 


1031-7 


3589-7 


1069.0 


3659.8 


1107.4 


3730.6 


1146.7 


3802.2 


8 


9 


.1500 


1032.3 


3590.9 


1069.6 


3661.0 


1108.1 


3731-7 


1147.4 


3803.4 


9 


IC 


.1667 


1032.9 


3592.1 


1070.2 


3662.2 ! 


1108.7 


3732.9 


1148.1 


3804.6 


10 


11 


.1833 


1033-5 


3593-3 


1070.9 


3663.4 


1 109.4 


3734-1 


1148.8 


3805.8 


11 


12 


.2000 


1034.I 


3594-4 


1071-5 


3664.5 


IIIO.O 


3735-3 


1149.4 


3807.0 


12 


13 


.2167 


1034.8 


3595-5 


1072. 1 


3665.7 


1110.7 


3736.5 


1150.1 


3808.2 


13 


14 


• 2333 


IQ35-4 


3596.7 


1072.7 


3666.9 


1111.3 


3737-7 


1150.7 


3809.4 


|I4 


IS 


.2500 


1036.0 


3597-9 


1073-4 


3668.O 


III2.0 


3738.9 


II5I-4 


3810.6 


! I5 


16 


.2667 


1036.6 


3599-1 


1074.0 


3669.2 


III2.6 


3740.I 


| 1152.0 


3811.8 


16 


17 


.2833 


IQ37-3 


3600.3 


1074-6 


3670.4 | 


IH3-3 


3741-3 


1152.7 


3813.0 


I 1 ! 


18 


.3000 


1037.9 


3601.4 


1075-2 


3671.6 j 


1113.9 


3742.4 


H53-3 


3814.2 


18 


19 


.3167 


1038.5 


3602.6 


10759 


3672.8 


1114.6 


3743-6 


H54-0 


3815.4 


19 

I 


20 


•3333 


1039.1 


3603.7 


1076.6 


3673.9 


11152 


3744-8 


H54-7 


3816.6 


20 


21 


•35oo 


1039.7 


3604.8 ; 


1077.2 


3675.0 


1115.9 


3746.o 


II55.4 


3817-8 


21 


22 


.3667 | 


1040.3 


3606.O 


1077-8 


3676.2 


1116.5 


3747-2 


1156.0 


3819.0 


22 


23 


•3833 ! 


1041.0 


3607.2 


1078.5 


3677.4 


1117.2 


3748.4 


1156.7 


3820.2 


23 


24 


.4000 


1 041.6 


3608.4 


1079. 1 


3678.6; 


1117.8 


3749-6 


II57.4 


3821.4 


24 


25 


.4167 | 


1042.2 


3609.5 


1079.8 


3679.7 


1118.5 


3750.7 


1158.1 


3822.6 


2 5 


26 


•4333 1 


1042.8 


3610.7 


1080.4 


3680.9 


IIIQ.I 


3751-9 


1158.7 


3823.8 


26 


27 


.4500 


1043 -5 


3611.9 


1081.1 


3682.I 


III9.8 


3753-1 


H59-4 


3825.0 


27 


28 


.4667 ; 


1044. 1 


3613.O 


1081.7 


3683.3 ! 


II2O.4 


3754-3 


1160.1 


3826.2 


28 


29 


.4833 I 


1044.7 


3614-1 


1082.4 


3684.5 


II2I.I 


3755.5 


1160.8 


3827.4 


29 


30 


.5000 


1045.3 


36I5.3 


1083.0 


3685.6 


II2I.7 


3756.7 


1161.4 


3828.6 


30 


31 


•5167 


1045.9 


3616.5 


1083.6 


3686.8 i 


II22.3 


3757-9 


1162.1 


3829.8 


31 


32 


•5333 


1046.5 


3617.7 


1084.2 


3688.0 


II23.O 


3759-1 


1162.8 


3831.0 


J32 


33 


•5500 


1047.2 


3618.9 ; 


1084.9 


3689.2 


II23.7 


3760.3 


1163.5 


3832.2 


33 


34 


•5667 , 


1047.8 


3620.O 


1085.5 


3690.4 


II24.3 


3761.5 


1164-1 


3833.4 


J34 


35 


.5833 


1048.4 


3621. 1 1 


1086.2 


3691.6 


II25.0 


3762.7 


1164.8 


3834-6 


35 


36 


.6000 


1049.0 


3622.3 


1086.8 


3692.7 


II2S.6 


3763.9 


1165.5 


3835-9 


36 


37 


.6167 


1049.7 


3623.5 


1087.5 


3693-9 ! 


II26.3 


3765-1 


1166.2 


3837-1 


37 


38 


•6333 


1050.3 


3624.7 


1088. 1 


3695-1 ! 


II26.9 


3766.3 


1166.8 


3838.3 


38 


39 


.6500 


1050.9 


3625.8 


1088.8 


3696.2 j 


II27.6 


3767.5 


1167.5 


3839.5 


39 


40 


.6667 


1051.5 


3627.O 


1089.4 


3697-4 


II28.3 


3768.7 


1 1168.2 


3840.7 


40 


4i 


.6833 


1052. 1 


3628.2 


1090.0 


3098.6 


II29.O 


3769.9 


1168.9 


3841.9 


41 


42 


.7000 


1052.7 


3629.4 


1090.6 


3699.8 


II29.6 


3771.0 


1169.5 


3843-1 


i 4 2 


43 


.7167 


1053.4 


3630.5 ! 1091.3 


3701.0 


H30.3 


3772.2 


1170.2 


3844-3 


43 


44 


•7333 


1054.0 


363L7 


j 1091.9 


3702.2 


II3O.9 


3773-4 


1170.9 


3845-5 


44 


45 


•7500 


1054.6 


3632.8 


I 1092.6 


3703-3 


II3I-6 


3774-6 


1 171. 6 


3846.7 


'45 


46 


.7667 


1055.2 


3634-0 


1093.2 


3704-5 


II32.2 


3775-8 


1172.2 


3847-9 


46 


47 


•7833 


1055.9 


3635-2 


; 1093.9 


3705-7 


II32.9 


3777.0 


1172.9 


3849-1 


47 


48 


.8000 


1056.5 


3636.4 


1094-5 


3706.9 


1 133 -5 


3778.2 


H73-6 


3850.4 


48 


49 


.8167 


1057.1 


3637.5 


1095.2 


3708.1 


H34-2 


3779-4 


1 1 74-3 


3851.6 


49 


50 


.8333 


1057.7 


3638.7 


1095.8 


3709-3 


H34-9 


378o.6 


1174.9 


3852.8 


50 


51 


.8500 


1058.4 


3639.9 


1096.4 


3710.5 


H35-6 


3781.8 


1175-6 


3854.0 


51 


52 


.8667 


1059.0 


364LI 


1097.0 


3711.6 


1136.2 


3783-0 


1176.3 


3855-2 


52 


53 


.8833 


1059.6 


3642.3 


1 1097-7 


3712.8 


1136.9 


3784.2 


1177-0 


3856.4 


53 


54 


.9000 


1060.2 


3643-4 


; 1098.3 


3714-0 


II37.5 


3785-4 


1177.6 


3857.6 


'54 


55 


.9167 


1060.9 


3644.6 


1099.0 


3715. 1 


1138.2 


3786.6 


II78.3 


3858.8 


55 


56 


•9333 


106 1. 5 


3645.7 


1099.6 


3716.3 


1138.8 


3787.8 


11790 


3860.0 


56 


57 


.9500 


1062. 1 


3646.9 


1 100.3 


3717-5 


1139-5 


; 3789.0 


H79-7 


3861.2 


57 


58 


.9667 


1062.7 


3648.1 


1 100.9 


3718.7 


1 140. 1 


3790.2 


1180.3 


3862.5 


58 


159 


.9833 


1063.4 


3649.2 


1101.6 


3719-9 


i 1 140.8 


! 3791.4 


1181.0 


3863.7 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 187 



Use 100' Chords up to 8° Curves 
Use 50' Chords up to 16° Curves 



Use 25' Chords up to 32 Curves 
Use 10' Chords above 32° Curves 



in 
6 

+-> 

P 

§ 




Dec. of 
Degree 


68° 


69° 


70° 


7i° 


1 "> 

! <u 
■*-> 

3 
C 

§ 


Ext. 


Tan. 


Ext. 


Tan. 


1 Ext. 


Tan. 


Ext. 


Tan. 


.0000 


1181.6 


3864.9 


1222.9 


3938.1 


1265.0 


401 2.1 


1308.4 


4087.1 





I 


.0167 


1182.3 


3866.1 


1223.6 


3939-4 


1265.7 


4013.4 


1309.2 


4088.4 


I 


2 


•0333 


1183.0 


3867.3 


1224.3 


3940.6 


1266.4 


4014.6 


1309.9 


4089.7 


2 


3 


.0500 


"83.7 


3868.5 


1225.0 


3941-8 


1267.2 


4015.9 


1310.6 


4091.0 


3 


4 


.0667 


1184.4 


3869.7 


1225.7 


3943-Q 


1267.9 


4017. 1 


1311-3 


4092.2 


4 


5 


.0833 


1185.1 


3870.9 


1226.4 


3944-2 


! 1268.6 


4018.4 


1312.1 


4093-5 


5 


6 


.1000 


1185.7 


3872.2 


1227. 1 


3945-5 


1269.3 


4019.6 


1312.8 


4094.7 


6 


7 


.1167 


1186.4 


3873-4 


1227.8 


3946.7 


1 1270.1 


4020.8 


1313-5 


4096.0 


7 


8 


•1333 


1187.1 


3874-6 


1228.5 


3947-9 


1270.8 


4022.1 


1314-2 


4097.2 


8 


9 


.1500 


1187.8 


3875-8 


1229.2 


3949-2 


1 1271-5 


4023.4 


1315-0 


4098.5 


9 


10 


.1667 


1188.5 


3877-0 


1229.9 


3950.4 


1272.2 


4024.6 


1315.7 


4099.8 


10 


11 


•1833 


1189.2 


3878.2 


1230.6 


3951-6 


' 1272.9 


4025.8 


1316.5 


4101.1 


11 


12 


.2000 


1189.8 


3879-5 


1231.3 


3952.9 


j 1273-6 


4027.1 


1317-2 


4102.3 


12 


13 


.2167 


1190.5 


3880.7 


1232.0 


3954-1 


1274.4 


4028.4 


I3I7-9 


4103.6 


13 


14 


•2333 ; 


1191.2 


3881.9 


1232.7 


3955-3 


1275.1 


4029.6 


1318.6 


4104.8 


14 


IS 


.2500 


1191.9 


3883.1 


1233-4 


3956.6 


1275-8 


4030.8 


1319-4 


4106. 1 


15 


16 


.2667 


1192.6 


3884.3 


1234-1 


3957-8 


: 1276.5 


4032.1 


1320.1 


4107-3 


16 


17 


.2833 


"933 


3885.6 


1234.8 


3959-Q 


j 1277-3 


4033-4 


1320.8 


4108.6 


17 


18 


.3000 


H93-9 


3886.8 


1235-5 


3960.2 


i 1278.0 


4034.6 


1321.5 


4109.8 


18 


19 


•3l67 


1194.6 


3888.0 


1236.2 


3961.5 


; 1278.7 


4035-9 


1322.3 


4111.1 


19 


20 


•3333 


"95-3 


3889.2 


1236.9 


3962.7 


1279.4 


4037.1 


1323.0 


4112.4 


20 


21 


•3500 


1196.0 


3890.4 


1237-6 


3964.0 


1280.1 


4038.4 


1323.7 


4113-7' 


21 


22 


.3667 


1196.7 


3891-6 


1238.3 


3965-2 


1280.8 


4039.6 


1324.4 


4II4-9 


22 


23 


•3833 


1197.4 


3892.9 


1239.0 


3966.4 


! 1281.6 


4040.9 


1325-2 


4116.2 


23 


24 


.4000 


1 198.0 


3894.1 


1239.7 


3967-6 


j 1282.3 


4042.1 


1325-9 


4II7-4 


24 


25 


.4167 


1198.7 


3895-3 


1240.4 


3968.9 


1283.0 


4043.4. 


1326.7 


4118.7 


25 


26 


•4333 


1199.4 


3896.5 


1241.1 


397o.i 


1283.7 


4044.6 


1327-4 


4119.9 


26 


27 


.4500 


1200. 1 


3897.7 


1241.8 


397L3 


1284.5 


4045-9 


1328.2 


4121.2 


27 


28 


.4667 


1200.8 


3898.9 


1242.5 


3972.5 


1285.2 


4047.1 


1228.9 


4122.4 


! 2 8 


29 


•4833 


1 201.5 


3900.2 


1243.2 


3973-8 


1285.9 


4048.4 


1329.7 


4123.7 


I 29 


30 


.5000 


1202. 1 


3901.4 


1243.9 


3975-0 


1286.6 


4049.6 


1330.4 


4125.0 


30 


3i 


•5167 


1202.8 


3902.6 


1244.6 


3976.3 ! 


1287.3 


4050.9 


i33i-i 


4126.3 


j 31 


32 


•5333 


1203.5 


3903-8 


1245-3 


3977-5 


1288.0 


4052.1 


I33I-8 


4127-5 


32 


33 


•55oo 


1204.2 


3905-0 


1246.0 


3978.8 J 


1288.8 


4053-4 


1332.6 


4128.7 


33 


34 


.5667 


1204.9 


3906.3 


1246.7 


3980.O 


1289.5 


4054.6 


1333.3 


4130.0 


34 


35 


•5833 


1205.6 


3907-5 


1247.4 


3981.2 


1290.2 


4055.9 


I334-I 


4131.5 


35 


36 


.6000 


1206.2 


3908.7 


1248.1 


3982.4 


1290.9 


4057-1 


1334.8 


4132.6 


36 


37 


.6167 


1206.9 


3909.9 


1248.8 


3983.7 


1 291.7 


4058.4 


1335-6 


4I33.9 


37 


38 


•6333 


1207.6 


3911.2 


1249.5 


3984.9 


1292.4 


4059-6 


1336.3 


4I35-I 


38 


39 


.6500 


1208.3 


3912.4 


1250.2 


3986.1 


1293-1 


4060.9 


1337. 1 


4136.4 


39 


40 


.6667 


1209.0 


39I3.6 


1250.9 


3987.4 


1293.8 


4062.1 


1337-8 


4137.7 


40 


41 


.6833 


1209.7 


3914-9 


1251.6 


3988.7 : 


1294.6 


4063.4 


1338.5 


4139-0 


41 


42 


.7000 


1210.3 


3916. 1 


1252.3 


3989-9 


1295.3 


4064.6 


1339-2 


4140.2 


42 


43 


.7167 


1211.0 


3917.3 


1253-0 


399I-I 


1296.0 


4065.9 


1340.0 


4i4i-5 


43 


44 


•7333 


1211.7 


3918.5 


1253-7 


3992.3 


1296.7 


4067.1 


1340.7 


4142.7 


44 


45 


•7500 


1212.4 


3919-8 


1254-4 


3993-6 


1297.5 


4068.4 


I34I-5 


4144.0 


45 


46 


.7667 


1213.1 


3921.0 


I255-I 


3994-8 


1298.2 


4069.6 


1342.2 


4145-3 


46 


4 l 


.7833 


1213.8 


3922.2 


1255-8 


3996.0 ; 


1298.9 


4070.9 


I343-Q 


4146.6 


47 


48 


.8000 


1214.5 


3923.4 


1256.5 


3997-3 


1299.6 


4072.1 


1343-7 


4147.8 


48 


49 


.8167 


1215.2 


3924-7 


1257.2 


3998.6 


1300.4 


4073-4 


1344-5 


4149.1 


49 


50 


•8333 


1215.9 


3925-9 


1257-9 


3999.8 


1301.1 


4074-6 


1345-2 


4150.4 


50 


51 


.8=500 


1216.6 


2927.1 


1258.6 


4001.0 


1301.9 


4075-9 


1346.0 


4151.7 


51 


52 


.8667 


1217.3 


3928.3 


1259-3 


4002.2 i 


1302.6 


4077.1 1 


1346.7 


4152.9 52 


53 


•8833 


1218.0 


3929-6 


1260.0 


4003.4 


1303-3 


4078.4 


1347.5 


4154-2 


53 


54 


.9000 


1218.7 


3930.8 


1260.7 


4004.7 


1304.0 


4079.6 


1348.2 


4155-4 


54 


55 


.9167 


1219.4 


3932.o 


1261.4 


4006.0 


1304.8 


4080.9 


13490 


4156.7 




56 


•9333 


1220. 1 


3933-2 


1262. 1 


4007.2 


\ 1305-5 


4082.1 


1349-7 


4158.0 


56 


57 


9500 


1220.8 


3934-4 


1262.8 


4008.5 


1306.2 


4083.4 


1350.5 


4159-3 


57 


58 


.9667 


1221.5 


3935-7 


1263.5 


4009.7 


1306.9 


4084.6 


I35I-2 


4160.5 


58 


59 


•9833 


1222.2 


3936.9 


1264.3 


4010.9 


[307.7 4085.0 


1352.O 4161.S 59 



1 88 THE SURVEY 

Use ioo' Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16 Curves Use 10' Chords above 32 Curves 

-.0 _„o _.o o 



a 


<u 


72° 


73° 


74° 


75° 


8 

3 

a 

9 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


13S2.7 


4163-1 


1398.1 


4240.0 


1444-7 


4317.8 


1492.5 


4396.7 





I 


.0167 


1353.5 


4164.4 


1398.9 


4241.3 


1445-5 


4319-2 


1493.3 


4398.1 


1 


2 


.0333 


1354-2 


4165.6 


1399-6 


4242.6 


1446.2 


4320.5 


I494-I 


4399-4 


2 


3 


.0500 


I355-Q 


4166.9 


1400.4 


4243-9 


1447.0 


4321.8 


1494.9 


4400.8 


3 


4 


.0667 


1355-7 


4168.2 


1401.2 


4245.1 


1447.8 


4323-1 


1495.7 


4402.1 


4 


S 


•0833 


1356.5 


4169.5 


1402.0 


4246.4 


1448.6 


4324-4 


1496.5 


4403.4 


5 


6 


.1000 


1357-2 


4170.7 


1402.7 


4247.7 


1449.4 


4325.7 


1497.3 


4404-7 


6 


7 


.1167 


1358.0 


4172.0 


1403-5 


4249-0 


1450.2 


4327.0 


1498.2 


4406.1 


7 


8 


•1333 


1358.7 


4173-3 


1404.2 


4250.3 


I45I.O 


4328.3 


1499.0 


4407.4 


8 


9 


.1500 


1359-5 


4174-5 


1405.0 


4251.6 


I45I.8 


4329-6 


1499.8 


4408.7 


9 


10 


.1667 


1360.2 


4175-8 


1405.8 


4252.9 


1452.6 


4330.9 


1500.6 


4410.0 


10 


n 


•1833 


1361.0 


4177. 1 


1406.6 


4254.2 


1453-4 


4332.3 


1501.4 


4411.4 


11 


12 


.2000 


1361.7 


4178.4 


1407-3 


4255.5 


I454-I 


4333-6 


1502.2 


4412.7 


12 


13 


.2167 


1362.5 


4179-7 


1408.1 


4256.8 


1454.9 


4334-9 


1503-0 


4414.0 


13 


14 


•2333 


1363.2 


4181.0 


1408.8 


4258.1 


1455.7 


4336.2 


1503.8 


4415.3 


14 


IS 


.2500 


1364-0 


4182.3 


1409.6 


4259.4 


1456.5 


4337-5 


1504.6 


4416.6 


15 


16 


.2667 


1364-7 


4183.5 


1410.4 


4260.7 


1457.3 


4338.8 


1505.4 


4418.0 


16 


17 


.2833 


1365.5 


4184.8 


1411.2 


4262.0 


I458.I 


4340.I 


1506.2 


4419.4 


17 


18 


.3000 


1366.2 


4186.1 


1411.9 


4263.2 


1458.9 


4341-4 


1507.0 


4420.7 


18 


19 


•3167 


1367.0 


4187.4 


1412.7 


4264.5 


1459.7 


4342.7 


1507.9 


4422.0 


19 


20 


•3333 


1367.7 


4188.6 


1413-5 


4265.8 


1460.5 


4344.0 


1508.7 


4423-3 


20 


21 


•35oo 


1368.5 


4189.9 


1414-3 


4267.1 


1461.3 


4345-4 


1509.5 


4424-6 


21 


22 


.3667 


1369.2 


4191-2 


1415.1 


4268.4 


1462.0 


4346.7 


1510.3 


4426.0 


22 


23 


.3833 


i37o.c 


4192.5 


1415-9 


4269.7 


1462.8 


4348.0 


1511.2 


4427.3 


23 


24 


.4000 


1370.7 


4193-7 


1416.6 


4271.0 


1463.6 


4349-3 


1512.0 


4428.6 


24 


25 


.4167 


I37I.5 


4195.0 


14174 


4272.3 


1464.4 


4350.6 


1512.8 


4430.0 


25 


26 


•4333 


1372.2 


4196.3 


1418.2 


4273-6 


1465.2 


4351-9 


1513-6 


443 1 -3 


26 


27 


.4500 


1373-0 


4197.6 


1419.0 


4274.9 


1466.0 


4353-2 


I5I4-5 


4432.7 


27 


28 


.4667 


1373-7 


4198.8 


1419-7 


4276.2 


1466.8 


4354-5 


I5I5-3 


4434.0 


28 


29 


.4833 


1374-5 


4200.1 


1420.5 


4277. 5 


1467.6 


4355-8 


1516.1 


4435-3 


29 


30 


.5000 


1375-2 


4201.4 


1421.3 


4278.8 


1468.4 


4357-1 


1516.9 


4436.6 | 


30 


3i 


•5167 


1376.0 


4202.7 


1422. 1 


4280.1 


1469.2 


4358.5 


I5I7.7 


4438.o 


3i 


32 


•5333 


1376.7 


4204.0 


1422.9 


4281.4 


1469.9 


4359-8 


1518.5 


4439-3 


32 


33 


.55oo 


1377.5 


4205.3 


1423.7 


4282.7 


1470.7 


4361. 1 


I5I9-4 


4440.7 


33 


34 


.5667 


1378.2 


4206.5 


1424.4 


4284.0 


I47I.5 


4362.4 


1520.2 


4442.0 


34 


35 


.5833 


1379-0 


4207.8 


1425.2 


4285.3 


1472.3 


4363.8 


1521.0 


4443-3 


35 


36 


.6000 


1379-7 


4209.1 


1426.0 


4286.6 


I473-I 


4365-1 


1521.8 


4444.6 


36 


37 


.6167 


1380.5 


4210.4 


1426.8 


4287.9 


1473-9 


4366.4 


1522.7 


4446.0 


37 


38 


•6333 


1381.2 


4211.7 


1427.5 


4289.2 


1474-7 


4367.7 


1523.5 


4447-3 


38 


39 


.6500 


1382.0 


4213.0 


1428.3 


4290.5 


1475.6 


4369-0 


1524.3 


4448.7 


39 


40 


.6667 


1382.8 


4214.3 


1429.1 


4291.8 


1476.4 


4370.3 


1525. 1 


4450.0 


40 


41 


•6833 


1383.6 


4215.6 


1429.9 


4293-1 


1477-2 


437L7 


1525-9 


4451-4 


41 


42 


.7000 


1384.3 


4216.8 


1430.7 


4294.4 


1478.0 


4373-0 


1526.7 


4452.7 


42 


43 


.7167 


1385. 1 


4218. 1 


I43T-5 


4295-7 


1478.8 


4374-3 


1527.6 


4454-0 


43 


44 


•7333 


1385.8 


4219.4 


1432.2 


4297.0 


1479-6 


4375-6 


1528.4 


4455-3 


44 


45 


•75oo 


1386.6 


4220.7 


i433.o 


4298.3 


1480.4 


4377-0 


1529-2 


4456.7 


45 


46 


.7667 


1387.4 


4222.0 


1433.8 


4299.6 


1481.2 


4378.3 


1530.0 


4458.o 


46 


47 


.7833 


1388.2 


4223.3 


1434.6 


4300.9 


1482.0 


4379-6 


1530.9 


4459-4 


47 


48 


.8000 


1388.9 


4224.5 


U35-3 


4302.2 


1482.8 


4380.9 


I53I-7 


4460.7 


48 


49 


.8167 


1389.7 


4225.8 


1436.1 


4303.5 


1483.6 


4382.2 


1532.5 


4462.1 


49 


50 


•8333 


1390.4 


4227.1 


1436.9 


4304-8 


1484.4 


4383.5 


1533-3 


4463.4 


50 


51 


.8500 


I39I-2 


4228.4 


1437.7 


4306.1 


1485.2 


4384.9 


1534-1 


4464.7 


51 


52 


.8667 


1392.0 


4229.7 


1438.5 


4307.4 


1486.0 


4386.2 


1534.9 


4466.0 


52 


53 


.8833 


1392.8 


4231.0 


1439.3 


4308.7 


1486.9 


4387.5 


1535-8 


4467.4 


53 


54 


.9000 


1393-5 


4232.3 


1440.0 


4310.0 


1487.7 


4388.8 


1536.6 


4468.7 


54 


55 


.9167 


1394-3 


4233-6 


1440.8 


43H-3 


1488.5 


4390.2 


1537.4 


4470.1 


55 


56 


•9333 


I395-Q 


4234.8 


1441.6 


4312.6 


1489.3 


4391-5 


1538.2 


4471.4 


56 


57 


•95oo 


1395-8 


4236.1 I 


1442.4 


4313-9 


1490.1 


4392.8 


I539-I 


4472.7 


57 


58 


.9667 ! 


1396.6 


4237.4! 


I443-I 


4315-2 


1490.9 


4394.1 


1539-9 


4474-1 


58 


59 


•9833 ; 


1397-4 


4238.7 ; 


1443-9 


4316.5 


I49I-7 


4395-4 


1540.7 


4475-4 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 189 





Use 100' Chords up to 8 


Curves 


Use 


25' Chords up to 


32 Curves 




Use 50 


Chords up to 16 


Curves Use 


10' Chords above 32 Curves 


c 


:/. 

QQ 


76° 


77° 


78° 


79° 


CA 

-4-1 

G 

s 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 

4723-4 





.0000 


IS4I-5 


4476.7 


I59I-7 


4557-8 


1643-1 


4640.0 


1696.0 


I 


.0167 


1542.4 


4478.1 


1592.6 


4559-2 


1644.0 


4641.4 


1696.9 


4724-8 1 


2 


.0333 


1543-2 


4479-4 


1593-4 


4560.5 


1644.8 


4642.8 


1697.7 


4726.2 2 


3 


.0500 


I544-I 


4480.8 


1594-3 


4561.9 


1645-7 


4644.2 


1 1698.6 


4727.6 3 


4 


.0667 


1544-9 


4482.1 


I595-I 


4563.3 


1646.6 


4645-6 


1699.5 


4729.0 4 


5 


.0833 


1545-7 


4483.5 


1596.0 


4564-7 


1647.5 


4647.0 


1 1700.4 


4730.4 5 


6 


.1000 


' 1546.5 


44^4-8 


1596.8 


4566.0 


1648.3 


4648.3 


1701.3 


4731-8 6 


7 


.1167 


1547-4 


4486.2 


1597-7 


4567.4 


1 1649.2 


4649-7 


1702.2 


4733-3 7 


8 


• 1333 


1548.2 


44^7-5 


1598.5 


4568.7 


1650.1 


4651-1 


1703. 1 
1 1704.0 


4734-7 8 


9 


.1500 


I549-I 


4488.9 


1599-4 


4570.I 


1651.0 


4652.5 


4736.1 9 


10 


.1667 


1549-9 


4490.2 


1600.2 


4571-5 


1651.8 


4653-9 


1704.9 


4737-5 10 


11 


.1833 


I550.7 


4491.6 


1601.1 


4572.9 


1652.7 


4655-3 


1 1705.8 


4738.9 11 


12 


.2000 


I55L5 


4492.9 


1601.9 


4574-2 


1653-6 


4656.7 


i 1706.6 


4740.3 12 


13 


.2167 


1552.4 


4494-3 


1602.8 


4575-6 


! 1654.5 


4658.1 


■ 1707-5 


4741-7 13 


14 


•2333 


1553.2 


4495-6 


1603.6 


4576.9 


1655.3 


4659.4 


j 1708.4 


4743-1 14 


15 


.2500 


I554-I 


4497 -o 


1604.5 


4578.3 


1656.2 


4660.8 


! 1709.3 


4744-5 15 


16 


.2667 


1554-9 


4498.3 


1605.3 


4579-7 


I657-I 


4662.2 


; 1710.2 


4745-9 16 


17 


• 2833 


1555-7 


4499-7 


1606.2 


4581. 1 


1658.O 


4663.6 


17111 


4747-3 17 


18 


.3000 


1556.5 


4501.0 


1607.0 


4582.4 


| 1658.8 


4665.0 


17 12.0 


4748.7 


18 


19 


•3167 


1557-4 


4502.4 


1607.9 


4583-8 


; 1659.7 


4666.4 


1712.9 


4750.I 


19 


20 


•3333 


1558.2 


4503-7 


1608.7 


4585-I 


; 1660.6 


4667.7 


1713.8 


4751-5 


20 


21 


.35oo 


I559-I 


4505.0 


1609.6 


4586.5 


' 1661.5 


4669.1 


1714-7 


4752.9 21 


22 


.3667 


1559-9 


4506.3 


1610.4 


4587.9 


1 1662.3 


4670.5 


I7I5-6 


4754-3 22 


23 


.3833 


1560.7 


4507-7 


1611.3 


4589-3 


; 1663.2 


4671.9 


1716.5 


4755-7 23 


24 


.4000 


1561.5 


4509-0 


1612.1 


4590.6 


1 664. 1 


4673-3 


| I7I7-4 


4757-1 24 


25 


.4167 


1562.4 


45I0.4 


1613.0 


4592.o 


1665.O 


4674.7 


1718.3 


4758.6 25 


26 


•4333 


1563.2 


45H-7 


1613.8 


4593-3 


1665.8 


4676.0 


1719.2 


4760.0 26 


27 


.4500 


1564-1 


45I3-I 


1614.7 


4594-7 


1666.7 


4677-4 


1720.1 


4761.4 27 


28 


.4667 


1564-9 


4514-4 


i6i5-5 


4596.o 


1667.6 


4678.8 


1721.0 


4762.8 


28 


29 


.4833 


1565.7 


4515-8 


1616.4 


4597-4 


1668.5 


4680.2 


1721.9 


4764.2 


29 


30 


.5000 


1566.5 


4517. 1 


1617.3 


4598.8 


1669.3 


4681.6 


! 1722.8 


4765-6 


30 


3i 


.5167 


1567.4 


4518.5 


1618.2 


4600.2 


167O.2 


4683.0 


i 1723-7 


4767.0 


31 


32 


•5333 


1568.2 


4519-8 


1619.0 


4601.5 


167I.I 


4684.4 


1724.6 


4768.4 


32 


33 


•5500 


1569-1 


4521. 1 


1619.9 


4602.9 


1672.O 


4685.8 


1725-5 


4769.8 


33 


34 


.5667 


1569.9 


452 2.5 


1620.7 


4604.3 


1672.8 


4687.2 


1726.4 


4771.2 


34 


35 


•5833 


I570.7 


4523-9 


1621.6 


4605.7 


1673.7 


4688.6 


1727-3 


4772.7 


35 


36 


.6000 


I57L5 


452 5-3 


1622.4 


4607.0 


1674.6 


4689.9 


1728.2 


4774-1 36 


37 


.6167 


1572.4 


4526.7 


1623.3 


4608.4 


I675-5 


4691.3 


1729.1 


4775-5 37 


38 


•6333 


1573-2 


4528.0 


1624. 1 


4609.8 ! 


1676.3 


4692.7 


1730.0 


47/6.9 38 


39 


.6500 


I574-Q 


4529.4 


1625.0 


4611.2 


I677-3 


4694.1 


1731-0 


4778.3 | 39 


40 


.6667 


1574.8 


4530.7 


1625.9 


4612.5 


1678.2 


4695-5 


I73I.9 


4779-7 40 


4i 


.6833 


1575-6 


4532.1 


1626.8 


4613.9 


I679-I 


4696.9 


1732.8 


4781. 1 41 


42 


.7000 


1576.4 


4533-4 


1627.6 


4615.3 


1679.9 


4698.3 


1733-7 


4782.6 42 


43 


.7167 ] 


1577-3 


4534-8 


1628.5 


4616.7 


1680.8 


4699.7 


1734-6 


4784.0 43 


44 


•7333 J 


I578.I 


4536.1 


1629.3 


4618.0 


1681.7 


4701. 1 


1735-5 


4785-4 44 


45 


•7500 


.I579-0 


4537-5 


1630.2 


4619.4 


1682.6 


4702.5. 


1736.4 


4786.8 45 


46 


.7667 


1579.8 


4538.8 


1631.0 


4620.8 


1683.5 


4703.9 


1737.3 


4788.2 46 


47 


•7833 


1580.7 


4540.2 


1631.9 


4622.2 


1684.4 


4705.3 


1738.2 


4789.6 47 


48 


.8000 


1581.5 


4541-5 


1632.7 


4623-5 


1685.3 


4706.7 


I739-I 


4791.0 48 


49 


.8167 


1582.4 


4542.9 


1633.6 


4624.9 


1686.2 


4708.1 


1740.0 


4792-5 49 


SO 


.8333 


1583.2 


4544-2 


1634-5 


4626.3 


1687. 1 


4709.5 


1740.9 


4793-9 : 50 


51 


.8500 


1584.1 


4545-6 


1635-4 


4627.7 


1688.O 


4710.9 


1741.8 


4795-3 5i 


52 


.8667 


1584.9 


4547-Q 


1636.2 


4629.0 


1688.8 


4712.2 


1742.7 


4796-7 52 


53 


.8833 


1585.8 


4548.4 


1637. 1 


4630.4 


1689.7 


4713-6 


1743-6 


4798.1 53 


54 


.9000 


1586.6 


4549-7 


1637.9 


4631.8 j 


169O.6 


47i5-o 


1744-5 


4799-5 54 


55 


.9167 


1587.5 


4551- 1 


1638.8 


4633-2 


I69I.5 


4716.4 


1745-4 


4801.0 


55 


56 


•9333 


1588.3 


4552.4 


1639.6 


4634-5 


1 1692.4 


4717-8 


1746.3 


4802.4 


56 


57 


.9500 


1589.2 


4553-8 


1640.5 


4635-9 


! 1693-3 


4719-2 


1747-2 


4803.8 


57 


58 


.9667 


i 1590.0 


4555-1 


1641-3 


4637-3 


1694.2 


4720.6 


1748.1 


4805.2 


58 


59 


.9833 


' I590.9 


4556.5 


j 1642.2 


4638.7 


1695-1 


4722 


1749-1 


4806.6 


5Q_ 



I go THE SURVEY 

Use ioo' Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16 Curves Use 10' Chords above 32 Curves 

^ « : 8o° 8i° 82 8^° 



C/3 
V 
4-1 

a 

§ 




Dec. of 
Degree 


8o° 


8i° 


82 


83° 


1) 

a 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


1750.0 


4808.0 


| 
1805.5 4893.9 


1862.3 


4981.0 


1920.6 


5069.4 





I 


.0167 


1750.9 


4809.5 


1806.4 4895-4 


1863.3 


4982.5 


1921.6 


5070.9 


1 


2 


•0333 


1751-8 


4810.9 


1807.3 4896.8 


1864.2 


4983.9 


1922.6 


5072.4 


2 


3 


.0500 


1752.8 


4812.3 


1808.3 ! 4898.3 


1865.2 


4985.4 


1923.6 


5073-9 


3 


4 


.0667 


1753-7 


4813.7 


1809.2 


4899.7 


1866.1 


4986.8 


1924.6 


5075.4 


4 


5 


.0833 


1754-6 


4815.2 


1810.2 


4901.2 


! 1867. 1 


4988.3 


1925.6 


5076.9 


5 


6 


.1000 


1755-5 


4816.6 


1811.1 


4902.6 


1868.1 


4989-8 


1926.5 


5078.4 


6 


7 


.1167 


1756.5 


4818.0 


1812.1 4904.0 


1869. 1 


499L3 


1927-5 


5079-9 


7 


8 


•1333 


1757-4 


4819.4 


1813.0 ■ 4905.4 


1870.0 


4992.7 


1928.5 


5081.4 


8 


9 


.1500 j 


I7S8.3 


4820.9 


1814.0 I 4906.9 


1871.0 


4994.2 


1929.5 


5082.9 


9 


10 


.1667 


1759-2 


4822.3 


18 14.9 ■ 4908.3 


1871.9 


4995-7 


1930.5 


5084.4 


10 


11 


.1833 


1760. 1 


4823.7 


1815.9 4909.8 


1872.9 


4997.2 


1931-5 


5085.9 


11 


12 


.2000 


1761.0 


4825.1 


1816.8 4911.2 


1873.9 


4998.6 ' 1932.4 


5087.3 


12 


13 


.2l67 ! 


1762.0 


4826.6 


1817.7 4912.7 


1874.9 


5000.1 


; 1933-4 


5088.8 


13 


14 


.2333 j 


1762.9 


4828.0 


1818.6 


49I4-I 


1875.8 


5001.5 


1934-4 


5090.3 


14 


IS 


.2500 


1763.8 


4829.4 


1819.6 


4915.5 


1876.8 


5003.0 


1935.4 


5091-8 


15 


16 


.2667 ; 


1764.7 


4830.8 


1820.5 


4917.0 


! 1877.7 


5004.5 


1936.4 


5093-3 


16 


17 


.2833 1 


1765.7 


4832.3 


1821.5 


4918.5 


i 1878.7 


5006.0 


1937.4 


5094.8 


17 


18 


.3000 


1766.6 


4833-7 


1822.4 


4919-9 


1879.7 


5007.4 


1938.4 


5096.3 


18 


IQ 


.3167 


1767.5 


4835-1 


1823.3 


4921.4 


1880.7 


5008.9 


1939.4 


5097.8 


19 


20 


•3333 


1768.4 


4836.5 


1824.2 


4922.8 


1881.6 


5010.3 


I940.4 


5099-3 


20 


21 


.35oo 


1769-3 


4838.0 


i 1825.2 


4924.3 


1882.6 


5011.8 


I94I-4 


5100.8 


21 


22 


.3667 


1770.2 


4839-4 


! 1826. 1 


4925.7 


1883.5 


5013-3 


1942.4 


5102.3 


22 


23 


.3833 


1771-2 


4840.8 


11827.1 


4927.2 


1884.5 


5014.8 


\ 1943-4 


5103.8 


23 


24 


.4000 


1772. 1 


4842.2 


1828.0 


4928.6 


1885.5 


5016.2 


1 1944-4 


5105-2 


24 


25 


.4167 ! 


1773.0 


4843-7 


' 1829.0 


4930.1 


1886.5 


5017.7 


1945-4 


5106.7 


25 


26 


.4333 


1773-9 


4845-1 


! 1829.9 


4931-5 


1887.4 


5019.2 


1946.4 


5108.2 


26 


27 


.4500 1 


1774-9 


4846.5 


I830.9 


4933 -o 


1888.4 


5020.7 


1947-4 


5109.7 


27 


28 


.4667 ! 


1775-8 


4847 9 


I83I.8 


4934-4 


1889.3 


5022.1 


1948.4 


5111.2 


28 


29 


.4833 


1776.7 


4849.4 


1832.8 


4935-8 


1890.3 


5023.6 


1949.4 


5112.7 


29 


30 


.5000 


1777.6 


4850.8 


1833.7 


4937-2 


1891.3 


5025.0 


1950.4 


5114.2 


30 


3i 


.5167 


1778.5 


4852.3 


1834.7 


4938.7 


1892.3 


5026.5 


I95I-4 


5II5-7 


3i 


32 


.5333 


1779-4 


4853-7 


1835.6 


4940.2 


1893.2 


5028.0 


j 1952.4 


5H7.2 


32 


33 


•5500 ; 


1780.4 


4855-1 


1836.6 


4941-7 


1894.2 


5029.5 


j 1953-4 


5118.7 


33 


34 


.5667 


1781.3 


4856.5 


1837.5 


4943-1 


1895.1 


5031.0 


1954-4 


5120.2 


34 


35 


.5833 


1782.2 


4858.0 


1838.5 


4944.6 


1896. 1 


5032.5 


1955-4 


5121.7 


35 


36 


.6000 


1783.1 


4859-4 


I839.4 


4946.0 


1897.1 


5033-9 


1956.4 


5123-2 


36 


37 


.6167 


1784.1 


4860.9 


184O.4 


4947-5 


1898.1 


5035-4 


1957-4 


5124-7 


37 


38 


.6333 


1785.0 


4862.3 


I84I.3 


4948.9 


1 1899.0 


5036.9 


1958.4 


5126.2 


38 


39 


.6500 1 


1785.9 


4863.7 


1842.3 


4950.4 


1900.0 


5038.4 


1959-4 


5127-7 


39 


40 


.6667 


1786.8 


4865.1 


1843.2 


4951.8 


1901.0 


5039.8 


1960.4 


5129.2 


40 


41 


.6833 


1787.7 


4866.6 


1844.2 


4953-3 


1902.0 


5041.3 


1961.4 


5130.7 


4i 


42 


.7000 


1788.6 


4868.0 


I845.I 


4954-7 


1902.9 


5042.8 


1962.4 


5132.2 


42 


43 


.7167 


1789.6 


4869.5 


I846.I 


4956.2 ! 


1903.9 


5044-3 


1963.4 


5133-7 


43 


44 


.7333 


1790.5 


4870.9 


1847.O 


4957-6 


1904.9 


5045.8 


1964.4 


5135-2 ; 


44 


45 


•7500 


I79I-5 


4872.4 


1848.O 


4959-1 j 


1905.9 


5047-3 


1965.4 


5136.7 


45 


46 


.7667 


1792.4 


4873.8 


1848.9 


4960.6 


1906.9 


5048.7 


1966.4 


5138.2 


46 


47 


•7833 


1793-4 


4875.2 


1849.9 


4962.1 


1907.9 


5050.2 


1967.4 


5139-7 


47 


48 


.8000 


1794-3 


4876.6 


I850.8 


4963.5 


1908.8 


5051.7 


1968.4 


5141-2 


48 


49 


.8167 


1795-3 


4878.1 


I85I.8 


4965.0 


1909.8 


5053.2 


1969.4 


5142.8 


49 


50 


.8333 


1796.2 


4879.5 


1852.7 


4966.4 


1910.8 


5054.6 


1970.4 


5144-3 I 


5o 


Si 


.8500 


I797- 1 


4880.9 


1853-7 


4967.9 


1911.8 


5056.1 


I97I-4 


5145-8 


51 


52 


.8667 


1798.0 


4882.4 


I854-6 


4969.3 


1912.8 


5057.6 


1972.4 


5147-3 


52 


S3 


.8833 


I799-0 


4883.9 j 


1855.6 


4970.8 


19138 


5059-1 


1973-4 


5148.8 


53 


54 


.9000 


1799.9 


4885.3 ! 


1856.5 


4972.2 


1914.7 


5060.6 


1974.4 


5150.3 


54 


55 


.9167 l 


1800.9 


4886.7 


I857.S 


4973-7 


1915.7 


5062.1 


1975-4 


5I5I.8 


55 


56 


•9333 


1801.8 


4888.1 


1858.4 


4975-1 


1916.7 


5063.5 


1976.4 


5153-3 


56 


57 


•9500 


1802.8 


4889.6 i 


I859.4 


4976.6 


1917.7 


5065.0 


1977-4 


5154-8 


57 


58 


.9667 


1803.7 


4891.0 ' 


I860.3 


4978.0 


1918.7 


5066.5 


1978.4 


5156.3 


58 


59 


.9833 


1804.6 


4892.5 j 


l86l.3 


4979-5 


1919.7 


5068.0 


1979.4 


5157-8 


59 



FUNCTIONS OF THF ONE-DEGREE CURVE 191 

Use ioo' Chords up to 8° Curves Use 25' Chords up to 32° Curves 
Use 50' Chords up to 16° Curves Use 10' Chords above 32° Curves 



C/3 

a 


Dec. of 
Degree 


8 4 ° s 5 ° 


86° 


87° 


t/3 

3 


Ext. 


Tan. 


| Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


1980.5 5159-3 


2041.8 


5250.6 


2104.8 


5343-3 


2169.5 


5437-5 


O 


I 


.0167 


1981.5 


5160.8 2042.9 


5252.1 


2105.9 


5344-9 


2170.6 


5439-1 


I 


2 


•0333 


1982.5 


5162.3 j 2043.9 


5253.6 


2106.9 


5346.4 


2171.6 


5440.7 


2 


3 


.0500 


1983-5 


5163.8 2045.0 


5255-2 


2108.0 


5348.0 


2172.7 


5442.3 


3 


4 


.0667 


1984-5 


5165.3 


2046.0 


5256.7 


2109. 1 

1 


5349-5 


2173-8 


5443-9 


4 


5 


.0833 


1985-6 


5166.9 


2047.0 


5258.3 


2110.1 


5351. 1 


2174.9 


5445-5 


5 


6 


.1000 


1986.6 


5168.4 2048.0 


5259.8 


2111.2 


5352.7 


2176.0 


5447-1 


6 


7 


.1167 


1987.6 


5169.9 


2049.1 


5261.4 


2112.3 


5354-3 


2177. 1 


5448.7 


7 


8 


•1333 


1988.6 


5I7I-4 


2050.1 


5262.9 


2113.4 


5355-8 


2178.2 


5450.3 


8 


9 


.1500 


1989.6 


5172.9 


2051.2 


5264.5 


2114.5 


5357-4 


2179.3 


5451-9 


9 


10 


.1667 ' 


1990.6 


5174-4 


2052.2 


5266.0 


2115.5 


5358.9 


2180.4 


5453-4 


10 


11 


.1833 


i99i-7 


5175-9 


2053.2 


5267.5 


2116.6 


5360.5 


2181.5 


5455-Q 


11 


12 


.2000 


1992.7 


5177.5 


2054.2 


5269.0 


2117.6 


5362.0 


2182.5 


5456.6 


12 


13 


.2167 


1993-7 


5i79-o 


| 2055-3 


5270.6 


2118.7 


5363-6 


2183.6 


5458.2 


13 


14 


•2333 


1994-7 


5180.5 


2056.3 


5272.1 


2119.8 


5365.2 


2184.7 


5459-8 


14 


IS 


• 2500 


1995-7 


5182.0 


2057.4 


5273.7 


2120.9 


5366.8 


2185.8 


5461.4 


15 


16 


.2667 


1996.7 


5183.5 


2058.4 


5275-2 


2121.9 


5368.3 ' 


1 2186.9 


54630 


16 


17 


•2833 


1997-8 


5185.0 2059.5 


5276.8 


2123.0 


5369-9 , 


2188.0 


5464.6 


17 


18 


.3000 


1998.8 


5186.6 ; 2060.5 


5278.3 


2124. 1 


5371-4 


2189. 1 


5466.2 18 


19 


.3167 


1999.8 


5188.0 


2061.6 


5279-9 


2125.2 


5373-0 


2190.2 


5467.8 


19 


20 


•3333 ' 


2000.8 


5189.6 


2062.6 


5281.4' 


2126.2 


5374-6 


\ 2191.3 


5469.4 


20 


21 


•3500 


2001.8 


5191.0 


2063.7 


5282.9 


2127.3 


5376.2 


2192.4 


547 1 -o 


21 


22 


.3667 


2002.8 


5192.6 


2064.7 


52S4.4 


2128.3 


5377-7 


2193-5 


5472.5 ; 


22 


23 


•3833 


2003.9 


5194-0 


2065.8 


5286.0 


2129.4 


5379-3 


2194.6 


5474-1 | 23 


24 


.4000 


2004.9 


5195.6 


2066.8 


5287.5 


2130.5 


538o.8 


2195-7 


5475-7 


24 


25 


.4167 I 


2005.9 


5197.2 


2067.9 


5289.1 


2131.6 


5382.4 


2196.8 


5477-3 


25 


26 


•4333 


2006.9 


5198.7 


i 2068.9 


5290.6 


2132.6 


5383-9 


2197.9 


5478.9 


26 


27 


.4500 


2007.9 


5200.2 


2070.0 


5292.2 


2133-7 


5385.5 


2199.0 


5480.5 


27 


28 


.4667 I 


2008.9 


5201.7 


207I.O 


5293-7 


2134.8 


5387.1 


2200.1 


5482.1 


28 


29 


.4833 


2010.0 


5203.2 


2072.I 


5295-2 


2135-9 


5388.7 


2201.2 


5483.7 


29 


30 


.5000 


201 1. 


5204.7 


2073.I 


5296.7 


2136.9 


5390.2 


2202.3 


5485.3 


30 


31 


•5167 ! 


2012.0 


5206.3 


2074.2 


5298.3 


2138.0 


5391-8 


2203.4 


5486.9 ! 31 


32 


•5333 


2013.0 


5207.8 


2075.2 


5299.8 


2139.0 


5393-4 


2204.5 


5488.5 


32 


33 


.55oo 


2014.0 


5209.3 


2076.3 


5301.4 


2140. 1 


5395-0 ; 


2205.6 


5490.I 


33 


34 


.5667 


2015.0 


5210.8 


2077.3 


5302.9 


2141.2 


5396.5 


2206.8 


549L7 


34 


35 


.5833 


2016.0 


5212.4 


2078.4 


5304.5 


2142.3 


5398.1 ' 


2207.9 


5493-3 


35 


36 


.6000 


2017.0 


5213-9 


2079.4 


5306.1 


2143-3 


5399-7 


2209.0 


5494-9 


36 


37 


.6167 


2018.0 


5215.4 


2080.5 


5307.7 i 


2144.4 


5401.3 ! 


2210.1 


5496.5 


37 


38 


•6333 


2019. 1 


S216.9 


208l.5 


5309.2 i 


2145-5 


5402.8 


2211.2 


5498.1 


38 


39 


.6500 


2020.1 


5218.4 H 2082.6 


53IO-8 


2146.6 


5404.4 


2212.3 


5499-7 


39 


40 


.6667 


2021.2 


5220.0 || 2083.7 


5312.3 


2147.7 


5406.0 


2213.4 


5501.3 


40 


4i 


.6833 


2022.2 


5221.6 i 2084.8 1 


5313-9 


2148.8 


5407.6 


2214.5 


5502.9; 


41 


42 


.7000 


2023.2 


5223.1 1 2085.8 ! 


53i5.4| 


2149.8 


5409-I i 


2215.6 


5504.5 


42 


43 


.7167 


2024.3 


5224.6 


2086.9 


53i7.o ! 


2150.9 


5410.7 


2216.7 


55o6.i 


43 


44 


•7333 


2025.3 


5226.1 


2087.9 


5318.5 


2152.0 


5412.3 


2217.8 


5507.7 


44 


45 


.75oo 


2026.4 


5227.7 


2089.O 


5320.1 


2I53-I 


5413-9 


2218.9 


5509.3 


45 


46 


.7667 ! 


2027.4 


5229.2 


2090.0 


5321.6 


2154.2 


5415.4 


2220.0 


55io.9 


46 


47 


.7833 


2028.4 


5230.7 


209I. I 


5323-2 


2155-3 


54i7.o 


2221.2 


5512.5 


47 


48 


.8000 


2029.4 


5232.2 


2092.I 


5324-7 


2156.4 


5418.6 


2222.3 


55I4-I 


48 


49 


.8167 


2030.5 


5233-8 


2093.2 


5326.3 ; 


2157.5 


5420.2 


2223.4 


5515-7 


49 


50 


.8333 


2031.5 


5235-3 


2094.2 


5327-8 ! 


2158.6 


5421.8 


2224.5 


5517.3 


50 


51 


.8500 


2032.6 


5236.8 


! 2095.3 


5329-4 


2159-7 


5423.4 


2225.6 


5518.9 


51 


52 


.8667 


2033.6 


5238.3 1 2096.3 


5330.9 


2160.7 


5424.9 


2226.7 


5520.5 52 


53 


.8833 


! 2034.6 


5239-9 j| 2097.4 


5332.5 


2161.8 


5426.5 ! 


2227.9 


5522.1 53 


54 


.9000 


i 2035.6 


5241.4 ,; 2O98.4 


5334-o 


2162.9 


5428.1 


2228.9 


5523-7 


54 


55 


.9167 


2036.7 


5243-0 


2099-5 


5335-6 


2164.0 


5429-7 


2230.0 


5525-3 


55 


56 


•9333 


2037.7 


5244-5 


2100.6 


5337-1 


2165. 1 


543T-2 


2231. 1 


5526.9 


56 


57 


•9500 


2038.7 


5246.0 


2101.7 


5338.7 


2166.2 


5432-8 2232.2 


5528.5 


57 


58 


.9667 


2039.8 


5247-5 


2102.7 


5340.2 


2167.3 


5434-4 2233.3 


5530.I 


58 


59 


.9833 


2040.8 


5249.1 


2103.8 


5341.8 


2168.4 


5436.0 2234.5 


5531-7 


59 



192 



Use ioo' Chords up to 8° Curves 
Use 50' Chords up to 16 Curves 



THE SURVEY 

Curves Use 25' Chords up to 32 Curves 
Use 10' Chords above 32 Curves 



C 


O <u 
. t-l 


88° 


89° 


90° 


91° 


en 
E> 

3 
C 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


2235.6 


5533-3 


2303.6 


5630.8 


2373-4 


573o.o 


2445.1 


5830.9 


O 


I 


.0167 


2236.7 


5535-o| 


2304.7 


5632.5 


2374.6 


5731.7 


i 2446.3 


5832.6 


I 


2 


•0333 


2237.8 


5536.6 1 


! 2305.6 


5634-1 


2375-8 


5733-3 


! 2447.5 


5834.3 


2 


3 


.0500 


2238.9 


5538.2 


2307.2 


5635.8 


2377.0 


5735-o 


2448.8 


5836.0 


3 


4 


.0667 


2240.1 


5539-8 


2308.1 


5637.4 


2378.2 


5736.7 


2450.0 


5837.7 


4 


5 


•0833 


2241.2 


5541-5 


2309-4 


5639-1 


2379-4 


5738.4 


2451.2 


5839.4 


5 


6 


.1000 


2242.3 


5543-1 


2310.5 


5640.7 


2380.5 


5740.0 


2452.4 


5841. 1 


6 


7 


.1167 


2243-5 


5544-7 


2311.6 


5642.4 


2381.7 


5741.7 | 2453.6 


5842.8 


7 


8 


•1333 


2244.6 


5546.3 


2312.8 


5644.0 


2382.9 


5743-4 


2454-8 


5844.5 


8 


9 


.1500 


2245.7 


5547-9 


2314-0 


5645.7 


2384-1 


5745-1 


2456.0 


5846.2 


9 


10 


.1667 


2246.8 


5549-5 


2315. 1 


5647.3 


1 2385.3 


5746.7 


2457-2 


5847-9 


10 


n 


•1833 


2248.0 


5551-2 


2316.3 


5649.0 


! 2386.4 


5748.4 


2458.5 


5849-6 


11 


12 


.2000 


2249.1 


5552-8 


2317-4 


5650.6 


2387.6 


5750.0 


2459-7 


5851.3 


12 


13 


.2167 


2250.2 


5554-4 


2318.6 


5652.3 


2388.8 


5751-7 


2460.9 


5853-o 


13 


14 


.2333 


2251.3 


5556.o 


23I9-7 


5653.9 


2390.0 


5753-4 


2462.1 


5854.7 


14 


15 


.2500 


2252.5 


5557-6 


2320.9 


5655-5 


2391.2 


5755-1 


2463-3 


5856.4 


15 


16 


.2667 


2253.6 


5559-2 


2322.0 


5657-1 


2392.4 


5756.7 


2464.5 


5858.1 


16 


17 


•2833 


2254-7 


5560.9 


2323.2 


5658.8 


2393-5 


5758.4 


2465.8 


5859.8 


17 


18 


.3000 


2255.8 


5562.5 


2324-3 


5660.4 


2394-7 


576o.i 


2467.0 


5861.5 


18 


19 


•3167 


2257.0 


5564.1 


2325.6 


5662.1 


; 2395-9 


5761.8 


2468.2 


5863.2 


19 


20 


.3333 


2258.1 


5565.7 


2326.7 


5663.7 


! 2397-1 


5763.4 


2469.4 


5864.9 


20 


21 


•3500 


2259-3 


5567.3 


2327.9 


5665.4 


! 2398.3 


5765-1 


2470.6 


5866.6 


21 


22 


•3667 


2260.4 


5568.9 


2329.0 


5667.0 


2399-5 


5766.8 


2471.9 


5868.3 


22 


23 


.3833 


2261.5 


5570.6 ; 


2330.1 


5668.7 


2400.7 


5768.5 


2473-1 


5870.1 


23 


24 


.4000 


2262.7 


5572.2; 


2331-3 


5670.3 


2401.9 


577o.i 


2474-3 


5871.8 


J24 


25 


.4167 i 


2263.8 


5573.8 i 


2332.5 


5672.0 


2403.1 


5771-8 


2475.5 


5873-5 


*5 


26 


•4333 


2264.9 


5575.4 ' 


2333-7 


5673-6 


2404.3 


5773-5 


2476.7 


5875.2 


26 


27 


.4500 


2266.0 


5577.0; 


2334.8 


5675-3 


2405-5 


5775-2 


2478.0 


5876.9 


27 


28 


.4667 i 


2267.2 


5578.6 


2336.0 


5676.9 


2406.6 


5776.9 


2479.2 


5878.6 


128 


29 


.4833 


2268.4 


5580.3 


2337-1 


5678.6 


2407.8 


5778.6 


2480.4 


5880.3 


29 


30 


.5000 


2269.5 


5581.9 


2338.3 


5680.2 


2409.0 


5780.2 


2481.6 


5882.0 


30 


31 


.5167 


2270.6 


5583.5 


2339-5 


5681.9 


2410.2 


5781.9 


2482.9 


5883.7 


31 


32 


•5333 i 


2271.7 


5585.1 


2340.7 


5683.5 


2411.4 


5783.6 


2484.1 


5885.4 


32 


33 


•55oo 


2272.8 


5586.8 


2341-9 


5685.2 


2412.6 


5785-3 


2485.3 


5887.2 


33 


34 


•5667 , 


2273.9 


5588.4 


2343-Q 


5686.8 


2413.8 


5787.0 


2486.5 


5888.9 


34 


35 


.5833 


2275.1 


5590.1 


2344-1 


5688.5 


2415.0 


5788.7 


2487.8 


5890.6 


35 


36 


.6000 


2276.2 


5591.7 


2345-3 


5690.2 


2416.2 


5790.3 


2489.0 


5892.3 


36 


37 


.6167 


2277.3 


5593-3 


2346.5 


5691.9- 


2417.4 


5792.0 


2490.3 


5894.0 


37 


38 


•6333 


2278.5 


5594-9 


2347.7 


5693-5 


2418.6 


5793-7 


2491.5 


5895-7 


138 


39 


.6500 


2279.7 


5596.6 


2348.9 


5695-2 


2419.8 


5795-4 


2492.7 


5897.5 


'39 


40 


.6667 


2280.8 


5598.2 


2350.0 


5696.8 


2421.0 


5797-1 


2493.9 


5899.2 


40 


41 


•6833 


2281.9 


5599-8 


2351-2 


5698.5 


2422.2 


5798.8 


2495.2 


5900.9 


4i 


42 


.7000 


2283.0 


5601.4 


2352.3 


5700.1 : 


2423-4 


5800.4 


2496.4 


5902.6 


42 


43 


.7167 


2284.1 


5603.1 


2353-5 


5701.8 ' 


2424.6 


5802.1 


2497.7 


5904-3 


43 


44 


•7333 


2285.3 


5604.7 


2354-7 


5703.4; 


2425.8 


5803.8 


2498.9 


5906.0 


44 


45 


.750O 


2286.5 


5606.4 


2355-8 


5705.1 ' 


2427.0 


5805.5 


2500.1 


5907-7 


45 


46 


.7667 


2287.6 


5608.0 


2357-o 


5706.8 


2428.2 


5807.2 


2501.3 


5909.4 


46 


47 


•7833 


2288.7 


5609.6 


2358.1 


5708.5 ; 


2429.4 


5808.9 


2502.6 


59H.2 


47 


48 


.8000 


2289.9 


5611.2 


2359-3 


5710.1 


2430.6 


5810.6 


2503.8 


5912.9 


48 


49 


.8167 


2291. 1 


5612.9 


2360.5 


57ii-8i 


2431-8 


5812.3 


2505.1 


59146 


49 


50 


.8333 


2292.2 


5614.5 


2361.7 


5713.4 


2433-0 


5814.0 


2506.3 


5916.3 


SO 


51 


.8500 


2293.3 


5616.2 


2362.9 


57I5-I 


2434.2 


5815.7 


2507-5 


59i8. 1 


5 1 


52 


.8667 


2294.4 


5617.8 ; 


2364.0 


5716.7 


2435-4 


5817.3 


2508.7 


5919.8 


52 


53 


.8833 


2295.6 


56l9.4i 


2365-1 


57i8.4 


2436.6 


5819.0 


2510.0 


5921-5 


53 


54 


.9000 


2296.7 


562I.O 


2366.3 


5720.0 


2437-9 


5820.7 


2511-2 


5923-2 


54 


55 


•9167 


2297.9 


5622.7 


2367.5 


5721.7 


2439.1 


5822.4 


2512.5 


5925.o 


55 


56 


•9333 ; 


2299.0 


5624.3 i 


2368.7 


5723-4 


2440.3 


5824.1 


2513-7 


5926.7 


56 


57 


.9500 ; 


2300.2 


5625.9 


2369.9 


5725.1 


2441.5 


5825.8 


2515-0 


5928.4 


57 


58 


.9667 1 


2301.3 


5627.5 


2371.0 


5726.7 


2442.7 


5827.5 


2516.2 


5930.I 5» 


59 


•9833 J 


2302.4 


5629.2 


2372.2 


5728.4 


2443.9 


5829.2 


2517-5 


5931-9 ., 59 



FUNCTIONS OF THE ONE-DEGREE CURVE 193 





Use ioc 


>' Chords 


ud to 8 


3 Curves 


Use 


25' Chords up to 


3 2 Curves 




Use 50' Chords up* to 16 Curves Use 10' Chords above 32 Curves 


m 
I 

a 



O !U 

. tl 
be 

<U V 


92° 93° 


94° 


95° 


I en 
<u 

■*-> 

d 

9 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. ! 


Ext. 


Tan. 


.0000 i 


2518.7 


5933-6 


2594.2 


6038.2 


2671.8 


6144.7 ; 


2751.5 


6253.2 





1 


.0167 i 


2520.0 


5935-3 i 


2595-5 


6040.0 


2673.1 


6146.5 


2752.9 


6255.1 


I 


2 


•0333 


2521.2 


5937-0 


2596.8 


6041.7 


2674-4 


6148.3 


2754-2 


6256.9 


2 


3 


.0500 


2522.4 


5938.8 ; 


2598.1 


6043.5 i 


2675-7 


6150. 1 


2755-6 


6258.7 


3 


4 


.0667 


2523.6 


S940-5 i 


2599-3 


6045.2 | 


2677.0 


6151.9 


2756.9 


6260.5 


4 


5 


.0833 


2524.9 


5942.3 


2600.6 


6047.O ■ 


2678.4 


6153-7 


2758.3 


6262.4 


5 


6 


.1000 


2526.1 


5944-0 


2601.9 


6048.7 i 


2679.7 


6155-4 


2759.6 


6264.2 


6 


7 


.1167 


2527.4 


5945-7 


2603.2 


6050.5 


26S1.0 


6157.2 


2761.0 


6266.0 


7 


8 


•1333 


2528.6 


5947-4 


2604.4 


6052.2 j 


2682.3 


6159.0 


2762.3 


6267.8 


8 


9 


.1500 


2529.9 


5949-2 


2605.7 


6054.O ! 


2683.6 


6160.8 


2763.7 


6269.7 


i 9 


10 


.1667 


2531-1 


5950.9 


2607.0 


6055.8 


2684.9 


6162.6 


2765.0 


6271.5 


10 


11 


.1833 


2532.4 


5952.7 


2608.3 


6057.5 2686.3 


6164.4 


2766.4 


6273.4 


II 


12 


.2000 


2533-6 


5954-4 


2609.6 


60S9.3 2687.6 


6166.2 


2767.7 


6275.2 


12 


13 


.2167 


2534-9 


5956.1 2610.9 


6o6l. I 26S8.9 


6168.0 


2769.1 


6277.0 


13 


14 


• 2333 


2536.1 


5957-8 


2612. 1 


6062.8 269O.2 


6169.8 


2770.4 


6278.8 


14 


IS 


.2500 


2537.4 


5959-6 


2613.4 


6064.6 ! 2691.5 


6171.6 


2771-8 


6280.7 


l g 


16 


.2667 


2538.6 


5961.3 


2614.7 


6066.4 ; 2692.8 


6173-4 


2773-1 


6282.5 


16 


17 


.2833 


2539-9 


5963-1 


2616.0 


6068.2 ; 2694.2 


6175-2 


2774-5 


6284.4 


17 


18 


.3000 


2541. 1 


5964-8 


2617.3 


6069.9 2695.6 


6177.0 


2775-8 


6286.2 


18 


19 


•3167 ; 


2542.4 


5966.5 


2618.6 


6071.7 


2696.9 


6178.8 


2777.2 


6288.0 


19 


20 


■3333 


2543-6 


5968.2 


2619.8 


6073.4 


' 2698.1 


6180.6 


2778.5 


6289.8 


20 


21 


•35oo 


2544.9 


5970.0 


2621. 1 


6075.2 


2699.5 


6182.4 


2779.9 


6291.7 


21 


22 


.3667 


2546.1 


5971-7 


2622.4 


6077.0 


2700.8 


6184.2 


2781.2 


6293-5 


22 


23 


.3833 


2547.4 


5973-5 


2623.7 


6078.8 


2702.1 


6186.0 


2782.6 


6295.4 


23 


24 


.4000 


2548.6 


5975-2 


2625.0 


6080.5 


2703-4 


6187.8 


2784.0 


6297.2 


24 


25 


.4167 


2549-9 


5977-0 


' 2626.3 


6082.3 


2704.8 


6189.7 


2785.4 


6299.1 


' 25 


26 


•4333 


2551-2 


5978.7 1 2627.6 


60S4.I 


2706.1 


6191.5 


2786.7 


6300.9 


26 


27 


.4500 


2552.5 


5980.5 , 2628.9 


6085.9 ij 2707.4 


6193-3 


2788.1 


6302.7 


27 


28 


.4667 


2553-7 


5982.2 II 2630.2 


6087.6 1 2708.7 


6195-1 


2789.4 


6304.6 


28 


29 


.4833 j 


2555-Q 


5983-9 


2631.5 


6089.4 


2710. 1 


6196.9 


2790.8 


6306.4 


29 


30 


.5000 


2556.2 


5985.6 


2632.7 


6091.2 


2711-4 


6198.7 


2792.1 


6308.2 


30 


3i 


.5167 


2557.5 


5987-4 


2634.0 


6093.0 


2712.7 


6200.5 


2793-5 


6310.1 


31 


32 


•5333 


2558.7 


5989.1 


; 2635.3 


6094.7 


2714.0 


6202.3 


2794-9 


6311.9 


32 


33 


.5500 


2560.0 


5990.9 


2636.6 


6096.5 


2715-4 


6204.1 


2796.3 


6313.8 


33 


34 


•5667 , 


2561.2 
2562.5 


5992.6 


i 2637.9 


6098.3 


2716.7 


6205.9 


2797-6 


6315.6 


34 


35 


.5833 


5994-4 


2639.2 


6100. 1 


2718.0 


6207.7 


2799.0 


6317.5 


35 


36 


.6000 


2563.8 


5996.1 


2640.5 


6101.8 


2719.3 


6209.5 


2800.3 


6319-3 


36 


37 


.6167 


2565.1 


5997-9 


2641.8 


6103.6 


2720.7 


6211.4 


2801.7 


6321.2 


37 


38 


•6333 


2566.3 


5999.6 


2643.1 


6105.4 


2722.0 


6213.2 


2803.1 


6323.0 


Li 38 


39 


.6500 


| 2567.6 


6001.4 


2644.4 


6107.2 


2723-4 


6215.0 


2804.5 


6324.9 


J 39 


40 


.6667 


! 2568.8 


6003.1 


2645.7 


6109.0 


' 2724.7 


6216.8 


2805.8 


6326.7 


40 


41 


.6833 


2570.1 


6004.9 


2647.0 


6110.8 


j 2726.0 


6218.6 


2807.2 


6328.6 


41 


42 


.7000 


2571.3 


6006.6 


1 2648.3 


6112.5 


1 2727.3 


6220.4 


2808.6 


6330.4 


42 


43 


.7167 


i 2572.6 


6008.4 


2649.6 


6114-3 


2728.7 


6222.3 


2810.0 


6332.3 


43 


44 


•7333 


J 2573.9 


6010.1 


2650.9 


6116.1 


1 2730.0 


6224.1 


2811.3 


6334-1 


|44 


45 


.7500 


! 2575.2 


6011.9 


1 2652.2 


6117.9 


1 2731.4 


6225.9 


2812.7 


6336.0 


45 


46 


.7667 


1 2576.4 ! 6013.6 


' 2653.5 


6119.7 


2732.7 


6227.7 


2814. 1 


6337.8 


46 


47 


.7833 


; 2577-7 


6015.4 


; 2654.8 


6121.5 


2734-1 


6229.5 


2815.5 


6339.7 ^7 


48 


.8000 


2578.9 


6017. 1 


; 2656.1 


6123.2 2J35-4 


6231.3 


2816.8 


6341.5 48 


49 


.8167 


2580.2 


6018.9 


2657.4 


6125.O 2736.7 


6233.2 


2818.2 


6343-4 


149 


50 


.8333 


2581.5 


6020.6 


2658.7 


6126.8 ' 2738.O 


6235.0 


2819.6 


6345-2 


SO 


5i 


.8500 


2582.8 


6022.4 


2660.0 


6l28.6 ; 2739.4 


6236.8 


2821.0 


6347.I 


51 


52 


.8667 


2584.0 


6024.1 


! 2661.3 


6130.4 


2740.7 


6238.6 


2822.3 


6349-0 52 


53 


.8833 


2585.3 


6025.9 


2662.6 


6132.2 


2742.1 


6240.5 


i 2823.7 


6350.9 53 


54 


.9000 


2586.6 


6027.6 


2663.9 


6133.9 


2 743-4 


6242.3 


i 2825.1 


6352.7 


54 


55 


.9167 


2587.9 


6029.4 


2665.3 


6135.7 


2744.8 


6244.2 


' 2826.5 


6354-6 


55 


56 


•9333 


2589.1 


6031. 1 


2666.6 


6137.5 


2746.1 


6246.0 


2827.8 


6356.4 


56 


57 


.9500 


2590.4 


6032.9 


2667.9 


6139-3 


2747-5 


6247.8 


2829.2 


6358.3 


57 


58 


.9667 


2591-7 


6034.6 


2669.2 


6141.1 


2748.8 


6249.6 


2830.6 


6560.1 


58 


59 

> 


.9833 


: 2593-0 | 6036.4 


, 2670.5 


6142.9 


2750.2 


6251.4 


2832.0 


6362.0 59 



194 THE SURVEY 

Use ioo' Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16 Curves Use 10' Chords above 32 Curves 



d 
3 


O <D 


96° 


97° 


98° 


99° 


+-> 
C 

3_ 
O 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


2833-4 


6363.8 


2917-5 


6476.6 


3004.0 


6591.6 


3092.9 


6709.0 


1 


.0167 


2834-8 


6365.7 


2918.9 


6478.5 


3005.5 


6593-6 


3094.4 


6711.0 


I 


2 


•0333 


2836.1 


6367.5 


2920.3 


6480.4 


3006.9 


6595.5 


3095-9 


6712.9 


2 


3 


.0500 


2837-5 


6369.4 


2921.8 


6482.3 


3008.4 


6597.5 


3097.4 


6714.9 


3 


4 


.0667 


2838.9 


6371.3 


2923.2 


6484.2 


3009.8 


6599.4 


3098.9 


6716.9 


4 


5 


•0833 


2840.3 


6373.2 


2924.6 


6486.1 


3011.3 


6601.3 


3100.4 


6718.9 


5 


6 


.1000 


2841.7 


6375-0 


2926.0 


6488.0 


3012.8 


6603.2 


3101.9 


6720.8 


6 


7 


.1167 


2843.1 


6376.9 


2927.5 


6489.9 


3014-3 


6605.2 


3103.4 


6722.8 


7 


8 


• 1333 


2844.5 


6378.7 


2928.9 


6491.8 


3015.7 


6607.1 


3104.9 


6724.8 


8 


9 


.1500 


2845.9 


6380.6 


2930.3 


6493.7 


3017.2 


6609.1 


3106.4 


6726.8 


9 


10 


.1667 


2847.2 


6382.5 


2931-7 


6495.6 


3018.6 


6611.0 


3107.9 


6728.8 


10 


11 


.1833 


2848.6 


6384.4 


2933.2 


6497.5 


3020.1 


6613.0 


3109.5 


6730.8 


11 


12 


.2000 


2850.0 


6386.2 


2934.6 


6499.4 


3021.6 


6614.9 


3111.0 


6732.7 


12 


13 


.2167 


2851.4 


6388.1 


2936.1 


6501.3 


3023.1 


6616.9 


3112.5 


6734-7 


13 


14 


•2333 


2852.8 


6389.9 


2937.5 


6503.2 


3024.5 


6618.8 


3114-0 


6736.7 


14 


15 


.2500 


2854.2 


63918 


2938.9 


6505.2 


3026.0 


6620.8 


3II5-5 


6738.7 


x 5 


16 


.2667 


2855-6 


6393.7 


2940.3 


6507.1 


3027.5 


6622.7 


3ii7.o 


6740.7 


16 


17 


.2833 


2857.0 


6395-6 


2941.8 


6509.0 


3029.0 


6624.7 


3118.5 


6742.7 


17 


18 


.3000 


2858.4 


6397-4 


2943.2 


6510.9 


3030.4 


6626.6 


3120.0 


6744.6 


18 


19 


.3167 


2859.8 


6399-3 


2944.7 


6512.8 


3031.9 


6628.6 


3121.5 


6746.6 


19 


20 


•3333 


2861.2 


6401.2 


2946.1 


6514-7 


3033.3 


6630.5 


3123-1 


6748.6 


20 


21 


•3500 


2862.6 


6403.1 


2947.5 


6516.6 


3034-8 


6632.5 


3124.6 


6750.6 


21 


22 


.3667 


2864.0 


6404.9 


2948.9 


6518.5 


3036.3 


6634.4 


3126. 1 


6752.6 


22 


23 


.3833 


2865.4 


6406.8 


2950.4 


6520.4 


3037-8 


6636.4 


3127.6 


6754-6 


23 


24 


.4000 


2866.7 


6408.7 


2951.8 


6522.3 


3039-3 


6638.3 


3129.1 


6756.6 


24 


25 


.4167 


2868.1 


6410.6 


2953-3 


6524-3 


3040.8 


6640.3 


3130.7 


6758.6 


25 


26 


•4333 


2869.5 


6412.4 


2954-7 


6526.2 


3042.2 


6642.2 


3132.2 


6760.6 


26 


27 


.4500 


2870.9 


6414.3 


2956.2 


6528.1 


3C43.7 


6644.2 


3133-7 


6762.6 


27 


28 


.4667 


2872.3 


6416.2 


2957.6 


6530.0 


3045-2 


6646.1 


3135-2 


6764.6 


28 


29 


.4833 


2873.7 


6418. 1 


2959.0 


6531.9 


3046.7 


6648.1 


3136.7 


6766.6 


29 


30 


.5000 


2875.1 


6419.9 


2960.4 


6533.8 


3048.1 


6650.0 


3138.3 


6768.6 


30 


3i 


.5167 


2876.5 


6421.8 


2961.9 


6535-8 


3049.6 


6652.0 


3139-8 


6770.6 


3i 


32 


• 5333 


2877.9 


6423.7 


2963.3 


6537-7 


3051-1 


6653.9 


3I4I-3 


6772.6 


32 


33 


.55oo 


2879.4 


6425.6 


2964.8 


6539-6 


3052.6 


6655.9 


3142.9 


6774-6 


33 


34 


.5667 


2880.8 


6427.5 


2966.2 


6541.5 


3054-1 


6657.8 


3144-4 


6776.6 


34 


35 


.5833 


2882.2 


6429.4 


2967.7 


6543-4 


3055-6 


6659.8 


3145-9 


6778.6 


35 


36 


.6000 


2883.6 


6431.2 


2969.1 


6545-3 


3057-0 


6661.7 


3147.4 


6780.6 


36 


37 


.6167 


2885.0 


6433-1 


2970.6 


6547-3 


3058.5 


6663.7 


3149.0 


6782.6 


37 


38 


•6333 


2886.4 


6435.0 


2972.0 


6549-2 


3060.0 


6665.7 


3150.5 


6784.6 


38 


39 


.6500 


2887.8 


6436.9 


2973.5 


6551-1 


3061.5 


6667.7 


3152.0 


6786.6 


39 


40 


.6667 


2889.2 


6438.8 


2974.9 


6553.0 


3063.0 


6669.6 


3153-5 


6788.6 


40 


4i 


.6833 


2890.6 


6440.7 


2976.4 


6555.o 


3064.5 


6671.6 


I3I55.I 


6790.6 


41 


42 


.7000 


2892.0 


6442.5 


2977.8 


6556.9 


3066.0 


6673.5 


3156.6 


6792.6 


42 


43 


.7167 


2893.4 


6444.4 


2979.3 


6558.8 


3067. 5 


6675-5 


3158.2 


6794-6 


43 


44 


•7333 


2894.8 


6446.3 


2980.7 


6560.7 


3068.9 


6677.4 


3159.7 


6796.6 


44 


45 


.7500 


2896.3 


6448.2 


2982.2 


6562.7 


3070.4 


6679.4 


3161.2 


6798.6 


45 


46 


.7667 


2897.7 


6450.1 


2983.6 


6564.6 


3071.9 


6681.4 


3162.7 


6800.6 


46 


47 


.7833 


2899.1 


6452.0 


2985.1 


6566.5 


3073-4 


6683.4 


3164.3 


6802.6 


47 


48 


.8000 


2900.5 


6453-9 


2986.5 


6568.4 


3074-9 


6685.3 


3165-8 


6804.6 


J48 


49 


.8167 


2901.9 


6455.8 


2988.0 


6570.4 


3076.4 


6687.3 


3167.4 


6806.6 


49 


50 


.8333 


2903.3 


6457.6 


2989.4 


6572.3 


3077.9 


6689.2 


3168.9 


6808.6 


SO 


51 


.8500 


2904.7 


6459-5 


2990.9 


6574-3 


3079-4 


6691.2 


3170.5 


6810.6 


51 


52 


.8667 


2906.1 


6461.4 


2992.3 


6576.2 


3080.9 


6693.2 


3172.0 


6812.6 


52 


53 


.8833 


2907.6 


6463.3 


2993.8 


6578.1 


3082.4 


6695.2 


3173-6 


6814.7 


53 


54 


.9000 


2909.0 


6465.2 


2995.2 


6580.0 


3083.9 


6697.1 


3I75-I 


6816.7 


54 


55 


.9167 


2910.4 


6467.1 


2996.7 


6582.0 


3085.4 


6699.1 


3176.6 


6818.7 


55 


56 


•9333 


2911.8 


6469.0 


2998.1 


6583.9 


3086.9 


6701. 1 


3178.1 


6820.7 


56 


57 


.9500 


2913-3 


6470.9 


2999.6 


6585.8 


3088.4 


6703.2 


3179-7 


6822.7 


57 


58 


.9667 


2914.7 


6472.8 


3001. 1 


6587.7 


3089.9 


6705.2 


3181.2 


6824.7 


58 




.9833 


2916. 1 


6474.7 


3002.6 


6589.7 


3091.4 


6707.1 


3182.8 


6826.8 


59 



FUNCTIONS OF THE ONE-DEGREE CURVE 195 



Use ioo' Chords up to 8 
Use 50' Chords up to i6' 



Curves 
Curves 



Use 25' Chords up to 3 2° Curves 
Use 10' Chords above 32 Curves 



en 

<v 
■*-> 


^S 


IOO° 


; co 

1 <U 




a 

s 




QQ 




3 

s 




Ext. 


Tan. 


. 


.0000 


3184.3 


6828.8 







I 


.0167 


3185-9 


6830.8 


I 




2 


•0333 


3187-4 


6832.8 


2 




3 


.0500 


3189.0 


6834-8 


3 




4 


.0667 


3190.5 


6836.8 


4 




5 


.0833 


3192. 1 


6838.9 


5 




6 


.1000 


3193-6 


6840.9 


6 




7 


.1167 


3195-2 


6842.9 


7 




8 


• 1333 


3196.7 


6844.9 


8 




9 


.1500 


3198.3 


6847.0 


9 




10 


.1667 


3199-8 


6849.0 


10 




11 


.1833 


3201.4 


6851.0 


11 




12 


.2000 


3202.9 


6853-0 


12 




13 


.2167 


3204.5 


6855.1 


13 




U 


•2333 


3206.0 


6857.1 


14 




15 


.2500 


3207.6 


6859-1 


15 




16 


.2667 


3209.1 


6861. 1 


16 




17 


.2833 


3210.7 


6863.2 


17 




18 


.3000 


3212.2 


6865.2 


18 




19 


•3167 


3213-8 


6867.2 


19 




20 


•3333 


3215-4 


6869.2 


20 




21 


•3500 


3217.0 


6871.3 


21 




22 


.3667 


3218.5 


6873.3 


22 




23 


.3833 


3220.1 


6875.4 


23 




24 


.4000 


3221.6 


6877.4 


24 




25 


.4167 


3223.2 


6879-4 


25 




26 


•4333 


3224.7 


6881.4 


26 




27 


.4500 


3226.3 


6883.5 


27 




28 


.4667 


3227.9 


6885.5 


28 




29 


.4833 


3229.5 


6887.6 


29 




30 


.5000 


3231.0 


6889.6 


30 




31 


•5167 


3232.6 


6891.7 


3i 




32 


•5333 


3234-1 


6893.7 


32 




33 


•55oo 


3235-7 


6895.7 


33 




34 


.5667 


3237.3 


6897-8 


34 




35 


.5833 


3238.9 


6899.8 


35 




36 


.6000 


3240.4 


6901.8 


36 




37 


.6167 


3242.0 


6903.9 


37 




38 


•0333 


3243-5 


6905.9 


38 




39 


.6500 


3245-1 


6908.0 


39 




40 


.6667 


3246.7 


6910.0 


40 




41 


.6833 


3248.3 


6912. 1 


4i 




42 


.7000 


3249-8 


6914. 1 


42 




43 


.7167 


3251-4 


6916.2 


43 




44 


•7333 


3253-0 


6918.2 


44 




45 


•7500 


3254-6 


6920.3 


45 




46 


.7667 


3256.2 


6922.3 


46 




47 


.7833 


3257-8 


6924.4 


47 




48 


.8000 


3259-3 


6926.4 


48 




49 


.8167 


3260.9 


6928.5 


49 




50 


•8333 


3262.5 


6930.5 


50 




51 


.8500 


3264.1 


6932.6 


51 




52 


.8667 


3265.7 


6934.6 


52 




53 


.8833 


3267.3 


6936.7 


53 




54 


.9000 


3268.8 


6938.7 


54 




55 


.9167 


3270.4 


6940.8 


55 




56 


•9333 


3272.0 


6942.8 


56 




57 


.9500 


3273.6 


6944.9 


57 




58 


.9667 


3275-2 


6946.9 


58 




59 -9833 


3276.8 


6949.0 


59 





196 THE SURVEY 

Use 100' Chords up to 8° Curves Use 25' Chords up to 32 Curves 
Use 50' Chords up to 16 Curves Use 10' Chords above 32 Curves 



0) 

a 


IOI° 


I02° 


103° 


104 


105 


en 
V 

-4-) 

3 
C 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 
3474-6 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





3278.3 


6951-0 


3375-1 


7076.0 


7203.6 


3577-1 


7334-1 


3682.6 


7467.5 


O 


10 


3294-3 


6971.7 3391-5 


7097.1 


3491-5 


7225.1 


3594-4 


7356.1 


3700.4 


7490.0 


IO 


20 


3310.3 


6992.4I 3407.9 


7118.2 


3508.4 


7246.8 


3611.9 7378.2 


3718.4 


7512.6 


20 


30 


3326.4 


7013.23424.5 


7139-4 


3525-5 


7268.5 


3629.4 7400.4 


3736.5 


7535-3 


30 


40 


3342.5 


7034.0; 3441. 1 


7160.7 


3542.6 


7290.3 


3647.1I7422.7I3754.6 


7558.1 


40 


50 


3358.8 


7055.013457.8 


7182. 1 


, 3559-8 


7312. 1 


3664.8I7445.0 3772.9 


7581.0 


50 


60 


3375-1 


7076.0,3474.6 


7203.6 


3577-1 


7334-1 


3682.6J7467.5 


3791-2 


7604.0 


60 


t/5 


106 


107° 
1 


108 


109 


IIO° 


m 

<v 

C 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





3791.2 


7604.0 


3903-1 


7743-7 


4018.5 


7886.7 


4137-4 


8033.2 


4260.0 


8183.3 





10 


3809.6 


7627.0 


3922.1 


7767.3 


4038.0 


7910.8 


4157-5 


8057.9 


4280.8 


8208.7 


IO 


20 


3828.1 


7650.2 


3941-2 


7791.0 


4057.7 


7935-1 


4177-8 


8082.8; i 4 30i. 7 


8234.2 


20 


39 


3846.7 


7673-4 


3960.4 


7814.7 


4077-5 


7959-5 


4198.2 


8107.8 


4322.7 


8259.8 


30 


40 


3865.4 


7696.7 


3979-6 


7838.6 


4097.3 


7983.91 


4218.7 


8132.81 


4343-8 


8285. 5| 


40 


50 


3884.2 


7720.1 


3999-Q 


7862.6 


41 1 7-3 


8oo8.5l4239-3 


8158.0 


4365-1 


8311-3 


50 


60 


3903-1 


7743-7 


4018.5 7886.7 

1 


4137.4 


8033.2 4260.0 8183.3 


4386.4 


8337-2 


60 


w 


iii° 


H2° 


113° 


114 


ii5° 


m 


<L> 


































O 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


N 


4386.4 


8337-2 


4516.9 


8495.1 


4651.6 


8657.1 


4790.7 


8823.4 


4934-4 


8994o 


O 


IO 


4407.9 


8363.2 


4539-1 8521.8 


4674-5 


8684.5 


4814.4 8851.61 


4958.9 


9023.2 


IO 


20 


4429.5,8389.4 


4561.3 


8548.6 


4697.5 8712.0 


4838.1 8879.9 


4983.4 


9052.3 


20 


30 


4451.2)8415.6 


4583.7 


8575-6 


4720.6I8739.7 


4862.0 8908.3! 5008.1 


9081.5 


30 


40 


4473.0 8442.0 
4494.9J8468.5 


4606.2 


8602.6 


4743.9I8767.5 


4885.0 8936.8,5032.9 


9110.8 


40 


50 


4628.9 


8629.8 


4767.2 8795.4 


4910.2 8965.51 5057-9 


9*40.3 


50 


60 


4516.9 8495.1 


4651.6 


8657.1 


4790.7 8823.4 


4934-4 8994-3 5083.0 


9169.9 


60 




116 


H7° 


118 


ii9° 


120 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





5083.0 


9169.9 


5236.6 


9350.5 


5395-4 


9536.3 


5559-7 


9727.6 


5730.0 


9,924-6 





IO 


5108.2 


9199-7 


5262.6 9381. 1 


5422.4 


9567.8 


5587.7 


9760.0 5758.9 


9,958.i 


10 


20 


5133-6 


9229.6 


5288.9 94H-9 


5449-5 


9599-5 


5615-8 


9792.6 5788.0 


9,990.6 


20 


30 


5I59-I 


9259.6 


5315-3 9442.8JJ5476.8 


9631-3 


5644.1 


9825.4 


5817.3 


10,025.6 


30 


40 


5184.8 


9289.8 


534i-8|9473-8 


5504.3 


9663.2 


5672.6 


9858.3 


5846.8 


10,059.7 


40 


50 


5210.6 


9320.1 


5368.5 9505.0 


!5532.o 


9695-3 


5701.2 


9891.4 


5876.4 


10,093.7: 


50 


60 


5236.6 


9350.5 


5395-4 9536.3'5559.7 

1 I' 


9727.6 


5730.0 


9924.6 


5906.1 

i 


10,127.7 


60 



METHODS OF RUNNING CURVES 197 

r w A central angle 

L = 100 X-=:= ~ 1 ^— X 100. 

D Degree of curvature 

For the convenience of the field engineer column 1, Table 30, 

gives the central angle (A) in degrees and minutes (as read by 

the transit) ; column 2 gives the same angle expressed in degrees 

and decimals for figuring curve lengths. 

Externa^ 
PC. \ PI 

-— \*r 




Center of Curve 
Fig. 52 

Tangent length and externals. 
Sketch No. 52 shows a general curve problem. The deflection 
angle between the tangents at the point of intersection (P.I.) = 
the central angle of the curve that will fit these tangents; it is 
referred to as A. 

The tangent distances equal the distance from the P. C. (be- 
ginning of curve) to the P. I. or P. I. to P. T. (end of curve) and is 
expressed by the formula 

T = Radius X tangent of — (4) 

Therefore, for a given central angle A, the tangent length is 
directly proportional to the radius. If the tangent lengths of a 
i° curve for different A's are tabulated, the tangent length for 
any desired degree of curve equals tangent length for i° curve 
for the specified A divided by the degree of the desired curve 
expressed in degrees and decimals of a degree. 

Expressed as a formula this reads: 

„, . . Tangent i° curve for specified A (5) 
Tangent for desired curve = — 

and reversing the formula we can determine the desired degree 
of curve for a specified tangent length by the formula 

Tangent i° curve for specified A (6) 

Specified tangent length desired. 
The external is the distance from the P. I. to the curve arc on 
the line between the P. I. and the center of the curve. It is 
determined by the formula: 

\ (7) 

Ext = — — : t — Radius = Radius! — — ; s — 1 land is directly 

Cosine A \ Cosine A / 



198 



THE SURVEY 



proportional to the radius in the same manner as the tangent 
length; therefore, the external of any desired curve for a specified 
A equals the external of a i° curve for that A divided by the 
degree of curvature. 



- Point of Tangency 



Tangent^ 



A ng/e -i Central Angle A 




Xenter of Curve 

Fig. 53 




4 Curve. 
The Distances along the Arc 
between (HZ) (2-3) (3 - 4 J etc. are 
each 100'. 



Fig. 54 

Expressed as a formula this reads: 

. '. , Ext. i° curve for specified A (8) 
External for desired curve = ■= 



METHODS OF RUNNING CURVES 199 

and reversing, as for tangents, the desired degree of curvature is 

obtained that gives a specified external distance, by the formula, 

Ext. i° curve for specified A (9) 

Specified Ext. distance desired. 

Methods of running curves. Curves are run in the field by 
tangent offsets, middle ordinates or deflection angles. Deflec- 
tion angles is the simplest method and is almost universally 
used. It is based on the principle that the angle 5 between the 
tangent and arc chord, one end of which is at the point of tangency, 
is equal to \ the central angle subtended by that chord. Sup- 
pose the angle A is 4 and the arc length ST = 100 feet. This 
curve would then be a 4 curve. From the previous definitions 
locate the point T (Fig. 53) by turning the deflection angle 
S = 2 from the tangent and measuring 100 feet of arc in 
such a position that the end of the arc would be on the line of 
the chord ST. It is impossible to conveniently measure the arc 
distance and for all practical purposes a chord length of ioo' 
will answer for a 4 curve (see discussion, page 173). 

Suppose we wish to locate the points 2, 3, 4, 5, and 6 on the 

4 curve from point 1 or the P. C. of a curve (Fig. 54). 

A 
Set the transit at the P. C; if we turn a deflection— = 2 from 

2 

the tangent xy the line of sight will pass through the point 2; 

if we turn — = 4 the line of sight will pass through point 3; 6°, 

point 4, etc.; it only remains to measure to these points to locate 
them definitely. This can be done in two ways, by measuring 
the distances 1-2, 1-3, 1-4, 1-5, etc., or by measuring 1-2, 2-3, 

3-4, 4-5, etc. 

In the first case the difference between the length of arc and 
the chord length becomes so great that, unless a correction is 
made, the points are not exactly located; that is, the length of 
arc between points 1, 2, 3, 4, 5, 6, = 500' while the chord length 
1-6 = 497.5'; also, it takes longer to measure the distances 1-2, 
1-3, 1-4, 1-5, 1-6, etc., than it would 1-2, 2-3, 3-4, 4-5, etc. 

In the second method we can use chords of ioo' from 1-2, 
2-3, etc., with no appreciable error, as the distance measured by 
chords 1, 2, 3, 4, 5, 6, = 499-94'. 

Therefore, the method usually adopted is to turn the deflection 
^4 
angle— and measure the chord 1-2, which locates the point 2; 

2 D 

then turn the deflection angle — and measure the chord distance 

2-3, locating point 3, etc. 

The fact has been mentioned that the use of the chord distance 
as equal to the arc introduces an error but that this error is of 
no importance for a 4 curve: As the degree of curvature increases, 
the difference between an arc length of ioo' and the chord length 
becomes greater, and it is necessary to determine the limit of 
curvature that will allow the use of ioo' chords in locating curve 



2oo THE SURVEY 

points. On page 145 the statement is made that center line chain- 
ing should be correct to within 0.1' per 100' of length, which allows 
a difference in arc and chord of 0.1' This occurs when the 
degree of curvature reaches g° per 100'. The difference can then 
be reduced by the simple expedient of using 50' chords, which 
reduces the error for this degree of curvature from 0.10' per 
100' of length using 100' chords to 0.02' using 50' chords; 50' 
chords can be used up to 18 curves and beyond that point 25' 
chords. 

It is better not to use the full limit of allowable error, and a good 
working rule is ioo' chords up to 8° curves, 50' chords up to 
1 6° curves, 25' chords to 32 and beyond that io' chords. 

For any given curve the deflection angle and central angle 
are directly proportional to the length of the arc, and if the de- 
flection angle for 100' arc of io° curve equals 5 the deflection 

angle for one foot of arc of io° curve equals-^— = = 

100 100 

3 minutes. 

An example of a typical simple curve problem can now be 

given: 



k Tan.Ler?gth-—^ PL=5t ^ 22f4Z6 B 




Fig. 55 

To determine the degree of curvature desired from a fixed external 

distance 

At station 23 + 42.6 we have a deflection angle of 25 10' be- 
tween tangents AB and B'C; suppose upon examining the ground 
it is decided that to fit the old roadbed and give good alignment 
the curve should be located somewhere between 13. 5' and 14. 5' 
to the right of the transit point at station 23 + 42.6. Proceed 
as follows: from table 30 pick out the external for a i° curve 
for A = 25 10', this equals 141.0'. 

The problem is to determine the degree of curvature that will 
give an external of between 13.3' and I4-5'- Use formula (9). 
= Ext. x° curve for 25° 10' = 141^ = . curve> 

13-5 , 13.5 

Ext. i° curve for 25° 10 = 14^0 = . curye 

14.5' 14.5 

To fit the conditions some curve must be selected between a 



SIMPLE CURVE PROBLEM 



20I 



10.44 and a 9.72 . A io° curve would be naturally selected as 
being the simplest to figure. 

To determine the required degree of curvature for a fixed tangent 

length 
Take the same problem as above except there must be a tangent 
length of between 127' and 12c/. Use formula (6). 

Tangent i° curve for 25 10' 1279.1' 
D = — — — , = 10. 07 curve. 



12 



D = 



Tangent i° curve for 25° 10 



127 
1279. 1 



9. 91 curve. 



129 129 

Table No. 30 gives tangent for 25 10' — 1 279.1'. 
These limiting values would result in the selection of a io° 
curve. The degree of the desired curve is usually selected in one 
of these two ways; ordinarily it is determined by the external 
distance. 




A=25°W 

D= 10° R= 573.0 
T~ 127.9 L- 251.7 

RC=5ta.22H4.7 
P.T.^Sta. 24+66.4 



Fig. 56 

Simple Curve Problem. Case 1. 

To compute the notes for a io° curve for a deflection angle of 

25 10' between tangents at station 23 + 42.6. 

Central angle = 25 10'. 

Table No. 30 gives the tangent i° curve for 25 10' = 1 279.1. 

1 2 70. 1 

Tangent io° curve = — = 127.91 

10 

The station of the P.C. then equals station 23 + 42.6 P.I. 

minus 127.9' = station 22 + 14.7. 

rpi , .* r A 25.16667° , , 

The length of curve = — = -^ — 5 — X 100 = 251.7 feet. 

D 10 

The station of the P. T. (Tangent point, or end of the curve) 
as measured around the arc is then station (22 + 14-7 P.C.) + 
251.7' = station 24 + 66.4. 

The rule for running curves requires the use of 50' chords for 
a io° curve. We must, therefore, figure the deflections for the 
even stations and the 50' stations as follows: 

Station 22 + 50, 23 + 00, 23 + 50, 24 + 00, 24 + 50, and 
to check the curve station 24 -f- 66.4. 

For a io° curve, Table No. 29. 



202 THE SURVEY 

The deflection for ioo' of arc = 5 

1' " " = ° 03' 

The distance from the P.C. station 22 + 14.7 to station 

22 + 50 is 35.3'; the deflection per foot = o° 03', for 
35-3' = 35-3 X o° 03' = 105.9 minutes = i° 46'. 

The distance P.C. to station 23 +00 equals 85.3', or 50' 
farther than for station 22 + 50; the deflection per 50' of arc 
equals 2 30'; therefore, the deflection for station 23 + 00 equals 
the deflections for station 22 + 50 (i° 46') plus 2 30', the de- 
flection for 50' of arc or 4 16'; in a like manner the deflection 
for station 23 + 50 is 6° 46'; for 24 + 00, 9 16'; for 24 + 50, 
ii° 46'; the distance from station 24 + 50 to the P.T. station 
24 + 66.4 is 16.4'; the deflection for 16.4' equals 16.4 X 
o° 03' = 49. 2'; the deflection for station 24 + 66.4 is, therefore, 
(n° 46' + 49O = 12° 35'; if the deflection notes have been 
properly figured this last deflection to the P.T. should always 
be § the central angle of the curve; in this case \ of 25 io', 
which equals 12 35', checking the notes. 

To run the curve. Set up the transit at the P. I.; sight along 
the tangent (B.A.), measure off the distance 127.9 (tangent 
length) along this line and set the P. C. exactly on the line. In 
a like manner set the P.T. on the forward tangent (B'.C.) 
127.9' from the P.I. Then set up the transit on the P.C. and 
with the vernier at o° 00' sight on the P. I., using the lower plate 
motion. Loosen the upper motion and deflect i° 46'; measure 
along this line 35.3', which locates station 22 + 50 on the curve 
arc; then loosen the upper motion and set the vernier to read 
4 16'; measure 50' from the just located station 22 + 50, so that 
the forward end of the tape is in line with the transit deflection 
of 4 16'; this locates station 23 + 00 on the curve arc. In a like 
manner deflect 6° 46' and measure forward 50' from station 

23 + 00 to station 23 + 50, etc., until the P.T. is reached. If 
the curve has been correctly run the last deflection of 12 35' 
will strike the previously located P. T. and the distance from 
station 24 + 50 to this P.T. will be 16.4'; if the distance checks 
within 0.2' it is sufficiently close. 

The above problem and method of laying out a curve is the 
simplest form encountered; in it we assume that the P. I., P.T. 
and all intermediate points on the curve are visible from the 
P.C. and that the P.I. is accessible. 

In nine cases out of ten this method is applicable to road 
curves, but where the P.I. occurs outside of the road fences it 
sometimes is located in a stream, pond, building, etc., and cannot 
be occupied. This is known as the problem of the inaccessible 
P.I. More often it is impossible to see the P.T., or some inter- 
mediate point on the curve from the P.C, which necessitates 
intermediate transit points on the curve. The problem of inac- 
cessible P.C.s or P.T.s is so rare it will not be illustrated. 



I 



PROBLEM OF THE INACCESSIBLE P. I. 203 

Problem of the Inaccessible P. I. Case 2. 

The point H {P-L) cannot be occupied. Locate any two 
convenient points, <> and t on the tangents A.B. and B'.C. and 
measure the distance st equals, say, 110.5'. 

Set the transit at s and measure the angle between the line 
A.s. produced and st, say, 5 10'; in a similar manner measure the 
angle at t between st produced and the forward tangent /C, 
say 20 00'. The total deflection then between the tangent 
AsB and B'tC or the central angle of the curve to be run is 
the sum of these two deflections, angles (5 10') + (20 oo') = 

25 10'. 

Assuming a io° curve is desired we must locate the P.C. from 
the point s and the P.T. from the point t. 

k _ 127.9- >j 

W—39.0'-** 88.9'— -A , , LI o 

[PC \S=Sta. 22+53.7. H jt ?.T. inaccessible D 




Fig. 57 

In the preceding simple curve problem the tangent length of 
a io° curve with a central angle of 25 10' was figured to be 
127.0/; it, therefore, remains to compute the distance sH which 
subtracted from 127.9' will give the distance from s along the 
tangent sA to the P.C, of the curve. In a similar manner compute 
tH, which subtracted from 127.0/ gives the distance along the 
forward tangent tC to the P. T. of the curve. 

Knowing the station of the point s as measured along the 
tangent A.B. the station of the P.C. is determined;, then figure 
the deflections in the usual manner and run the curve. 

For the values given the computations are as follows: 

To determine sH and Ht. Use the law of sines (see Trigono- 
metric formulae, page 477). 
sH:st: sin 20 oo': sin 25 10' 

_ st sin 20 oo r = 110.5 X 0.34202 = gg , 

s ~ sin 25 io 7 " ' 0.42525 

= st sin 5 io' = 110.5 X 0.09005 = / 

sin 25 io' 0.42525 

Therefore, the distance from ^ to the P.C. is 127.9' — 88.9' = 
39. o'. 

The distance from t to the P.T. is 127.9 — 23.4 = 104.5. 
Having these distances the P.C. and P.T. are located. As- 
sume that station of s was measured along the tangent AB 
and found to be station 22 -f- 53.7. 



204 



THE SURVEY 



The station of the P.C. then equals 22 -\- 14.7 

" " P.I. " " 23 + 42.6 

" " P.T. " " 24 + 66.4, using the length 

of curve figured in Case 1. 

The deflections are figured and the curve run as in Case 1, 
assuming that all the curve points are visible from the P.C. 

Case 3. Where the P.T. or intermediate points on the curve 
are not visible from the P.C. 

(a) Where an intermediate set-up is required. Use the same 
curve as in Case 1. 

The deflections for the different curve points were figured as 
follows: 



Deflections. 


Instrument at P.C. 


, foresight 


on P.I. 








P.C. Station 


22 


+ 14-7 


Deflection 


o° 


OO' 






22 


+ 5o 




i° 


46 






23 


+ 00 




4° 


16' 






23 


+ so 




6° 


46' 






24 


+ 00 




9° 


16' 






24 


+ 5o 




n° 


46' 






24 


+ 66.4 




12° 


35' 




P.C. 22+ 14.7 




RI. 









Z2+50 




P.T. 24+66.4- 



FlG. 58 



Set up the instrument at the P.C. and locate the points 

22 + 50, 23 + 00 and 23 + 50; suppose 24 + °° is not visible, 
set up at station 23 + 50, set the vernier at o° 00' and back 
sight on the P.C; transit the telescope and finish the curve, 
using the same deflections as figured for the instrument set up 
at the P.C; that is, turn the deflection of 9 16' for station 
24 + 00, ii° 46' for 24 + 50, and 12 35' for the P.T. In 
general it can be said that whenever the P.C is used as a back- 
sight from the intermediate set-up, set the vernier at o° oo' 
when sighting on the P.C; transit the telescope and use original 
notes for the balance of the curve. 

(b) Where two or more intermediate set-ups are required. 
For the first set-up, say, at 23 + 50, proceed as above and set 
station 24 + 00; suppose 24 + 50 is not visible from station 

23 + 50; set up at station 24 + 00 and with the vernier reading 
6° 46' back sight on station 23 + 50; transit the telescope, set the 
vernier to read n° 46' for station 24 + 5°> and proceed, using 
the same deflections as originally figured. In general, where 
the P.C is not visible from, the intermediate set-up, set the 



PROBLEM OF THE INACCESSIBLE P. I. 205 

vernier to read the deflection figured for the point used as a 
backsight; transit the telescope and proceed with the curve, 
using the notes originally figured. That is, if the instrument 
is set up at station 24 -f- 00 and 22 + 50 used as a backsight, 
the vernier is set at i° 46', and using the lower motion the wire 
is set on station 22 + 50; then transiting the telescope the curve 
is run by setting the vernier at n° 46' for station 24 + 50, etc. 

If station 23 -f- 00 is used as a backsight, set the vernier at 
4° 16' when sighting the machine; then transit and proceed as 
above. 

These three cases cover any ordinary road curve problems. 



CHAPTER IX 



OFFICE PRACTICE 

Under office practice we include 

i. Mapping the preliminary survey. 

2. Designing the improvement and estimating the quantities. 

3. Producing a finished set of plans from which the road can 
be constructed. 

1. Mapping the preliminary survey. 

The mapping of the preliminary survey serves as a base from 
which the design of the new work, and the quantities necessary 
thereto, can be built up. It consists of three views of the road: 
the plan, showing the topographic features; the profile, showing 
the longitudinal differences of elevation, and the cross-sections, 
showing the constantly changing transverse shape. 

The scales in general use are as follows: 



Plan 


Profile 


Cross-sections 


1" = 100' 


1" = 
1" = 


100' horizontal 
io' vertical 


1" = 10' 


1"= so' 


1* = 

1" = 


50' horizontal 
io' vertical 


1" = 5' 
or 1" = 4' 


i" = 20' 


1" = 
1" = 


20' horizontal 
5' vertical 


1*= 5' 

or 1" = 4' 


I" = I0' 


1" = 
1* = 


10' horizontal 
10' vertical 


1" = 2' 



The 100' scale is too small for convenience in design, and earth- 
work quantities figured from cross-sections plotted 1" to 10' 
are not reliable. For work on ordinary country roads, the 50' 
scale is generally adopted, using cross-sections plotted 1" to 5' 
or 1" to 4 r ; this scale is satisfactory for laying the grade line and 
computing the earthwork. 

The larger scales of 1" = 20' or 1" = io' are useful in village 
work where a large amount of detail must be shown. 

Plotting the center line. 

The survey center line can be plotted by deflection angles at 
the transit points, using a table of natural tangents, a vernier 

206 



PLOTTING THE CENTER LINE 207 

protractor or an ordinary paper protractor graduated to 15 
minutes. 

Where the center line has been well located in the field and 
there seems to be no necessity for a paper re-location, no great 
care need be taken in plotting the deflection angles, as in such a 
case the map serves more as a picture of the topographic features 
than as a basis for alignment. 

Where a random line has been run in the field and some shifting 
of the center line is necessary, both angles and distances must be 
accurately plotted. If any extensive change of alignment is 
made, the new deflections and distances should be checked by 
figuring the difference of latitude and longitude for both the 
survey line and the office line between the points of equality. 

Where the consideration of sight distance (see page 17) 
governs, Table No. 31 will be of service. 

For convenience in plotting the topography, the 100' survey 
stations are plainly marked. 

The most common mistakes in plotting the map are made by 
reversing the deflection, as right instead of left and vice versa, 
or in adding or omitting 100' in scaling long-tangent distances. 
The work should be checked for mistakes of this nature. 
All curve data is marked plainly on the map near the P.I. 
and shows 

The deflection angle A 
The degree of curve D 
The radius of curve R 
The tangent length T 
The length of curve L 
The station of the P.I. 
The station of the P.C. 
The station of the P. T. 

If the curves have been figured in the office and have not been 
run in the field it is good practice to scale the offsets from the 
tangent to the curve and mark them on the map. 

These offsets from the center line as run are then transferred 
to the cross-sections and the profile plotted from center line 
elevations on the cross-sections. 

Table No. 31 gives the approximate distance that an auto- 
mobile driver can see an approaching car, assuming that he is 
driving in the center of the macadam and that the approaching 
car is also in the center. Two distances are given for each curve, 
the first assuming that the line of sight is six feet from the ground, 
which is about right if the curve is on a straight grade, and makes 
the line of sight tangent to the cut slope of 1 on ij 19 feet off 
center for the narrow section shown in Fig. No. 7, page 30, 
and, second, assuming that the line of sight is close to the ground, 
as occurs on rounding the top of a hill, in which case the line 
of sight will be tangent to the side slope at, approximately, 
n' off center. 



208 



OFFICE PRACTICE 



Table 31 



Degree of 
Curvature 


Radius of Curve 
Feet 


Sight Distance 
Case One. Feet 


Sight Distance 
Case Two. Feet 


5 


1146.0 


400 


310 


6 

7 


955-o 
818.6 


375 
35o 


290 

270 


8 
9 


716.3 
636.6 


330 
3io 


250 
235 


10 


573-o 


295 


220 


12 


477-5 


270 


200 


14 
16 

18 
20 


409.3 
358.1 
318.3 
286.5 


245 
230 
220 
210 


18s 
17s 
165 

160 


30 


191. 


170 


130 


40 


143.2 


145 


no 


So 


114. 6 


130 


IOO 



Plotting the topography. 

If the topography has been recorded on a system of right-angle 
offsets, as suggested and illustrated on page 123, it can be easily 
and quickly plotted by using the transparent 
scale shown here. 

This scale gives the plus distance along the 
survey base line, or center line, and the offset 
distance from the line in one operation. 

As a general rule the plotting of the topog- 
raphy need not be checked. 

Level Computations. 

The survey computations of the Bench 
Levels are checked and a list of bench eleva- 
tions prepared; these elevations are used in 
cross-section level notes and from them the 
notes are computed between benches. As 
each bench is reached these notes are cor- 
rected to agree with the elevation adopted 
for that bench and then carried forward on 
the corrected basis. The allowable error for 
cross-section levels, as mentioned in the chap- 
ter on surveys, is less than 0.1 feet. The cor- 
rection of the levels at each bench prevents 
any cumulative error and makes the eleva- Fig. 59. — Conven- 
tions of the cross-section shots agree with ient Transparent 
the adopted bench elevations with an error Scale for Plotting 
of less than 0.1'. This is as close as the Topography 




PLOTTING THE PROFILE 



209 



readings can be plotted and as close as they can be read in the 
field. 

The computation of the bench levels and the adjustment of 
the cross-section notes should be checked by a competent man. 
The most common mistake in figuring the cross-section read- 
ings is to use the wrong height of instrument for a section. Such 
a mistake cannot be detected in plotting the sections, but is 
generally discovered when the profile is plotted. 

In checking the notes particular care should be taken on this 
one point. 

Pldtting the cross-sections. 

The cross-sections must be very carefully plotted, as the re- 
liability of the earthwork computation depends largely on their 
accuracy. 

The cross-section paper used should be exact in the divisions 
and should be printed or engraved from plates. 

Ruled paper is inaccurate. 

The plotting is checked by reliable men. Reading the shots 
back from the plotted cross-section is preferable to reading them 
from the book. The elevations of the center line and of the ditch 
line are written over the section. The station number or plus 
of each section is written on the right margin. The fact that 
the section has been graveled within the traveled way, that stone 
has been spread to a certain thickness, or any other fact that 
would influence the designer when laying a grade line, is noted on 
the section. See Fig. 60. 




Fig. 60 



It is common practice to allow the inexperienced men to plot 
and check the cross-sections. We believe this is a mistake. 
This part of mapping is the most important of the preliminary 
plans; and the work should be plotted and checked so that the 
points are correct to the nearest 0.1 feet in elevation. 

These points are then connected with a fine ink line. 

Plotting the profile. 

The profile is plotted from the center-line elevations given in 
the cross-section notes unless the proposed center line does not 
coincide with the survey center line, in which case the elevations 



210 OFFICE PRACTICE 

of the proposed line are projected from the previously plotted cros-s 
sections. 

It is not necessary to spend so much time for accuracy in plotting 
as on the sections, as the profile only serves as a guide in laying 
the grade line and no quantities depend upon its correctness. An 
error of 0.2 feet is allowable. 

The elevation of each plotted center-line point is recorded with 
its stationing. 

See Fig. 63. 

The Design. 

The completion of the profile finishes the preliminary mapping. 
The first operations of the office design are as follows : 

A . The selection of section. 

B. The depth of metalling. 

C. The laying of the grade line. 

These three points are so dependent on each other that they can- 
not be separated. 

The most experienced man available should do this part of the 
work. He should be thoroughly familiar with the road from field 
inspection, and in designing he follows the general principles dis- 
cussed in the chapters on Grades, Sections, and Foundations. His 
selection depends on a report of this character. 



PRELIMINARY DESIGN REPORT, NEW CONSTRUCTION 

Dec. 10, 1914. 
Division Engineer 
Dept. of Highways 

Dear Sir: 

In accordance with your request of Nov. 25th find enclosed 
report on a reasonable cost for the Town Line-Manitou State-County 
Highway. 

General Report and Estimate, Town Line — Manitou 
State-County Highway 

With a proper use of local materials a satisfactory road can be 
built at a cost of $94,000 or approx. $11,000 per mile including 
Engineering and Contingencies. An expenditure of $12,000 per 
mile would not however be excessive. 

The Braddocks Bay crossing is the expensive feature of this road; 
it raises the cost of the entire road about $1,000 per mile. 

Design No. 1 is recommended (see page 217). 

A detail report follows. 

Signed 

Designing Engineer. 



DESIGN REPORT 21 1 



Detail Report and Estimate, Town Line — Manitou 
State-County Highway 

Length. 8.51 miles from the Ridge Road to Manitou Beach. 

Foundation Soil. Heavy soil not particularly good foundation 
Sta. o to 133; sandy soil balance of distance except across Braddocks 
Bay. A 9" thickness of some form of macadam is advisable Sta. 
o to 133; 7" or 8" the balance of the distance should be satisfactory 
except across Braddocks Bay where it is safe to figure on 12" to 15* 
of Stone. 

Grade. The present surface can be followed closely. The 
excavation should not exceed 2800 cu. yds. per mile except across 
Braddocks Bay; a rough estimate of borrow excavation for this fill 
is 15,000 cu. yds. 

Alignment. Good; no right of way required except possibly at 
Sta. 350 near the schoolhouse at the turn to Manitou. 

Traffic and Section. There is a heavy volume of automobile 
pleasure traffic and a light volume of heavy hauling traffic on this 
road. 

The large amount of pleasure travel requires from 16' to 18' of 
stone surface; the heavy hauling does not require over 12' to 14' 
full depth metaling. We recommend a graded section 26' to 28' 
wide between ditches in cut with an' width of full depth metal with 
6' of extra width of local crusher run on the shoulders Sta. o to 133; 
a 14/ width with 4/ of stone on shoulders Sta. 133 to 260; a width 
of i2 r of full depth metal with 6' of stone on shoulders the balance of 
the distance except across Braddocks Bay where the entire width 
of metaling 16' should have the full depth. 

This road carries so much high speed traffic that it requires some 
form of bituminous macadam or if Waterbound is selected, it should 
be treated with calcium chloride immediately and have a surface 
coat of bitumen applied within three months. 

Railroad Crossings. Sta. 223 R. W. & O. Ry. crossing; no 
gates or flagman. In the summer time the crossing should have a 
flagman as the orchards cut off the view. The crossing is not par- 
ticularly dangerous, but during this season of the year the traffic on 
this road is entitled to better protection at this point. 

The approach grade from the south should be made easier. 

Drainage. No special features; approx. cost $3,500 exclusive 
of bridges above 5' span to be built by the towns. 

Dangerous Places. The Braddock Bay crossing is a dangerous 
one as the fill is high and the swamp is full of semi-fluid muck from 
6' to 12' deep; a first-class concrete guard rail protection should be 
provided. 

MATERIALS 

Filler Sand. In abundance along road and from roadbed excava- 
tion. 

Gravel. The only good gravel is Lake Gravel; this can be ob- 
tained up to approx. 6000 cu. yds. 1 \ miles north of Sta. 350 and 3000 



212 OFFICE PRACTICE 

yds. i mile west of Sta. 450. Probably this gravel can be used to 
advantage (screened or selected beach run) as bottom course Sta. 
350 to 450 or as filler for sub-base bottom and on the shoulders. 

Stone. 15,000 cu. yds. of fence stone are available within a mile 
and a half of the road Sta. o to 133. 

There is practically no local stone Sta. 133 to 350. 

4,000 cu. yds. of- fence stone are available within ij miles of Sta. 
35o. 

This material runs about 20 % granite fit for top and the balance soft 
sandstone fit for bottom either as a sub-base bottom or crushed 
stone bottom. 

There is sufficient stone at the south end of the road to build a 
sub-base bottom with crushed stone filler; a local granite top with 
crushed stone on the shoulders from Sta. o to 133 and a local crushed 
stone bottom 5" thick Sta. 133 to about Sta. 200. 

There is sufficient stone at the north end to build about if miles 
of crushed stone bottom with stone on shoulders or ij miles of sub- 
base bottom with crushed stone filler and crushed stone on shoulders. 
I do not think there is enough granite to make it worth while to try 
and use a local top on any part of the north end. 

It is probably better to use an imported top from Sta. 133 to 450 
and imported bottom Sta. 200 to 280. 

(See detail Stone Statement and Computations.) 

Crusher set up at Sta. 100. 15,000 cu. yds. field stone available 
within 3 miles maximum haul. Average haul 1 J miles. 

Assume for safety that only 11,000 cu. yds. are available with an 
average haul to crusher of 1 mile. 

Of this 11,000 cu. yds. field stone. 

3,000 c. y. used for sub-base bottom average haul \ mile 

u u i 1 . n, / haul to crusher \ mile 

1,000 c. y. crushed stone filler < tl frQm „ i u 

700 c.y. " " " " shoulders { h ^ ul fr t ^ rUS V r I m ^ e 

u a rry f haul to crusher 1 mile 

2,500 c. y. Top course < « frQm « 3 « 

7,200 c. y. field stone used for local macadam, from Sta. o. to 133, 
leaving 3,800 c. y. available for crushed bottom and shoulder stone 
for road north of Sta. 133. 

3,800 cu. yds. will produce approx. 3,000 cu. yds. of crushed bottom 
loose measure or about 2,300 cu. yds. of rolled measure. This will 
build 10,600 lin. ft. of 5" bottom 14' wide. We can therefore safely 
specify local bottom to Sta. 200 which will leave enough shoulder 
stone to use as far north as Sta. 300 if necessary. 

Crusher set up at Sta. 350. 4,000 cu. yds. available within i| miles, 
say average haul 1 mile. 

Assume for safety that 3,000 cu. yds. only are available average 
haul 1 mile. This will produce about 2400 cu. yds. crushed bottom 
stone loose measure or approx. 1,800 cu. yds. rolled measure. 1800 
cu. yds. will build approx. 90 sta. of 12' bottom 5* deep which makes 
it safe to specify a local bottom using crushed stone and lake gravel 






DESIGN REPORT 



213 



as far south as Sta. 280 with either gravel or crusher run the entire 
length of road on the shoulders. 

Imported bottom should be used Sta. 200 to 280. 

Imported Stone. $1.25 per ton f. o. b. switch. Switch can be 
built at Sta. 233 for $300 to $400. 

Water. Can be obtained at all seasons at intervals from 1 mile 
to 1 J miles all along the road. 

Cost of Different Types 

Grubbing and clearing $ 300.00 

23,000 cu. yds. Roadbed excavation @ $.50 11,500.00 

15,000 " " Brow Exc. across Braddock Bay @ $.45 6,750.00 

800 " " Sub. -base @ $1.25 1,000.00 

4,000 lin. ft. Concrete G. R. across Braddock's Bay @ $1.00. . 4,000.00 

Drainage of system 3,500.00 

Minor points @> 400 per mile 3,400.00 

Engineering and Contingencies 8,000.00 



Total cost of items other than metalling $38,450.00 



Schedule of Unit Prices 

Imported Waterbound Top Sta. 133 to 450 $5.00 per cu. yd. rolled 

Bit. Mac. " " " " " 7-30 

* Local Granite Bit. Mac. Top Sta. o to 133 6.00 

* Imported Limestone Water Mac. Sta. o to 133 5.50 

Sub-base Bottom Crushed stone filler o to 133 1.50 

Local crushed Bottom Sta. 133 to 200 2.50 

Imported Mac. Bottom Sta. 200 to 280 3.20 

Local Crushed Bottom Sta. 280 to 350 2.30 

Lake Gravel Bottom Sta. 350 to 450 1.90 

Crushed stone or gravel on shoulders 1.50 ' loose 

Tarvia B 0.08 per gal. in place 



Table of Comparative Cost 



Type 


Approx. Cost including 
Eng. and Contingencies 


Cost 
per 
mile 


Total 
Cost 


Design No. 1 (For details see Cost. Est. Sheet) 

Design No. 2 ( " " " " " " ) 

Design No. 3 ( " " " " " " ) 

Design No. 4 ( " " " " " " ) 


$11,000 
11,300 
12,000 
12,500 


$ 93,5oo 

96,200 

102,200 

106,000 



Overhead approx. 30^ per cu. yd 
overhead estimated on other items. 



Computation of Unit Prices 

of Bottom and Top Stone. No 



* Note. — There is no difference in cost Sta. 0-133 between a local granite Bit. 
Mac. Top and an imported limestone Waterbound Top when treated with Tarvia B. 



214 OFFICE PRACTICE 

Sub-base Bottom Course Crushed Stone Filler Sta. 0-133 

Cost of Stone in fences $0.10 

Loading 0.15 

Hauling j mile. . 0.12 

Placing and Sledging 0.20 

Rolling 0.05 

Crushed Stone Filler (See Filler) 0.35 cu. yd 0.40 

$1.02 

20% profit 20 

Overhead 0.30 

Estimate $1.52 

Say $1.50 

Crushed Stone Filler (Crusher Run) per cu y( j 

Cost of stone in fences $0.10 

Loading 0.15 

Haul to crusher 1 mile 0.35 

Crushing 0.10 

Cost in bins $0.70 

Loading to wagons 0.01 

Haul to road f mile. 0.22 

Spreading and brooming 0.20 

$1.13 
0.35 cu. yd. per yd. of Sub-base = $0.40 

Local Crushed Stone Bottom Sta. 133 to 200 

Cost in bins $0.70 

Loading to wagons 0.01 

Hauling to road 1 1 miles 0.40 

Spreading 0.06 

Rolling 0.05 

$1.22 
Consolidation 0.3 0.37 

$i.59 
Filler 0.20 

$i.79 

20% profit 0.36 

Overhead 0.30 

Say $2.50 $ 2 -45 

Stone on shoulders $1.50 per cu. yd. loose. 

Local Granite Bit. Mac. Top Sta. o to 133 

Stone in fences $0.10 

Loading 0.15 

Blasting and sledging 0.15 

Hauling to crusher 0.35 

Crushing 0.15 

$0.90 in bins 

Loading to wagons 0.01 

Hauling to road f 0.22 

Spreading 0.06 

Rolling 0.08 

$1.27 
Consolidation 0.38 

$1.65 

Screenings No. 2 and Bit 310 

Profit 0.90 

Overhead 0.30 

Estimate $5-95 

Say $6.00 



DESIGN REPORT 215 

No. 2 Screenings and Bitumen. Note. There should be enough local screenings 
for about f of the top course. Use imported for the balance. 

Cost 0.45 cu. yd. screenings and No. 2 at bin $0.40 

Hauling f mile 0.10 

Spreading 0.12 

Manipulation 21 gals, bitumen @ i\<fc 0.32 

Cost 21 gals, bitumen on road @ 8^ 1.82 

$2.74 

Imported Screenings and No. 2 

Cost 0.45 cu. yd. f. o. b. switch @ $1.25 per ton $0.70 

Unloading 0.05 

Hauling 3 miles 0.90 

Spreading 0.12 

Manipulation 21 gals. Bit. @ \\t 0.32 

Cost 21 gals, bitumen on road @ 8^ 1.80 

Average price $3.10 ^.89 

Imported Limestone Waterbound Mac. Sta. 0-133 
Materials 

4400 lbs. of stone @ $1.25 per ton $2.75 

6% profit 0.15 

$2.90 

Labor 

Unloading $0.10 

Hauling 3 miles @ $0.25 0.75 

Spreading 0.08 

Rolling and puddling 0.10 

$1.03 
Consolidation 0.3 0.31 

$1.34 

Screenings 0.55 

20% profit 0.38 

Overhead 0.30 

Materials 2.90 

Estimate $5-47 

Screenings 

Unloading $0.05 

Hauling 3 mi 0.40 

Spreading and brooming 0.10 

$0.55 

Imported Limestone Waterbound Mac. Sta. 133 to 450 

Materials $2.90 

Labor 

Unloading $0.10 

Hauling 90 sta. if miles 0.55 

Spreading 0.08 

Rolling and puddling 0.10 

$0.83 
Consolidation 0.25 

$1.08 

Screenings 0.45 

20% profit 0.30 

Overhead 0.30 

Materials 2.90 

Estimate $5-°3 

Say $5.00 



216 OFFICE PRACTICE 

Screenings 

Unloading $0.05 

Hauling if miles 0.30 

Spreading and Brooming 0.10 

$0.45 



Imported Limestone Bituminous Macadam Sta. 133 to 450 

Materials 

4200 lbs. @ $1.25 f. o. b. per ton $2.62 

6% profit 0.15 

Labor 

Unloading $0.10 

Hauling 0.55 

Spreading 0.08 

Rolling 0.08 

$0.81 
Consolidation 0.3 0.24 

$1.05 

Screenings and Bit 2.52 

20% profit 0.70 

Overhead 0.30 

Materials 2.77 

Estimate $7-34 



Screenings, No. 2 and Bitumen 

Unloading $0.05 

Hauling 0.25 

Spreading and brooming • 0.12 

21 gals. Bit. A @ 8^. 1.78 

Manipulation of Bitumen 0.32 

$2.52 

Imported Limestone Bottom Sta. 200 to 280 
Materials 

3200 lbs. stone @ $1.25 per ton $2.00 

Profit. 0.10 

Total Materials $2.10 

Labor 

Unloading $0.10 

Hauling average distance, 20 sta 0.55 

Spreading 0.06 

Rolling 0.05 

$0.36 
Consolidation 0.3 0.11 

$0.47 
Filler 0.20 

$0.67 

20% profit 0.13 

Overhead 0.30 

Materials 2.10 

$3.20 



DESIGN REPORT 217 

Local Stone Mac. Bottom Sta. 280 to 350 

Stone in fences $0.10 

Sledging 0.05 

Loading _ 0.15 

Hauling to crusher 1 mile 0.35 

Crushing 0.12 

Cost in bins $0.77 

Loading to wagons 0.01 

Haul to road 0.7 mile 0.22 

Spreading °-o6 

Rolling Q-Q5 

$1.11 

Consolidation 0.3 0.33 

$1.44 
Filler 0.20 

$1.64 

20% profit 0.33 

Overhead 0.30 



Say $2.30 

Lake Gravel Bottom Sta. 350 to 450 

Assume 1 material from Manitou Beach. 

" I " from beach 1^ miles north of Sta. 350. 



Selected Beach Run of Gravel 

Cost on beach $0.10 

Loading 0.15 

Hauling average 2 miles 0.70 

Spreading 0.05 

Rolling 0.04 

Loam and Flushing 0.05 

$1.09 
Consolidation 0.2 0.22 

$1.31 

20% profit 0.26 

Overhead. 0.30 

Say $1.90 ^ x - 8 7 



$2.27 



Design No. 1. 



Approximate Cost Estimates 



I 12' wide 6" sub-base 3" bit. mac. local top 6' of stone 
Sec. No. 1 < on shoulders. Treated with Tarvia B or No. 4 Road 
[ Oil. Sta. 0-133. 

f 14/ wide 5" local mac. bot. 3* waterbound imported 
No. 2 \ lime-stone top. Treated with Tarvia B. 4/ stone on 
[ shoulders. Sta. 133 to 200. 

u ^- f 14' wide 5" imported bottom; same top as from Sta. 
I z 33 to 200 Sta. 200 to 260. 4' stone on shoulders. 

" No a i I2 ' w ^ e $" i m P orte( i bottom 3" water imported top 
\. Tarvia B. . 6' of stone on shoulders Sta. 260 to 280. 

" No c { I2 ' w ^ e 5" ^ oca ^ mac * bottom 3" water imported top 
. ' 5 \ Tarvia B. 6' stone on shoulders. Sta. 280-310. 



218 OFFICE PRACTICE 

" 1ST 6 / I ^' W ^ e 9" su b-base bottom 3" water mac. top Tarvia 
\ B. No stone on shoulders. Sta. 310 to 335. 

u -^ f 12' wide 5" local mac. bottom 3" water mac. top 
' ' \ Tarvia B. 6' of stone on shoulders. Sta. 335 to 350. 

" N R / I2 ' w ^ e 5" ^ e g rave l bottom 3" water mac. top Tarvia 
°" \ B. 6' of gravel or stone on shoulders. Sta. 350 to 450. 

Sec. 1. Sta. o to 133 Approx. Amount 

3000 cu. yds. 6" Sub-base Bottom @ $1.50 $ 4500.00 

1500 " " 3" Bit. Mac. (Local) Top @ $6.00 9000.00 

730 " " Stone on Shoulders (loose) @ $1.50 1100.00 

3500 gals. Tarvia B on Stone Shoulders @ $0.08 280.00 

Sec. 2. Sta. 133 to 200 

1450 cu. yds. 5" Local Mac. Bottom @ $2.50 3625 00 

870 >% " 3" Imported Waterbound Top @ $5.00 . . 4350.00 

270 " " Stone on Shoulder @ $1.50 405.00 

5400 gals. Tarvia B @ $0.08 430.00 

Sec. 3. Sta. 200 to 260 

1300 cu. yds. 5" Imported Bottom @ $3.20 $4150.00 

780 " " 3" Water Mac. Top @ $5.00 . . 3900.00 

240 " Stone on Shoulders @ $1.50 360.00 

4800 gals. Tarv'a B @ $0.08 385.00 

Sec. 4. Sta. 260 to 280 

370 cu. yds. 5" Imported Bottom @ $3.20 $ 1185.00 

230 " " 3" " Water Mac. Top @ $5.00 . . 1150.00 

no " Stone on Shoulders @ $1.50 165.00 

1600 gals. Tarvia B @ $0.08 130.00 

Sec. 5. Sta. 280 to 310 

560 cu. yds. 5" Local Bottom @ $2.30 $ 1290.00 

340 " " 3" Water Mac. Top @ $5.00 1700.00 

170 " " Stone on Shoulders @ $1.50 255.00 

2400 gals. Tarvia B @ $0.08 190.00 

Sec. 6. Sta. 310 to 335 

1130 cu. yds. 9" Sub-base Bottom @ $1.75 $ 1980.00 

380 " " f Water Mac. Top @ $5.00 1900.00 

1800 gals. Tarvia B @ $0.08 i45-oo 

Sec. 7. Sta. 335 to 350 

280 cu. yds. 5" Local Bottom @ $2.30. ". $ 645.00 

170 " " f Water Mac. Top @> $5.00 850.00 

80 " " Stone on Shoulders @ $1.50 120.00 

1200 gals Tarvia B @ $0.08 95-oo 

Sec. 8. Sta. 350 to 450 

1900 cu. yds. 5" Lake Gravel Bottom @ $1.90 $ 3600.00 

1150 " " f Water Mac. Top @, ^5.00 5750-oo 

550 " " Gravel on Shoulders @ $1.50 825.00 

8000 gals. Tarvia B @ $0.08 640.00 

Totals $55100.00 

Items other than Metal 38450.00 

Total Estimate $93550.00 

Design No. 2. Same widths and foundation construction as Design No. 1 except 
that a 2\" Imported Limestone Bituminous Macadam is substituted for the 3" 
Waterbound Top treated with Tarvia B. 

Cost of 3" Water Mac. Top Design No. 1 $19,600 

" " Tarvia B on Mac. Top Design No. 1 1,500 

Total $21,100 

Cost of 2\" Bit. Mac. Top 23,800 

Increased Cost Design No. 2 over No. 1 % 2,700 

Design No. 3. 16' road entire distance local bottom Sta. o to 200 and 280 to 450 
and imported bottom Sta. 200 to 280 with 3" Imported Waterbound Macadam 
treated with 0.4 gal. Tarvia B or 0.25 gal. No. 4 Road Oil. 



SHRINKAGE OF EARTHWORK 219 

9200 cu. yds. local bottom 5" thick @ $2.25 $ 20,700 

1970 " " imported bottom 5" thick @ $3.20 6,300 

6700 " " Top 3" thick @ $5.10 34,200 

32000 gals. Tarvia B @ $0.08 2,560 

$ 63,760 
Items other than metalling 38,450 

$102,210 

Design No. 4. Substitute a 2\" Bit. Mac. Top for the 3" Waterbound Top of 
Design No. 3. This increases the cost approx. $4000. 

Signed 

Designing Engineer. 

Maximum gradients for the various types of pavement are as 
follows : 

Wooden block 2 % 

Asphalt block 4 % 

Brick 5% 

Concrete 5 % 

Bituminous macadam with flush or squeegee coat 4 % 

(In sandy country, six per cent when coarse sand is sprinkled on surface.) 

Bituminous macadam without squeegee 8% 

Waterbound macadam 8 % 

''Hillside" brick 12% 

Stone block with open joints 12% 

Shrinkage of Earthwork. 

We have made no mention heretofore of the shrinkage of earth 
cut when placed in fill. This is an important factor of an eco- 
nomical grading design. 

Trautwine states that for railroad work it takes 

1.08 cu. yds. gravel or sand excavation to make 1 cu. yd. em- 
bankment. 

1. 10 cu. yds. clay excavation to make 1 cu. yd. embankment. 

1. 1 2 cu. yds. loam excavation to make 1 cu. yd*, embankment. 

1. 1 5 cu. yds. vegetable surface soil excavation to make 1 cu. yd. 
embankment. 

The quantities 1.08 cu. yds. gravel, etc., refer to the volume 
occupied by the material before removal. 

Trautwine also states that in loosening earth and loading into 
wagons or cars 1 cu. yd. of earth swells about one-fifth and measures 
loose practically 1.2 cu. yds. 

These values, however, cannot be used in roadwork, as a certain 
percentage of the excavation is sod or vegetable matter that is not 
suitable for embankment and must be wasted. 

This waste material raises the percentage of cut necessary to make 
the fill. 

The correct ratio for roadwork has been a source of contention 
among engineers, and we believe that the use of too high a value 
has resulted in a needless waste of thousands of dollars during 
the last five years in New York State alone. 

Under this head it may be stated that on several roads under 
the supervision of W. G. Harger, a careful study of this point 



2 20 



OFFICE PRACTICE 



was made, taking unusual care with the original and final 
cross-sections, the plotting and planimeter work, and it was found 
that for the cases investigated, the ratio of cut to fill varied 
from 1. 1 5 in heavy cuts to 1.27 in light skimming work. 

It is the general opinion among engineers of Division 5, 
N. Y. S. Dept. of Highways, that the percentage formerly used 
(namely 1.35) is too high. In nearly all cases where the work 
was at all heavy, a large excess of dirt had to be wasted. There 
have been some roads designed on a basis of 1.35 where more 
dirt was needed, but in the authors' opinion this was due to dis- 
crepancies in the field or office work or by allowing the con- 
tractor to use the roadbed excavation for filler or concrete 
material. If the soil encountered is suitable for such purposes, 
it is plainly up to the contractor to furnish other material for the 
places excavated. 



~^\ 




k 


~^^-^_ 


*! 


<b ~"""""^"— -^ 


t: 


,C; J 


vS 


" 1 



Fig. 61. — Transparent Templet for Use on Cross-Sections Giving 
Finished Shape of Road 




Fig. 62. — Transparent Templet with Stone Trench Cut; Saves Time 
in Drawing in Sections for Figuring Cut and Fill 

The authors believe that the following ratios will be satis- 
factory for ordinary cases: 

Table 32 

Light skimming work, large amount of heavy sod 1.35 

Light skimming work, considerable sod 1.30 

Light skimming work, not much sod 1.25 

Medium work 1.20 

Heavy work 1.15 

Trautwine's earth ratios are correct where earth borrow is 
obtained from a pit. 

Trautwine states that 1.0 cu. yd. of solid rock, when broken 
up, will make 1.66 to 1.75 cu. yds. of rock fill. 

In this statement he assumes that the fill is made of stone alone 



ECONOMICAL GRADE LINE 



221 



and that the voids are not filled. In most roadwork, the small 
quantities of rock encountered are dumped in with the earth as 
embankment, and as the voids are all filled with earth it is evi- 
dent that i cu. yd. of rock will make only i cu. yd. of fill; how- 
ever, if a large unmixed stone fill is made, his ratio holds. 

The discussion of these ratios has been carried out to some 
length because we believe it is one of the points that illustrate 
the advantage of careful engineering. Several of the New York 
State plans, the cost of which has ranged from $100 to $200 per 
mile, have been revised with this end in view; the revision costing 
an additional $15 to $30 per mile, with a resultant saving in con- 
struction cost of from $200 to $300 per mile. 

The use of a rolling grade was recommended in the chapter on 
Grades. The designer is cautioned, however, not to carry this to 
extremes as there are many short, small hummocks which must be 
disregarded if a reasonably good profile is to be obtained. Fig. 62 A 
indicates a proper and improper use of an undulating profile. 



.-Undulating Orade } Proper Use Saves Excavation and is 
at the Same Time an easy 
Riding Prof fie. 




s hump of this Kind must be 

Disregarded 




Illustrating Proper Use of 
Straight and Undulating Grades 

Fig. 62 a 



Templets. 

For the convenience of the designer in drawing the shape of 
the finished road on the cross-sections, a number of transparent 
composition templets are made, cut to proper scale, represent- 
ing the different shaped sections to be used. See Figs. 61 and 62. 

Economical Grade Line. 

On page 13, the most economical grading conditions were 
mentioned. A convenient method of laying a grade line that 
will approximate these conditions is as follows: take the case of 
determining an economical profile for a road from station n 
to station 16, where the grade can be placed at any desired ele- 
vation (see page 13). Place the adopted templet on each cross- 
section so that the cut will just make the fill (this position is 



222 



OFFICE PRACTICE 



estimated) and note 

Z'tZZI 
S'lZZI 



iSI'PZ£l 



ztz£i° 




{ $L'ZZ£I 



sv£Z£i 



9£Z£I 



£'+Z£l 
plet, with which all 



the elevation of the center line of the pro- 
^ posed finished road for this posi- 
tion of the templet; mark this 
elevation on the profile for each 
section between stations n and 
16; to connect these points would 
give the most economical grade 
line, but this can rarely be done 
with a resulting smooth profile. 
The adopted grade is obtained 
by drawing in a smooth grade 
line, that averages the elevations 
of these points and varies in ele- 
vation above or below them as 
little as possible. 

The adopted grade elevation 
at each station is then figured, 
the shape of the finished road 
drawn on the cross-sections at 
these elevations, and the exca- 
vation and embankment com- 
puted. If the ratio of cut to 
fill is not correct, the grade is 
raised or lowered slightly to 
produce the desired ratio. This 
method is illustrated in Fig. 63. 

For each stretch of road 
where economy of grading gov- 
erns the profile, this procedure 
is repeated, and for the sections 
of road where other considera- 
tions govern, the grade is placed 
at the required elevation and 
the borrow, waste, or overhaul 
figured. 

To obtain a smooth grade line 
vertical curves are used at the 
intersection of the different tan- 
gent rates of grade. Vertical 
curves are not usually used where 
the difference in rates of grade is 
less than \ per cent. 

For the final plans these ver- 
tical curve elevations may be 
computed by the following for- 
mulae, but for the trial grade line 
they can be scaled from the 
profile, drawing in the curve by 
means of a regular curve tem- 
modern offices are equipped. 



VERTICAL CURVE COMPUTATION 



223 



V- C Formula: 

Formula A. Difference in elevation at Center of Curve. 

d expressed in feet = j- (Algebraic difference of the tangent 

grades expressed in feet per 100) X 
(length of curve expressed in stations 
of ioo'). 



Intersection of 

Tangent Grade* 



Difference in Elevation 
of V. C. and Tangent Intersection 




k Length of Curve — 

Formula A 



---^ 









Formula B 

Formula B. Intermediate differences of Elevations between 
tangent grades and points on vertical curve. 

d':d::t' 2 :t 2 



d' 



t 2 




Sta 10 



10+50 



11+00 



11+50 



1Z+00 



Example of Vertical Curve Computation 

It is required to figure the vertical curve elevations for a 
vertical curve 200' long between tangent grades of + 2 -o% 
and — 3.0% meeting at station 11+ooatan elevation of 12 10.3. 

First, find the middle correction d: use formula A. 

d = I (2.0 - (- 3.0)) X (2) 
d = i (S) X (2) = V = 1-25' 
Second, determine the corrections d\ and di\ use formula B. 



2 24 OFFICE PRACTICE 

i = — = 1.25 — 2 = 1.25 X I = 0.31 feet 

d 2 = 1.25—^-= 0.31 feet, 
iocr 

Third, determine the elevation of the tangent grades at 
10 + 50 and 11 + 50. 

Fourth, subtract the V.C. corrections d h d, and d 2 from these 
tangent grades at 10 + 50, n +00 and n +50. 

Vertical Curve Elevations 

Sta. 10 + 50 = Tangent Elev. 1209.3 — 0.31 = 1208.99 
" 11 + 00 = " " 1210.3 — 1.25 = 1209.05 

" 11 + 50 = " " 1208.8 - 0.31 = 1208.49 

The following table, No. 33, is useful for draftsmen in picking 
out the correct curve to use in inking in the vertical curves. 
This table is compiled for a horizontal scale of 1" = 50', and a 
vertical scale of 1" = io'. For other scales a similar table can 
be constructed. 

Explanation of Table 33. 

Suppose it is required to pick out the correct curve templet 
to draw in a vertical curve 300' long between two tangent grades 
having an algebraic difference of 5 per cent (say a + 2.0 per cent 
grade and a — 3.0 per cent grade). On the line opposite 5.0 
in column 1 representing the algebraic difference of rate, pick 
out the value 24 in the column headed 300' curve; this means 
that a curve having a radius of 24 inches will fit the conditions. 
This curve can be found easily from the collection of curve 
templets which have been previously marked with their radii 
in inches. 

The limit of sight due to vertical curves is shown in Table 34. 

Table 34 gives the distance ahead that a driver can see on a 
straight road, assuming that his eye is 6 feet above the road, 
for vertical curves of 200 feet, 150 feet, and 100 feet long between 
grades having a large difference of rate. 

Example. Suppose a plus 5 percent grade meets a minus 7 
per cent grade and that it is desired to put in the minimum 
length curve that will allow a sight ahead of 300 feet. The 
difference in gradient is 5 + 7 = 12 per cent. From table 
34, opposite 12 per cent, we can readily pick the length re- 
quired; it will be about 170 feet and 200 feet would probably 
be used. It is rare that the sight distance governs in the selec- 
tion of length of curve. 

Placing the Templets and Planimetering the Areas. 

After the trial grade line has been placed the center line ele- 
vations of the proposed finished road are figured for each point 
on the profile where cross-sections have been taken and the 
section selected is drawn on the original cross-sections at these 
elevations, using the templets mentioned above. 

Because it is comparatively easy to make a mistake of one 



RADII FOR PLOTTING VERTICAL CURVES 



225 



Table ^- Table of Radii for Plotting Vertical Curves 

on Profiles 



Algebraic 


10c/ Curve 


200' Curve 


300' Curve 


400' Curve 


Diff. 


Rad. 


Rad. 


Rad. 


Rad. 


I.O 


40 


80 


I20 


160 


1.2 


33 


67 


IOO 


132 


1.4 


29 


57 


85 


116 


1.6 


25 


5o 


75 


IOO 


1.8 


22 


44 


65 


88 


2.0 


20 


40 


60 


80 


2.2 


l8 


36 


55 


72 


2.4 


i6i 


33 


50 


66 


2.6 


isi 


30 


46 


62 


2.8 


I4a 


29 


43 


58 

• 


3-o 


I3§ 


27 


40 


54 


3-2 


I2| 


25 


37 


50 


3-4 


12 


23 


35 


48 


3-6 


11 


22 


33 


44 


3-8 


io£ 


21 


32 


42 


4.0 


10 


20 


30 


40 


4-5 


9 


18 


27 


36 


5-o 


8 


16 


24 


32 


5-5 


7 


142 


22 


28 


6.0 


6| 


13* 


20 


26 


7.0 


6 


Hi 


17 


24 


8.0 


5 


10 


16 


20 


9.0 


4i 


9 


13! 


18 


10. 


4 


8 


12 


16 


11. 


3l 


7 


11 


I4» 


12.0 


3i 


6J 


10 


i3i 


13.0 


3 


6 


9 


I2| 


14.0 


3 


5i 


8| 


"I 



Table 34 



Difference in 
Rate of Grades 


Sight Distance for 
200 ft. V. C. 


Sight Distance for 
150 ft. V. C. 


Sight Distance for 
100 ft. V. C. 


8% 
10% 
12% 
14% 
16% 


355 feet 
320 " 
290 " 
260 " 


315 feet 

290 " 
260 " 

230 " 


370 feet 
290 " 
260 " 
230 " 
210 " 



226 OFFICE PRACTICE 

foot or five feet in elevation, the elevation of new grade, as 
shown by the position of the templet, should be checked from 
the profile before computing the cuts and fills. 

Because of the small, irregular shape of these areas it is not 
possible to compute them arithmetically and the areas are 
determined by planimeters. Great care must be exercised if 
the work is to be reliable; a double run is made and the second 
run should be twice the first area. A certain limit of error in 
the second area is adopted. 1 This method is sufficiently ac- 
curate for preliminary estimating. On final estimate work, where 
the payment for earth excavation depends on the planimeter 
work, a satisfactory method is to have two men, using sepa- 
rate planimeters, compute the areas independently without any 
knowledge of each other's result. If the amount of excavation as 
figured separately varies more than 2 per cent, a third run is made. 

The reason that it is difficult to get accurate planimeter re- 
sults is that the work is monotonous, confining, and hard on 
the eyes, and the tendency is toward carelessness unless the men 
know that their work is being checked. 

The temptation is strong to make the second reading equal 
twice the first, and unless some such method is used to check up, 
small errors will be passed over. 

As a matter of interest three miles of planimeter work, 
checked in this manner, was examined to see the average differ- 
ence in areas, where two careful men using different planimeters 
computed their results separately. 

The sections used were plotted 1" = 5'; areas read to nearest 
0.1 sq. ft. 

The average percentage of difference for single areas were 

1. Small areas below 10 sq. ft per cent of difference 5% 

2. " " 10 to 30 " " " " " " 2% 

3. Areas above 30 ^ ""......" " " " 1% 

However, these differences for single areas compensate, as some 

are above and some below the mean value, and computing the 
two separate results for the three miles gave the following result. 
Percentage differences for work of two men for three miles, 
showing the reduction of error due to compensation. 

1. Small areas below 10 sq. ft per cent of difference 1.0 % 

2. " " 10 to 30 " " . . . . " " " " 0.5 % 

3. Areas above 30 ""...." " " " 0.05 % 
The average excavation per mile will run about 3,000 cu. yds., 

which means the average area of cut is about 16 sq. ft. 

This comes under the second division and makes the probable 
error of final estimate planimeter work sufficiently close for all 
practical purposes. 

Areas by measuring the depth of cut or fill at intervals of one foot 
across the section. 

It is often necessary for the field men to make a change in grade 
or alignment, and the following method of estimating section areas 

1 A satisfactory rule has been to allow a difference of 0.4 sq. ft. for areas up to 
50 sq. ft., and 1.0 sq. ft. error above 50 sq. ft. 



AREAS BY MEASURING DEPTH 



227 



is convenient when no planimeter is available. The method is illus- 
trated in the figures shown below: — 




Measure the depth of the cutting on vertical No. 1. Call this 
depth i'. It can be readily seen that this depth is the average depth 
for the first foot of the cross section, and if multiplied by one foot 
equals] the area of the first foot of the section. In like manner 
measure the depth of the section on vertical No. 2. This is the 
average depth of the second foot of the section, and multiplied by 
one foot equals the area of the second foot of the section. If the 
sum of the depths 1', 2', 3', etc., is obtained for the entire width of 
the section it is evident that the sum must equal the area of the 
section. 

This summation can readily be made graphically as shown below 
by marking off on the edge of a piece of paper the successive depths. 






35' 



?fer 



Reference 
Mark 



End 
Mark 



Strip of Paper 

Scale the distance from the reference mark to the end mark, using 
the same scale by which the cross section is plotted and the area of 
the section is obtained. This method is as reliable as planimeter 
work, but is necessarily slower. 

Computation of Earthwork. 

Earthwork is usually computed from the planimeter results 
by the method of end areas; where 50-ft. sections are used the 
following table is convenient. 

Explanation of Table 35. 

Suppose the area of excavation at, say, station 22+00 is 
30.6 sq. ft.; suppose the excavation area at station 22 -f- 50 is 
20.1 sq. ft. To get the number of cubic feet of excavation from 
station 22 + 00 to 22 -f 50 add 30.6 + 20.1 = 50.7. In Table 
35 an area of 50.7 gives an excavation quantity of 1267.5 cu. ft. 
Where the normal cross-section interval is 50 ft. this table is a 
great time-saver. 

Table 36 is convenient in changing cubic feet to cubic yards. 

Table 37 is convenient for preliminary estimates, as it gives 
the cubic yards directly for the sum of the end areas in square 
feet. It, however, is not figured exactly and is not suitable for 
final estimate work. 



228 OFFICE PRACTICE 

Table 35. Volume oe 50-FT. Sections in Cubic Feet for 
Sum of End Areas 



COMPILED BY J. H. 


HUBER 


, ASSISTANT ENGINEER. BUFFALO, N.Y. 




Sum of 






















End Areas 


0.0 


O.I 


0.2 


0-3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


Sq. Ft. 




























2.5 


5.0 


7-5 


10.0 


12.5 


15.0 


17.5 


20.0 


22.5 


1 


25.0 


27.5 


30.0 


32.5 


35.0 


37-5 


40.0 


42.5 


45-o 


47-5 


2 


50.0 


52.5 


55-0 


57-5 


60.0 


62.5 


65.0 


67.5 


70.0 


72.5 


3 


75-o 


77.5 


80.O 


82.5 


85.0 


87.5 


90.0 


92.5 


95-o 


97-5 


4 


100. 


102.5 


IO5.O 


I07.5 


IIO.O 


112. 5 


115.0 


117. 5 


120.0 


122.5 


5 


125.0 


127.5 


I30.0 


132.5 


i35-o 


137.5 


140.0 


142.5 


145.0 


147.5 


6 


150.0 


152.5 


I55.0 


157.5 


160.0 


162.5 


165.0 


167.5 


170.0 


172.5 


7 


175-0 


177.5 


180.O 


182.5 


185.0 


187.5 


190.0 


192.5 


195.0 


197.5 


8 


200.0 


202.5 


205.O 


207.5 


210.0 


212.5 


215.0 


217.5 


220.0 


222.5 


9 


225.0 


227.5 


23O.O 


232.5 


235-0 


237-5 


240.0 


242.5 


245.0 


247-5 


10 


250.0 


252.5 


255.0 


257.5 


260.0 


262.5 


265.0 


267.5 


270.0 


272.5 


11 


275.0 


277.5 


280.O 


282.5 


285.0 


287.5 


290.0 


292.5 


295.0 


297-5 


12 


300.0 


302.5 


305.0 


307.5 


310.0 


312.5 


3I5-0 


317.5 


320.0 


322.5 


13 


325-o 


327.5 


330.0 


332.5 


335-o 


337-5 


340.0 


342.5 


345-0 


347-5 


14 


350.0 


352.5 


355-o 


357-5 


360.0 


362.5 


365.0 


367.5 


370.0 


372.5 


15 


375-o 


377.5 


380.0 


382.5 


385.0 


387.5 


390.0 


392.5 


395-o 


397-5 


16 


400.0 


402.5 


405-0 


407.5 


410.0 


412.5 


415.0 


417.5 


420.0 


422.5 


17 


425.0 


427.5 


430.0 


432.5 


435-o 


437-5 


440.0 


442.5 


445-Q 


447-5 


18 


450.0 


452.5 


455-o 


457-5 


460.0 


462.5 


465.0 


467-5 


470.0 


472.5 


19 


475-0 


477-5 


480.0 


482.5 


485.0 


487.5 


490.0 


492.5 


495-Q 


497-5 


20 


500.0 


502.5 


505-0 


507-5 


510.0 


512.5 


5I5-0 


517.5 


520.0 


522.5 


21 


525-o 


527.5 


530-0 


532.5 


535.o 


537-5 


540.0 


542.5 


545-o 


547.5 


22 


55o.o 


552.5 


555-0 


557.5 


560.0 


562.5 


565.0 


567.5 


57o.o 


572.5 


23 


575-o 


577-5 


580.0 


582.5 


585.0 


587.5 


590.0 


592.5 


595-0 


597-5 


24 


600.0 


602.5 


605.0 


607.5 


610.0 


612.5 


615.0 


617.5 


620.0 


622.5 


25 


625.0 


627.5 


630.0 


632.5 


635-o 


637.5 


640.0 


642.5 


645.0 


647.5 


26 


650.0 


652.5 


655.o 


657.5 


660.0 


662.5 


665.0 


667.5 


670.0 


672.5 


27 


675.0 


677.5 


680.0 


682.5 


685.0 


687.5 


690.0 


692.5 


695.0 


697.5 


28 


700.0 


702.5 


705.0 


707.5 


710.0 


712.5 


7i5-o 


717.5 


720.0 


722.5 


29 


725.0 


727-5 


730.0 


732.5 


735-0 


737-5 


740.0 


742.5 


745-0 


747.5 


30 


750.0 


752.5 


755-0 


757-5 


760.0 


762.5 


765.0 


767.5 


770.0 


772.5 


31 


775-0 


777-5 


780.0 


782.5 


785.0 


787.5 


790.0 


792.5 


795-0 


797-5 


32 


800.0 


802.5 


" 805.0 


807.5 


810.0 


812.5 


815.0 


817.5 


820.0 


822.5 


33 


825.0 


827.S 


830.0 


832.5 


835.0 


837.5 


840.0 


842.5 


845-0 


847.5 


34 


850.0 


852.5 


855.o 


857.5 


860.0 


862.5 


865.0 


867.5 


870.0 


872.5 


35 


875.0 


877.5 


880.0 


882.5 


885.0 


887.5 


890.0 


892.5 


895-0 


897.5 


36 


900.0 


902.5 


905.0 


907-5 


910.0 


912.5 


915.0 


917.5 


920.0 


922.5 


37 


925.0 


927.5 


930.0 


932.5 


935-o 


937-5 


940.0 


942.5 


945.o 


947-5 


38 


950.O 


952.5 


955-0 


957-5 


960.0 


962.5 


965-0 


967.5 


970.0 


972.5 


39 


975.o 


977-5 


980.0 


982.5 


985-0 


987.5 


990.0 


992.5 


995-0 


997-5 


40 


1000.0 


1002.5 


1005.0 


1007.5 


IOIO.O 


1012.5 


1015.0 


1017.5 


1020.0 


1022.5 


41 


1025.0 


1027.5 


1030.0 


1032.5 


1035-0 


1037.5 


1040.0 


1042.5 


1045.0 


I047-5 


42 


1050.0 


1052.5 


1055-0 


I057.5 


1060.0 


1062.5 


1065.0 


1067.5 


1070.0 


1072.5 


43 


1075.0 


1077.5 


1080.0 


1082.5 


1085.0 


1087.5 


1090.0 


1092.5 


1095.0 


1097.5 


44 


IIOO.O 


1102.5 


1105.0 


1107.5 


IIIO.O 


1112.5 


1115.0 


HI7-5 


1 1 20.0 


1122.5 


45 


1125.0 


1127.5 


1130.0 


1132.5 


H35-0 


II37.5 


1140.0 


1142.5 


1145.0 


II47.5 


46 


1150.0 


1152.5 


H55-0 


II57.5 


1160.0 


1162.5 


1165.0 


1167.5 


1170.0 


1172.5 


47 


1175.0 


II77-5 


1180.0 


1182.5 


1185.0 


1187.5 


1190.0 


1192.5 


ii95-o 


II97.5 


48 


1200.0 


1202.5 


1205.0 


1207.5 


1210.O; 


1212.5 


1215.0 


1217.5 


1220.0 


1222.5 


49 


1225.0 


1227.5 


1230.0 


1232.5 


1235.0 


1237.5 


1240.0 


1242.5 


1245.0 


1247.5 


50 


1250.0 


1252.5 


1255-0 


I257-5; 


1260.0 


1262.5 


1265.0 


1267.5 


1270.0 


1272.5 



Note. — For volumes larger than those given, use figures in the table, 
decimal point one place to the right and add proportional part. 



moving 



VOLUME OF 50-FOOT SECTIONS 



229 



Table 35. Volume of 50-FT. Sections in Cubic Feet for 
Sum of End Areas. — Continued 

COMPILED BY J. H. HUBER, ASSISTANT ENGINEER, BUFFALO, N.Y. 



Sum of 






















End Areas 


0.0 


O.I 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


Sq.Ft. 






















50 


1250.0 


1252.5 


1255-0 


1257.5 


1260.0 


1262.5 


1265.C 


1267.5 


1270.C 


1272.5 


5i 


1275.0 


1277.5 


1280.0 


1282.5 


1285.0 


1287.5 


1290.C 


1292.5 


1295.C 


1297-5 


52 


1300.0 


1302.5 


1305-0 


1307.5 


1310.0 


1312.5 


1315-c 


I3I7.5 


1320.C 


1322.5 


53 


1325-0 


1327-5 


1330.0 


1332.5 


I335-Q 


1337.5 


1340.0 


1342.5 


I345-C 


1347-5 


54 


1350.0 


1352.5 


1355-0 


1357-5 


1360.0 


1362.5 


1365-0 


1367.5 


1370.0 


1372.5 


55 


I375-0 


1377.5 


1380.0 


1382.5 


1385-0 


1387.5 


1390.0 


1392.5 


1395-0 


1397.5 


56 


1400.0 


1402.5 


1405-0 


1407-5 


1410.0 


1412.5 


1415-0 


I4I7.5 


1420.0 


1422.5 


57 


1425.0 


1427-5 


1430.0 


1432.5 


1435-0 1437-5 


1440.0 


1442.5 


1445.0 


1447.5 


58 


1450.0 


1452.5 


I455-Q 


1457-5 


1460.0 1462.5 


1465.0 


1467-5 


1470.0 


1472.5 


59 


I475-Q 


1477.5 


1480.0 


1482.5 


1485.0 1487.5 


1490.0 


1492.5 


1495.0 


1497.5 


60 


1500.0 


1502.5 


1505-0 


1507.5 


1510.0 


1512.5 


i5i5-o 


1517.5 


1520.0 


1522.5 


61 


1525-0 


1527.5 


1530.0 


1532.5 


I535-0 


1537.5 


1540.0 


1542.5 


I545-Q 


1547.5 


62 


1550.0 


1552.5 


I555-0 


1557.5 


1560.0U562.5 


1565.0 


1567.5 


1570.0 


1572.5 


63 


I575-Q 


1577.5 


1580.0 


1582.5 


1585.0 1587.5 


1590.0 


1592.5 


I595-0 


1597.5 


64 


1600.0 


1602.5 


1605.0 


1607.5 


1610.OJ1612.5 


1615.0 


1617.5 


1620.0 


1622.5 


65 


1625.0 


1627.5 


1630.0 


1632.5 


1635.0 1637.5 


1640.0 


1642.5 


1645.0 


1647.5 


66 


1650.0 


1652.5 


1655-0 


1657-5 


1660.0,1662.5 


1665.0 


1667.5 


1670.0 


1672.5 


67 


1675.0 


1677.5 


1680.0 


1682.5 1685.0I1687.5 


1690.0 


1692.5 


1695.0 


1697.5 


68 


1700.0 


1702.5 


1705.0 


1707.5 1710.0 1712. 5 


1715-0 


I7I7.5 


1720.0 


1722.5 


69 


1725.0 


1727-5 


1730.0 


i732.5|i735-o 1737-5 


1740.0 


1742.5 


i745.o 


1747.5 


70 


1750.0 


1752.5 


I755-Q 


1757.5 


1760.0 


1762.5 


1765.0 


1767.5 


1770.0 


1772.5 


7i 


i775.o 


1777.5 


1780.0 


1782.5 


1785.0 


1787.5 


1790.0 


1792.5 


I795-0 


1797-5 


72 


1800.0 


1802.5 


1805.0 


1807.5 


1810.0 


1812.5 


1815.0 


1817.5 


1820.0 


1822.5 


73 


1825.0 


1827.5 


1830.0 


1832.5 


1835-0 


1837.5 


1840.0 


1842.5 


1845.0 


1847.5 


74 


1850.0 


1852.5 


1855-0 


1857.5 


1860.0 


1862.5 


1865.0 


1867.5 


1870.0 


1872.5 


75 


1875-0 


1877-5 


1880.0 


1882.5 


1885.0 


1887.5 


1890.0 


1892.5 


1895.0 


1897.5 


76 


1900.0 


1902.5 


1905.0 


1907.5 


1910.0 


1912.5 


1915-0 


I9I7.5 


1920.0 


1922.5 


77 


1925.0 


1927-5 


1930.0 


1932.5 


i935.o 


1937.5 


1940.0 


1942.5 


1945.0 


1947.5 


78 


1950.0 


1952.5 


I955-Q 


1957.5 


1960.0 


1962.5 


1965.0 


19670 


1970.0 


1972.5 


79 


i975.o 


1977.5 


1980.0 


1982.5 


1985.0 


1987.5 


1990.0 


1992.5 


1995.0 


1997.5 


80 


2000.0 


2002.5 


2005.0 


2007.5 


2010.0 


2012.5 


2015.0 


2017.5 


2020.0 


2022.5 


81 


2025.0 


2027.5 


2030.0 


2032.5 


2035.0 


2037.5 


2040.0 


2042.5 


2045.0 


2047.5 


82 


2050.0 


2052.5 


2055.0 


2057.5 


2060.0 


2062.5 


2065.0 


2067.5 


2070.0 


2072.5 


83 


2075-0 


2077.5 


2080.0 


2082.5 


2085.0 


2087.5 


2090.0 


2092.5 


2095.0 


2097.5 


84 


2100.0 


2102.5 


2105.0 


2107.5 


2110.0 


2112.5 


2115.0 


2117.5 


2120.0 


2122.5 


85 


2125.0 


2127.5 


2130.0 


2132.5 


2135.0 


2137-5 


2140.0 


2142.5 


2145-0 


2147.5 


86 


2150.0 


2152.5 


2i55-o 


2157-5 


2160.0 


2162.5 


2165.0 


2167.5 


2170.0 


2172.5 


87 


2175.0 


2177.5 


2180.0 


2182.5 


2185.0 


2187.5 


2190.0 


2192.5 


2195.0 


2197-5 


88 


2200.0 


2202.5 


2205.0 


2207.5 


2210.0 


2212.5 


2215.0 


2217.5 


2220.0 


2222.5 


89 


2225.0 


2227.5, 


2230.0 


2232.5 


2235.0 


2237-5 


2240.0 


2242.5 


2245.0 


2247-5 


go 


2250.0 


2252.5 


2255.0 


2257.5 


2260.0 


2262.5 


2265.0 


2267.5 


2270.0 


2272.5 


91 


2275-0 


2277.5 


2280.0 


2282.5 


2285.0 


2287.5 


2290.0 


2292.5 


2295.0 


2297.5 


92 


2300.0! 


2302.5 


2305.0 


2307.5 


2310.0 


2312.5 


2315-0 


23I7.5 


2320.0 


2322.5 


93 


2325-0 


2327.5 


2330.0 


2332.5 


2335-o 


2337-5 


2340.0 


2342.5 


2345-0 


2347.5 


94 


2350.0 


2352.5 


2355-0 


2357-5 


2360.0 


2362.5 


2365.0 


2367.5 


2370.0 


2372.5 


95 


2375-0 


2377.5, 


2380.0 


2382.5 


2385.0 


2387.5 


2390.0 


2392.5 


2395-0 


2397.5 


96 


2400.0 


2402.5! 


2405.0 


2407.5 


2410.0 


2412.5 


2415.0 


24I7.5 


2420.0 


2422.5 


97 


2425.0 


2427.5J 


2430.0 


2432.5 


2435-0 


2437-5 


2440.0 


2442.5 


2445.o 


2447-5 


98 


2450.0 


2452-5 : 


2455.0 


2457-5 


2460.0 


2462.5 


2465.0 


2467-5 


2470.0 


2472.5 


99 


2475-0 


2477-5, 


2480.0 


2482.5 


2485.0 


2487.5 


2490.0 


2492.5 


2495.0 


2497-5 


100 


2500.0 


2502.5 


2505.0 


2507.5 


25IO.O ( 


2512.5 


2515-0 


2517.5 


2520.0 


2522.5 


PROPORTI 


ONAL PARt!°-° oi ° 2 °-3 °4 0.5 0.6 0.7 0.8 0.9 










2-5 5- 


7.5 


10. ] 


■ 2.5 1 


5-o 17 


5 20. 


22.5 



230 OFFICE PRACTICE 

Table 36. Cubic Feet and Cubic Yards 



0-1350 


I350- 


-2700 


2700-4050 


4050-5400 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


27 


1 


77 


5i 


2,727 


101 


77 


151 


54 


2 


1,404 


2 


54 


2 


4,104 


2 


81 


3 


3i 


3 


81 


3 


3i 


3 


108 


4 


58 


4 


2,808 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


1,512 


6 


62 


6 


4,212 


6 


89 


7 


39 


7 


89 


7 


39 


7 


216 


8 


66 


8 


2,916 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


10 


1,620 


60 


70 


no 


4,320 


160 


97 


1 


47 


1 


97 


1 


47 


1 


324 


2 


74 


2 


3,024 


2 


74 


2 


5i 


3 


1,701 


3 


5i 


3 


4,401 


3 


78 


4 


28 


4 


78 


4 


28 


4 


40S 


5 


55 


5 


3,105 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


1,809 


7 


59 


' 7 


4,509 


7 


86 


8 


36 


8 


86 


8 


36 


8 


5i3 


9 


63 


9 


3,213 


9 


63 


9 


40 


20 


90 


7o 


40 


120 


90 


170 


67 


1 


i,9i7 


1 


67 


1 


4,617 


1 


94 


2 


44 


2 


94 


2 


44 


2 


621 


3 


7i 


3 


3,32i 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


2,025 


5 


75 


.5 


4,725 


5 


702 


6 


52 


6 


3,402 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


2,106 


8 


56 


8 


4,806 


8 


83 


9 


33 


9 


83 


9 


33 


9 


810 


30 


60 


80 


3,5io 


130 


60 


180 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


2,214 


2 


64 


2 


4,914 


2 


91 


3 


41 


3 


9i 


3 


41 


3 


918 


4 


68 


4 


3,6i8 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


2,322 


6 


72 


6 


5,022 


6 


99 


7 


49 


7 


99 


7 


49 


7 


1,026 


8 


76 


8 


3,726 


8 


76 


8 


53 


9 


2,403 


9 


53 


9 


5,103 


9 


80 


40 


30 


90 


80 


140 


30 


190 


1,107 


1 


57 


1 


3,807 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


2,511 


3 


61 


3 


5,2n 


3 


88 


4 


38 


4 


88 


4 


38 


4 


1,215 


5 


65 


5 


3-915 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


2,619 


7 


69 


7 


5,319 


7 


96 


8 


46 


8 


96 


8 


46 


8 


1,323 


9 


73 


9 


4,023 


9 


73 


9 


50 


50 


2,700 


100 


50 


150 


5,400 


2 00 



CUBIC FEET AND CUBIC YARDS 

Table 36 — continued 



231 



5400-6750 


6750-8100 


8100-9450 


9450-10,800 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


5,427 


201 


77 


251 


8,127 


301 


77 


35i 


54 


2 


6,804 


2 


54 


2 


9,504 


2 


81 


3 


3i 


3 


81 


3 


3i 


3 


5,5o8 


4 


58 


4 


8,208 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


6,912 


6 


62 


6 


9,612 


6 


89 


7 


39 


7 


89 


7 


39 


7 


5,6i6 


8 


66 


8 


8,316 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


210 


7,020 


260 


70 


310 


9,720 


360 


97 


1 


47 


1 


97 


1 


47 


1 


5,724 


2 


74 


2 


8,424 


2 


74 


2 


51 


3 


7,101 


3 


5i 


3 


9,801 


3 


78 


4 


28 


4 


78 


4 


28 


4 


5,805 


5 


55 


5 


8,505 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


7,209 


7 


59 


7 


9,909 


7 


86 


8 


36 


8 


86 


8 


36 


8 


5,9i3 


9 


63 


9 


8,613 


9 


63 


9 


40 


220 


90 


270 


40 


320 


90 


37o 


67 


1 


7.317 


1 


67 


1 


10,017 


1 


94 


2 


44 


2 


94 


2 


44 


2 


6,021 


3 


71 


3 


8,721 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


7,425 


5 


75 


5 


10,125 


5 


6,102 


6 


52 


6 


8,802 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


7,5o6 


8 


56 


8 


10,206 


8 


83 


9 


33 


9 


83 


9 


33 


9 


6,210 


230 


60 


280 


8,910 


330 


60 


380 


37 


1 


87 


1 


• 37 


1 


87 


1 


64 


2 


7,6i4 


2 


64 


2 


10,314 


2 


9i 


3 


41 


3 


9i 


3 


41 


3 


6,318 


4 


68 


4 


9,018 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


7,722 


6 


72 


6 


10,422 


6 


99 


7 


49 


7 


99 


7 


49 


7 


6,426 


8 


76 


8 


9,126 


8 


76 


8 


53 


9 


7,803 


9 


53 


9 


10,503 


9 


80 


240 


30 


290 


80 


340 


30 


390 


6,507 


1 


57 


1 


9,207 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


7,9H 


3 


61 


3 


10,611 


3 


88 


4 


38 


4 


88 


4 


38 


4 


6,615 


5 


65 


5 


9,3i5 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


8.019 


7 


69 


7 


10,719 


7 


96 


8 


46 


8 


96 


8 


46 


8 


6,723 


9 


73 


9 


9,423 


9 


73 


9 


50 


250 


8,100 


300 


50 


350 


10,800 


400 



232 



OFFICE PRACTICE 

Table 36 — continued 



10,800-12,150 


12,150-13,500 


13,500-14,850 


14,850-16,200 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


10,827 


401 


77 


45i 


13,527 


501 


177 


55i 


54 


2 


12,204 


2 


54 


2 


14,904 


2 


81 


3 


3i 


3 


81 


3 


31 


3 


10,908 


4 


58 


4 


13,608 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


12,312 


6 


62 


6 


15,012 


6 


89 


7 


39 


7 


89 


'7 


39 


7 


11,016 


8 


66 


8 


I3,7i6 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


410 


12,420 


460 


70 


5io 


15,120 


560 


97 


1 


47 


1 


97 


1 


47 


1 


11,124 


2 


74 


2 


13,824 


2 


74 


2 


5i 


3 


12,501 


3 


5i 


3 


15,201 


3 


78 


4 


28 


4 


78 


4 


28 


4 


11,205 


5 


55 


5 


13,905 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


12,609 


7 


59 


7 


15,309 


7 


86 


3 


36 


8 


86 


8 


36 


8 


11,313 


9 


63 


9 


14,013 


9 


63 


9 


40 


420 


90 


470 


40 


520 


90 


570 


67 


1 


12,717 


1 


67 


1 


15,417 


1 


94 


2 


44 


2 


94 


2 


. 44 


2 


11,421 


3 


7i 


3 


14,121 


3 


7i 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


12,825 


5 


75 


5 


15,525 


5 


11,502 


6 


52 


6 


14,202 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


12,906 


8 


56 


8 


15,606 


8 


83 


9 


33 


9 


83 


9 


33 


9 


11,610 


430 


60 


480 


i4,3io 


530 


60 


580 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


13,014 


2 


64 


2 


15,714 


2 


9i 


3 


41 


3 


9i 


3 


4i 


3 


11,718 


4 


68 


4 


14,418 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


13,122 


6 


72 


6 


15,822 


6 


99 


7 


49 


7 


99 


7 


49 


7 


11,826 


8 


76 


8 


14,526 


8 


76 


8 


53 


9 


13,203 


9 


53 


9 


15,903 


9 


80 


440 


30 


490 


80 


540 


30 


590 


11,907 


1 


57 


1 


14,607 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


I3,3H 


3 


61 


3 


16,011 


3 


88 


4 


38 


4 


88 


4 


38 


4 


12,015 


5 


65 


5 


14,715 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


13,419 


7 


69 


7 


16,119 


7 


96 


8 


46 


8 


96 


8 


46 


8 


12,123 


9 


73 


9 


14,823 


9 


73 


9 


50 


450 


13,500 


500 


50 


55o 


16,200 


600 



CUBIC FEET AND CUBIC YARDS 
Table 36 — continued 



233 



16,200-17,550 


17,550-18,900 


18,900-20,250 


20,250- 


21,600 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


16,227 


601 


77 


651 


18,927 


701 


77 


75i 


54 


2 


17,604 


2 


54 


2 


20,304 


2 


81 


3 


3i 


3 


81 


3 


31 


3 


16,308 


4 


58 


4 


19,008 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


17,712 


6 


62 


6 


20,412 


6 


89 


7 


39 


7 


89 


7 


39 


7 


16,416 


8 


66 


8 


19,116 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


610 


17,820 


660 


70 


710 


20,520 


760 


97 


1 


47 


1 


97 


1 


47 


1 


16,524 


2 


74 


2 


19,224 


2 


74 


2 


5i 


3 


17.901 


3 


51 


3 


20,601 


3 


78 


4 


28 


4 


78 


4 


28 


4 


16,605 


5 


55 


5 


19,305 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


18,009 


7 


59 


7 


20,709 


7 


86 


8 


36 


8 


86 


8 


36 


8 


16,713 


9 


63 


9 


19,413 


9 


63 


9 


40 


620 


90 


670 


40 


720 


90 


770 


67 


1 


18,117 


1 


67 


1 


20,817 


1' 


94 


'2 N 


44 


2 


94 


2 


44 


2 


16,821 


3 


71 


3 


19,521 


3 


7i 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


18,225 


5 


75 


5 


20,925 


5 


16,902 


6 


52 


6 


19,602 


6 


52 


6 


29 


7 


•79 


7 


29 


7 


79 


7 


56 


8 


18.306 


8 


56 


8 


21,006 


8 


83 


9 


33 


9 


83 


9 


33 


9 


17,010 


630 


60 


680 


19,710 


730 


60 


780 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


18,414 


2 


64 


2 


21,114 


2 


9i 


3 


41 


3 


9i 


3 


41 


3 


17,118 


4 


68 


4 


19,818 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


18,522 


6 


72 


6 


21,222 


6 


99 


7 


49 


7 


99 


7 


49 


7 


17,226 


8 


76 


8 


19,926 


8 


76 


8 


53 


9 


18,603 


9 


53 


9 


21,303 


9 


80 


6.10 


30 


690 


80 


740 


30 


790 


17,307 


1 


57 


1 


20,007 


1 


5 7 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


18,711 


3 


61 


3 


21,411 


3 


88 


4 


38 


4 


88 


4 


38 


4 


I7,4i5 


5 


65 


5 


20,115 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


18,819 


7 


69 


7 


21,519 


7 


96 


8 


46 


8 


96 


8 


46 


8 


17.523 


9 


73 


9 


20,223 


9 


73 


9 


50 


6,0 


iS.oco 


700 


50 


75o 


21,600 


800 



234 



OFFICE PRACTICE 

Table 36 — continued 



21,600-22,950 


22,950-24,300 


24,300-25,650 


25,650- 


27,000 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


21,627 


801 


77 


851 


24,327 


901 


77 


95i 


54 


2 


23,004 


2 


54 


2 


25,704 


2 


81 


3 


3i 


3 


81 


3 


31 


3 


21,708 


4 


58 


4 


24,408 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


23,112 


6 


62 


6 


25,812 


6 


89 


7 


39 


7 


89 


7 


39 


7 


21,816 


8 


66 


8 


24,516 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


810 


23,220 


860 


70 


910 


25,920 


960 


97 


1 


47 


1 


97 


1 


47 


1 


21,924 


2 


74 


2 


24,624 


2 


74 


2 


5i 


3 


23,301 


3 


51 


3 


26,001 


3 


78 


4 


28 


4 


78 


4 


28 


4 


22,005 


5 


55 


5 


24,705 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


50 


7 


23,409 


7 


59 


7 


26,109 


7 


86 


8 


36 


8 


86 


8 


36 


8 


22,113 


9 


63 


9 


24,813 


9 


63 


9 


40 


820 


90 


870 


40 


920 


90 


970 


67 


1 


23,517 


1 


67 


1 


26,217 


1 


94 


2 


44 


2 


94 


2 


44 


2 


22,221 


3 


71 


3 


24,921 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


23,625 


5 


75 


5 


26,325 


5 


22,302 


6 


52 


6 


25,002 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


23,706 


8 


56 


8 


26,406 


8 


83 


9 


33 


9 


83 


9 


33 


9 


22,410 


. 830 


60 


880 


25,110 


930 


60 


980 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


23,814 


2 


64 


2 


26,514 


2 


9i 


3 


41 


3 


9i 


3 


41 


3 


22,518 


4 


68 


4 


25,218 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


23,922 


6 


72 


6 


26,622 


6 


99 


7 


49 


7 


99 


7 


49 


7 


22,626 


8 


76 


8 


25,326 


8 


76 


8 


53 


9 


24,003 


9 


53 


9 


26,703 


9 


80 


840 


30 


890 


80 


940 


30 


990 


22,707 


1 


57 


1 


25,407 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


24,111 


3 


61 


3 


26,811 


3 


88 


4 


38 


4 


88 


4 


38 


4 


22,815 


5 


65 


5 


25,515 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


24,219 


7 


69 


7 


26,919 


7 


96 


8 


46 


8 


96 


8 


46 


8 


22,923 


9 


73 


9 


25,623 


9 


73 


9 


50 


850 


24,300 


900 


50 


95o 


27,000 


1000 



CUBIC FEET AND CUBIC YARDS 
Table 36 — continued 



235 



27,000-28,350 


28,350-29,700 


29,700- 


31,050 


31,050-32,400 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


27,027 


IOOI 


77 


1051 


29,727 


IIOI 


77 


1151 


54 


2 


28,404 


2 


54 


2 


31,104 


2 


81 


3 


3i 


3 


81 


3 


3i 


3 


27,108 


4 


58 


4 


29,808 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


28,512 


6 


62 


6 


31,212 


6 


89 


7 


39 


7 


89 


7 


39 


' 7 


27,216 


8 


66 


8 


29,916 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


IOIO 


28,620 


1060 


70 


IIIO 


31,320 


1 1 60 


97 


1 


47 


1 


97 


1 


47 


1 


27,324 


2 


74 


2 


30,024 


2 


74 


2 


5i 


3 


28,701 


3 


5i 


3 


31,401 


3 


78 


4 


28 


4 


78 


4 


28 


4 


27,405 


5 


55 


5 


30,105 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


28,809 


7 


59 


7 


31,509 


7 


86 


8 


36 


8 


86 


8 


36 


8 


27,513 


9 


63 


9 


30,213 


9 


63 


9 


40 


1020 


90 


1070 


40 


1120 


90 


1170 


67 


1 


28,917 


1 


67 


1 


31,617 


X 


94 


2 


44 


4 


94 


2 


44 


2 


27,621 


3 


71 


3 


30,321 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


29,025 


5 


75 


5 


31,725 


5 


27,702 


6 


52 


6 


30,402 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


29,106 


8 


56 


8 


31,806 


8 


83 


9 


33 


9 


83 


9 


33 


9 


27,810 


1030 


60 


1080 


30,510 


1130 


60 


1180 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


29,214 


2 


64 


2 


31,914 


2 


9i 


3 


4i 


3 


9i 


3 


4i 


3 


27,918 


4 


68 


4 


30,618 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


29,322 


6 


72 


6 


32,022 


6 


99 


7 


49 


7 


99 


7 


49 


7 


28,026 


8 


76 


8 


30,726 


8 


76 


8 


53 


9 


29,403 


9 


53 


9 


32,103 


9 


80 


1040 


30 


1090 


80 


1 140 


30 


1 190 


28,107 


1 


57 


1 


30,807 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


29,5H 


3 


61 


3 


32,211 


3 


88 


4 


38 


4 


88 


4 


38 


4 


28.215 


5 


65 


5 


30,915 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


29,619 


7 


69 


7 


32,319 


7 


96 


8 


46 


8 


96 


8 


46 


8 


28,323 


9 


73 


9 


31,023 


9 


73 


9 


50 


1050 


29,700 


1 100 


50 


1150 


32,400 


1200 



236 



OFFICE PRACTICE 
Table 36 — continued 



32,400-33,750 


33,75o- 


35,ioo 


35,ioo- 


36,450 


36,450-37,800 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


32,427 


1201 


77 


1251 


35,127 


1301 


77 


I35i 


54 


2 


33,804 


2 


54 


2 


36,504 


2 


81 


3 


3i 


3 


81 


3 


3i 


3 


32,508 


4 


58 


4 


35,2o8 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


33,912 


6 


62 


6 


36,612 


6 


• 89 


7 


39 


7 


89 


7 


39 


7 


32,616 


8 


66 


8 


35,3i6 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


1210 


34,020 


1260 


70 


1310 


36,720 


1360 


97 


1 


47 


1 


97 


1 


47 


1 


32,724 


2 


74 


2 


35,424 


2 


74 


2 


51 


3 


34,ioi 


3 


5i 


3 


36,801 


3 


78 


4 


28 


4 


78 


4 


28 


4 


32,805 


5 


55 


5 


35,505 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


34,209 


7 


59 


7 


36,909 


7 


86 


8 


36 


8 


86 


8 


36 


8 


32,913 


9 


63 


9 


35,6i3 


9 


63 


9 


40 


1220 


90 


1270 


40 


1320 


90 


1370 


67 


1 


34,317 


1 


67 


1 


37,oi7 


1 


94 


2 


44 


2 


94 


2 


44 


2 


33,021 


3 


7i 


3 


35,721 


3 


7i 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


34.425 


5 


75 


5 


37,125 


5 


33, 102 


6 


52 


6 


35,8o2 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


34,5o6 


8 


56 


8 


37,2o6 


8 


83 


9 


33 


9 


83 


9 


33 


9 


33,2io 


1230 


60 


1280 


35,9io 


1330 


60 


1380 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


34,6i4 


2 


64 


2 


37,314 


2 


9i 


3 


41 


3 


9i 


3 


4i 


3 


33,3i8 


4 


68 


4 


36,018 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


34,722 


6 


72 


6 


37,422 


6 


99 


7 


49 


7 


99 


7 


49 


7 


33,426 


8 


76 


8 


36,126 


8 


76 


8 


53 


9 


34,803 


9 


53 


9 


37,503 


9 


80 


1240 


30 


1290 


80 


1340 


30 


1390 


33,507 


1 


57 


1 


36,207 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


34,9H 


3 


61 


3 


37,6u 


3 


88 


4 i 


38 


4 


88 


4 


38 


4 


33,6i5 


5 


65 


5 


36,315 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


35-OI9 


7 


69 


7 


37,719 


7 


96 


8 


46 


8 


96 


8 


46 


8 


33,723 


9 


73 


9 


36,423 


9 


73 


9 


50 


1250 


35,ioo 


1300 


50 


1350 


37,8oo 


1400 

1 



CUBIC FEET AND CUBIC YARDS 

Table 36 — continued 



237 



37,800-39,150 


39,150-40,500 


40,500-41,850 


41,850-43,200 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


37,827 


1401 


77 


1451 


40,527 


1 501 


77 


I55i 


54 


2 


39,204 


2 


54 


2 


41,904 


2 


81 


3 


3i 


3 


81 


3 


3i 


3 


37,9o8 


4 


58 


4 


40,608 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


39,312 


6 


62 


6 


42,012 


6 


89 


7 


39 


7 


89 


7 


39 


7 


38,016 


8 


66 


8 


40,716 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


1410 


39,420 


1460 


7o 


1510 


42,120 


1560 


97 


1 


47 


1 


97 


1 


47 


1 


38,124 


2 


74 


2 


40,824 


2 


74 


2 


51 


3 


39,5oi 


3 


51 


3 


42,201 


3 


78 


4 


28 


4 


78 


4 


28 


4 


38,205 


5 


55 


5 


40,905 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


39,609 


7 


59 


7 


42,309 


7 


86 


8 


36 


8 


86 


8 


36 


8 


38,313 


9 


. 63 


9 


41,013 


9 


63 


9 


40 


1420 


90 


1470 


40 


1520 


90 


I570 


67 


1 


39,717 


1 


67 


1 


42,417 


1 


94 


2 


44 


2 


94 


2 


44 


2 


38,421 


3 


7i 


3 


41,121 


3 


7i 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


39,825 


5 


75 


5 


42,525 


5 


38,502 


6 


52 


6 


41,202 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


39,906 


8 


56 


8 


42,606 


8 


S3 


9 


33 


9 


83 


9 


33 


9 


38,610 


1430 


60 


1480 


4i,3io 


1530 


60 


1580 


37 


1 


87 


1 


37 


1 


87 


1 


64 


2 


40,014 


2 


64 


2 


42,714 


2 


9i 


3 


41 


3 


9i 


3 


41 


3 


38,718 


4 


68 


4 


41,418 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


40,122 


6 


72 


6 


42,822 


6 


99 


7 


49 


7 


99 


7 


49 


7 


38,826 


8 


76 


8 


41,526 


8 


76 


8 


53 


9 


40,203 


9 


53 


9 


42,903 


9 


80 


1440 


30 


1490 


80 


I540 


30 


I590 


38,907 


1 


57 


1 


41,607 


1 


57 


1 


34 


2 


84 


2 


34 


2 


84 ' 


2 


61 


3 


40,311 


3 


61 


3 


43,on 


3 


88 


4 


38 


4 


88 


4 


38 


4 


39,oi5 


5 


65 


5 


4i,7i5 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


40,419 


7 


69 


7 


43,H9 


7 


96 


8 


46 


8 


96 


8 


46 


8 


39,123 


9 


73 


9 


41,823 


9 


73 


9 


50 


1450 


40,500 


1500 


50 


I550 


43,200 


1600 



2 3 8 



OFFICE PRACTICE 



Table 37. New York State Department of Highways. 

Earthwork Computation Tables 

Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


D'uble 
i Areas 


0.0 


O.I 


O.I 


O.I 


O.I 


0.1 


O.I 


0.2 


0.2 


0.2 


j 0.2 


0.2 


0.3 j 1 .0 


0.0 


O.I 


O.I 


O.I 


O.I 


0.2 


0.2 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 2 


O.I 


O.I 


O.I 


O.I 


0.2 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.3 


0.4I 4 


O.I 


O.I 


O.I 


O.I 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 6 


O.I 


O.I 


O.I 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 


0.5 8 


O.I 


O.I 


O.I 


0.2 


0.2 


0.3 


0.3 


o.3 


0.4 


0.4 


0.4 


0.5 


0.5 


2.0 


O.I 


O.I 


0.2 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.4 


0.5 


0.5 


0.6 


2 


O.I 


O.I 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.4 


0.5 


0.5 


0.6 


0.6 


1 4 


O.I 


O.I 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.5 


0.5 


0.6 


0.6 


0.7 


6 


O.I 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.5 


0.5 


0.6 


0.6 


0.7 


0.7 


8 


O.I 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.5 


0.6 


0.6 


0.7 


0.7 


0.8 


3-0 


O.I 


0.2 


0.2 


0.3 


0.4 


0.4 


0.5 


0.5 


0.6 


0.7 


0.7 


0.8 


0.8 


2 


O.I 


0.2 


0.3 


0.3 


0.4 


0.4 


0.5 


0.6 


0.6 


0.7 


0.8 


0.8 


0.9 


4 


O.I 


0.2 


0.3 


0.3 


0.4 


0.5 


0.5 


0.6 


0.7 


0.7 


0.8 


0.9 


0.9 


6 


O.I 


0.2 


0.3 


0.4 


0.4 


0.5 


0.6 


0.6 


0.7 


0.8 


0.8 


0.9 


1.0 


8 


O.I 


0.2 


0.3 


0.4 


0.4 


0.5 


0.6 


0.7 


0.7 


0.8 


0.9 


1.0 


1.0 


4.0 


0.2 


0.2 


0.3 


0.4 


0.5 


0.5 


0.6 


0.7 


0.8 


0.9 


0.9 


1.0 


1.1 


2 


0.2 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.7 


0.8 


0.9 


1.0 


I.I 


1.1 


4 


0.2 


0.3 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


0.9 


1.0 


I.I 


1.2 


6 


0.2 


0.3 


0.4 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


1.2 


8 


0.2 


0.3 


0.4 


0.5 


0.6 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


i-3 


5-o 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


1-3 


i-3 


2 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


1-3 


1.4 


4 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


1-3 


1-5 


6 


0.2 


0.3 


0.4 


0.5 


0.6 


0.8 


0.9 


1.0 


I.I 


1.2 


1-3 


1.4 


i-5 


8 


0.2 


0.3 


0.4 


0.6 


0.7 


0.8 


0.9 


1.0 


I.I 


1.2 


i-3 


1.4 


1.6 


6.0 


0.2 


0.3 


0.5 


0.6 


0.7 


0.8 


0.9 


1.1 


I.I 


1-3 


1.4 


i-5 


1.6 


2 


0.2 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.1 


1.2 


1-3 


1.4 


i-5 


1-7 


4 


0.2 


0.4 


0.5 


0.6 


0.7 


0.9 


1.0 


1.1 


1.2 


1.3 


1-5 


1.6 


1-7 


6 


0.3 


0.4 


0.5 


0.6 


0.7 


0.9 


1.0 


1.1 


1-3 


1.4 


i-5 


1.6 


1.8 


8 


0.3 


0.4 


0.5 


0.6 


0.8 


0.9 


1.0 


1.2 


1-3 


1.4 


1.6 


i-7 


1.8 


7.0 


0.3 


0.4 


0.5 


0.7 


0.8 


0.9 


I.I 


1.2 


1-3 


1-5 


1.6 


1-7 


1.9 


2 


0.3 


0.4 


0.5 


0.7 


0.8 


1.0 


I.I 


1.2 


1.4 


1-5 


1.6 


1.8 


1.9 


4 


0.3 


0.4 


0.6 


0.7 


0.8 


1.0 


I.I 


i-3 


1.4 


i-5 


1-7 


1.8 


2.0 


6 


0.3 


0.4 


0.6 


0.7 


0.9 


1.0 


1.2 


i-3 


1.4 


1.6 


i-7 


1.9 


2.0 


8 


0.3 


0.4 


0.6 


0.7 


0.9 


1.0 


1.2 


1-3 


1-5 


1.6 


1.8 


1.9 


2.1 


8.0 


0.3 


0.5 


0.6 


0.8 


0.9 


I.I 


1.2 


1.4 


1-5 


i-7 


1.8 


2.0 


2.1 


2 


0.3 


0.5 


0.6 


0.8 


0.9 


I.I 


1.2 


1.4 


1.6 


1-7 


1.9 


2.0 


2.2 


4 


0.3 


0.5 


0.6 


0.8 


1.0 


I.I 


1-3 


1.4 


1.6 


1-7 


1.9 


2.1 


, 2.2 


6 


0.3 


0.5 


0.7 


0.8 


1.0 


I.I 


1-3 


i-5 


1.6 


1.8 


2.0 


2.1 


2-3 


8 


0.3 


0.5 


0.7 


0.9 


1.0 


1.2 


i-3 


1-5 


i-7 


1.8 


2.0 


2.2 


2.3 


9.0 


0.3 


0.5 


0.7 


0.9 


1.0 


1.2 


1.4 


1-5 


i-7 


1.9 


2.0 


2.2 


2.4 


2 


0.3 


0.5 


0.7 


0.9 


1.0 


1.2 


1.4 


1.6 


i-7 


1.9 


2.1 


2-3 


2.4 


4 


0.4 


0-5 


0.7 


0.9 


I.I 


1.2 


1.4 


1.6 


1.8 


2.0 


2.1 


2-3 


2-5 


6 


0.4 


0.5 


0.7 


0.9 


I.I 


1-3 


1.5 


1.6 


1.8 


2.0 


2.2 


2.4 


2-5 


8 


0.4 


0.6 


0.7 


0.9 


I.I 


1-3 


1.5 


1-7 


1.9 


2.0 


2.2 


2.4 


2.6 


10.0 


0.4 


0.6 


0.8 


1.0 


1.2 


1.4 


1.6 


1.8 


1.9 


2.1 


2-3 


2-5 


2.7 


5 


0.4 


0.6 


0.8 


1.0 


1.2 


1.4 


1.6 


1.8 


2.0 


2.2 


2.4 


2.6 


2.9 


11. 


0.4 


0.6 


0.9 


I.I 


1.3 


1-5 


1-7 


1.9 


2.1 


2.3 


2-5 


2.8 


3-o 


5 


0.4 


0.7 


0.9 


I.I 


1-3 


1.6 


1.8 


2.0 


2.2 


2.4 


2.7 


2.9 


3-i 


12.0 


0.5 


0.7 


0.9 


1.2 


1.4 


1.6 


1.9 


2.1 


2-3 


2-5 


2.8 


3-o 


3-2 


5 


0.5 


0.7 


1.0 


1.2 


i-5 


i-7 


2.0 


2.2 


2.4 


2.6 


2.9 


3.1 


3-4 


13.0 


0.5 


0.7 


1.0 


i-3 


i-5 


1.8 


2.0 


23 


2-5 


2.7 


3-0 


3-3 


3-5 


3 


0.5 


0.8 


1.0 


1-3 


1.6 


1.8 


2.1 


2-3 


2.6, 


2.8 


3-i 


3-4 


3-6 


14.0 



EARTHWORK COMPUTATION TABLES 



2 39 



Table 37. New York State Department of Highways. 

Earthwork Computation Tables. — continued 

Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 





























D'uble 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


Areas 


0.3 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 


0.4 


0.4 


0.4 


0, 


0.5 


0.5 


,0 


0.3 


0.4 


0.4 


0.4 


0.4 


0.4 


0.5 


0.5 


0.5 


0.5 


0.6 


0.6 


0.6 


2 


0.4 


0.4 


0.4 


0.5 


0.5 


0.5 


0.5 


0.6 


0.6 


0.6 


0.6 


0.7 


0.7 


4 


0.4 


0.5 


0.5 


0.5 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.8 


0.8 


6 


0.5 


0.5 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.8 


0.9 


0.9 


8 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


2.0 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


1.1 


1.1 


2 


0.7 


0.7 


0.8 


0.8 


0.8 


0.9 


0.9 


1.0 


1.0 


1.1 


1.1 


1.2 


1.2 


4 


0.7 


0.8 


0.8 


0.9 


0.9 


1.0 


1.0 


1.1 


1.1 


1.2 


1.2 


1-3 


1-3 


6 


0.8 


0.8 


0.9 


1.0 


1.0 


1.0 


1.1 


1.1 


1.2 


1.2 


i-3 


1.4 


1.4 


8 


0.8 


0.9 


0.9 


1.0 


1.1 


1.1 


1.2 


1.2 


i-3 


1-3 


1.4 


1.4 


1-5 


3-o 


0.9 


0.9 


1.0 


1.1 


1.1 


1.2 


1.2 


1-3 


1.4 


1.4 


1-5 


i-5 


1.6 


2 


0.9 


•i.o 


1.1 


1.1 


1.2 


1-3 


i-3 


1.4 


1-4 


1-5 


1.6 


1.6 


i-7 


4 


1.0 


1.1 


1.1 


1.2 


1-3 


i-3 


1.4 


i-5 


1-5 


1.6 


i-7 


i-7 


1.8 


6 


I.I 


1.1 


1.2 


1-3 


i-3 


1.4 


i-5 


i-5 


1.6 


i-7 


1.8 


1.8 


1.9 


8 


I.I 


1.2 


1-3 


1-3 


1.4 


1-5 


1.6 


1.6 


1-7 


1.8 


1.9 


1.9 


2.0 


4.0 


1.2 


1.2 


i-3 


1.4 


1-5 


1.6 


1.6 


1-7 


1.8 


1.9 


1.9 


2.0 


2.1 


2 


1.2 


1-3 


1.4 


1-5 


i-5 


1.6 


i-7 


1.8 


1.9 


2.0 


2.0 


2.1 


2.2 


4 


1-3 


1.4 


1.4 


1. 5 


1.6 


1-7 


1.8 


1.9 


2.0 


2.0 


2.1 


2.2 


2-3 


6 


1-3 


1.4 


i-5 


1.6 


i-7 


1.8 


1.8 


2.0 


20 


2.1 


2.2 


2-3 


2.4 


8 


1.4 


i-5 


1.6 


1-7 


1.8 


1.9 


1.9 


2.0 


2.1 


2.2 


2-3 


2.4 


2-5 


5.o 


1.4 


1-5 


1.6 


i-7 


1.8 


1.9 


2.0 


2.1 


2.2 


2-3 


2.4 


2-5 


2.6 


2 


1. 5 


1.6 


1-7 


1.8 


1.9 


2.0 


2.1 


2.2 


2-3 


2.4 


2-5 


2.6 


2-7 


4 


1.6 


i-7 


1.8 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2-5 


2.6 


2.7 


2.8 


6 


1.6 


i-7 


1.8 


2.0 


2.0 


2.2 


2.3 


2.4 


2-5 


2.6 


2-7 


2.8 


2.9 


8 


1.7 


1.8 


1.9 


2.0 


2.1 


2.2 


2-3 


2.4 


2.6 


2-7 


2.8 


2.9 


3-o 


6.0 


1-7 


1.8 


1.9 


2.1 


2.2 


2-3 


2.4 


2-5 


2.6 


2.8 


2.9 


3.o 


3-i 


2 


1.8 


1.9 


2.0 


2.1 


2.2 


2.4 


2-5 


2.6 


2-7 


2.8 


3-o 


3-i 


3-2 


4 


1.8 


2.0 


2.1 


2.2 


• 2.3 


2-5 


2.6 


2.7 


2.8 


2.9 


3-1 


3-2 


3-3 


6 


i.g 


2.0 


2.1 


2.3 


2.4 


2-5 


2.6 


2.8 


2.9 


3-o 


3-2 


3-3 


3-4 


8 


1.9 


2.1 


2.2 


2.3 


2-5 


2.6 


2.7 


2.9 


3-o 


3-i 


3-2 


3-4 


3-5 


7.0 


2.0 


2.1 


2.3 


2.4 


2-5 


2.7 


2.8 


2.9 


3-i 


3-2 


3-3 


3-5 


3-6 


2 


2.1 


2.2 


2.3 


2-5 


2.6 


2.7 


2.9 


3-o 


3-i 


3-3 


3-4 


3-6 


3-7 


4 


2.1 


2.3 


2.4 


2.5 


2-7 


2.8 


3-o 


3-i 


3-2 


3-4 


3-5 


3-7 


3-8 


6 


2.2 


2-3 


2.5 


2.6 


2.7 


2.9 


3-o 


3-2 


3-3 


3-5 


3-6 


3-8 


3-9 


8 


2.2 


2.4 


2.5 


2.7 


2.8 


3.o 


3-1 


3-3 


3-4 


3-6 


3-7 


3-9 


4.0 


8.0 


2.3 


2.4 


2.6 


2.7 


2.9 


3.o 


3-2 


3-3 


3-5 


3-6 


3-8 


4.0 


4.1 


2 


2.3 


2-5 


2.6 


2.8 


2.9 


3-i 


3-3 


3-4 


3-6 


3-7 


3-9 


4.1 


4.2 


4 


2.4 


2-5 


2.7 


2.9 


3-o 


3-2 


3-3 


3-5 


3-7 


3-8 


4.0 


4.1 


4-3 


6 


2.4 


2.6 


2.8 


2.9 


3-1 


3-3 


3-4 


3-6 


3-8 


3-9 


4.1 


4-- 


4.4 


8 


2.5 


2.7 


2.8 


3-o 


3-2 


3-3 


3-5 


3-7 


3-8 


4.0 


4.2 


4-; 


4-5 


9.0 


2.6 


2.7 


2.9 


3-i 


3-2 


3-4 


3-6 


3-8 


3-9 


4.1 


4-3 


4-4 


4-6 


2 


2.6 


2.8 


3-0 


3-i 


3-3 


3-5 


3-7 


3-8 


4.0 


4.2 


4.4 


4-5 


4-7 


4 


2.7 


2.8 


3-0 


3-2 


3-4 


3-6 


3-7 


3-9 


4.1 


4-3 


4-5 


4.6 


4.8 


6 


2.7 


2.9 


3-1 


3-3 


3-4 


3-6 


3-8 


4.0 


4.2 


4-4 


4-5 


4-7 


4-9 


8 


2.8 


3-o 


3-1 


3-3 


3-5 


3-7 


3-9 


4.1 


4.2 


4.4 


4.6 


4.8 


5.o 


100 


2.9 


3-i 


3-3 


3-5 


3-7 


3-9 


4.1 


4-3 


4-5 


4.6 


4.9 


5-o 


5-3 


5 


3.1 


3-3 


3-5 


3-7 


3-9 


4.1 


4-3 


4-5 


4-7 


4-9 


5-1 


5-3 


5-5 


11.0 


3-2 


3-4 


3-6 


3-8 


4.0 


4-3 


4-5 


4-7 


4.9 


5-1 


5-3 


5-5 


5-7 


5 


3-3 


3.6 


3.8 


4.0 


4.2 


4-5 


4-7 


4.9 


5-i 


5-3 


5-5 


5-8 


6.0 


12.0 


3-5 


3-7 


3-9 


4.2 


4.4 


4.6 


4.9 


5-i 


5-3 


5-5 


5.8 


6.0 


6.2 


5 


3-6 


3-8 


4.1 


4-3 


4.6 


4.8 


5.o 


5-3 


5-5 


5-8 


6.0 


6.3 


6.5 


13.0 


3-7 


4.0 


4.2 


4-5 


4.8 


5-o 


5-2 


5-5 


5-8 


6.0 


63 


6.5 


6.7 


5 


3- 9j 


4.1 


4.4 


4-7 


4.9 


5-2 


5-4 


5-7 


6.0 


6.2 


6-5 


6.7 


7.o 


14.0 



240 



OFFICE PRACTICE 



Table 37. — continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



28 


29 


30 


31 


32 


33 


34 


35 


36 


37 

0.7 


38 


39 


40 


D'uble 
; Areas 


0.5 


0.5 


0.6 


0.6 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.7 


1.0 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.8 


0.8 


0.8 


0.8 


0.9 


0.9 


0.9 


2 


0.7 


0.8 


0.8 


0.8 


0.8 


0.9 


0.9 


0.9 


0.9 


1.0 


1.0 


1.0 


1.0 


4 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


1.0 


1.0 


1.1 


1.1 


1.1 


1.2 


1.2 


6 


0.9 


1.0 


1.0 


1.0 


1.1 


1.1 


1.2 


" 


1.2 


1.2 


i-3 


1-3 


1-3 


8 


1.0 


1.1 


1.1 


1.2 


1.2 


1.2 


1-3 


1-3 


1-3 


i-4 


1.4 


i-5 


1-5 


2.0 


I.I 


1.2 


1.2 


.1.3 


i-3 


1-3 


1.4 


1.4 


1-5 


i-5 


1.6 


1.6 


1.6 


2 


1.2 


1-3 


1-3 


1.4 


1.4 


1-5 


1.5 


1.6 


1.6 


i-7 


1-7 


1-7 


1.8 


4 


1.4 


1.4 


1.4 


i-5 


i-5 


1.6 


1.6 


i-7 


i-7 


1.8 


1.8 


1.9 


1.9 


6 


1-5 


.1-5 


1.6 


1.6 


1-7 


i-7 


1.8 


1.8 


1.9 


1.9 


2.0 


2.0 


2.1 


8 


1.6 


1.6 


1-7 


1-7 


1.8 


1.8 


1.9 


1.9 


2.0 


2.1 


2.1 


2.2 


2.2 


3-o 


i-7 


1-7 


1.8 


1.8 


1.9 


2.0 


2.0 


2.1 


2.1 


2.2 


2-3 


2-3 


2.4 


2 


1.8 


1.8 


1.9 


2.0 


2.0 


2.1 


2.1 


2.2 


2.3 


2.3 


2.4 


2.5 


2-5 


4 


1.9 


1.9 


2.0 


2.1 


2.1 


2.2 


2-3 


2-3 


2.4 


2-5 


2.5 


2.6 


2.7 


6 


2.0 


2.0 


2.1 


2.2 


2-3 


2.3 


2.4 


2-5 


2-5 


2.6 


2.7 


2.8 


2.8 


8 


2.1 


2.2 


2.2 


2.3 


2.4 


2.5 


2-5 


2.6 


2.7 


2.7 


2.8 


2.9 


3.o 


4.0 


2.2 


2-3 


2-3 


2.4 


2-5 


2.6 


2.6 


2.7 


2.8 


2.9 


3.o 


3-o 


3-1 


2 


2.3 


2.4 


2.4 


2-5 


2.6 


2.7 


2.8 


2.9 


2.9 


3-o 


3-1 


3-2 


3-3 


4 


2.4 


2-5 


2.6 


2.6 


2.7 


2.8 


2.9 


3-o 


3-i 


3-2 


3-2 


3-3 


3-4 


6 


2.5 


2.6 


2.7 


2.8 


2.8 


2.9 


3-o 


3-1 


3-2 


3-3 


3-4 


3-5 


3.6 


8 


2.6 


2.7 


2.8 


.2.9 


3-o 


3-1 


3-i 


3-2 


3-3 


3-4 


3-5 


3-6 


3-7 


5.o 


2.7 


2.8 


2.9 


3-o 


3-i 


3-2 


3-3 


3-4 


3-5 


3-6 


H 


3-8 


3-9 


2 


2.8 


2.9 


3-o 


3-i 


3-2 


3-3 


3.4 


3-5 


3-6 


3 i 


3-8 


3-9 


4.0 


4 


2.9 


3-o 


3-1 


3-2 


3-3 


3-4 


3-5 


3-6 


3-7 


3-8 


3-9 


4.1 


4.2 


6 


3-o 


3-i 


3-2 


3-3 


3-4 


3-6 


3-7 


3-8 


3-9 


4.0 


4.1 


4.2 


4-3 


8 


3-1 


3.2 


3-3 


3-5 


3-6 


H 


3-8 


3-9 


4.0 


4.1 


4.2 


4-3 


4-5 


6.0 


3-2 


3.3 


3.5 


3.6 


3-7 


3-8 


3-9 


4.0 


4.1 


4-3 


4-4 


4-5 


4-6 


2 


3-3 


3-4 


3-6 


3-7 


3-8 


3-9 


4.0 


4.2 


4-3 


4.4 


4-5 


4.6 


4-7 


4 


3-4 


3.5 


3.7 


3-8 


3-9 


4.0 


4.2 


4-3 


4.4 


4-5 


4-7 


4.8 


4.9 


6 


3-5 


3-7 


3-8 


3-9 


4.0 


4.2 


4-3 


4.4 


4-5 


4.7. 


4.8 


4-9 


5.o 


8 


3-6 


3-8 


3-9 


4.0 


4.2 


4-3 


4.4 


4-5 


4-7 


4.8 


4.9 


5-i 


5-2 


7.0 


3-7 


3-9 


4.0 


4.1 


4-3 


4-4 


4-5 


4-7 


4.8 


4.9 


5-i 


5-2 


5-3 


2 


3-8 


4.0 


4.1 


4-3 


4.4 


4-5 


4-7 


4.8 


4.9 


5-i 


5-2 


5-4 


5-5 


4 


3-9 


4.1 


4.2 


4.4 


4-5 


4-7 


4.8 


4.9 


5-i 


5-2 


5-4 


5-5 


5-6 


6 


4.0 


4.2 


4-3 


4-5 


4.6 


4.8 


4.9 


5-i 


5-2 


5-4 


5-5 


5-6 


5-8 


8 


4.2 


4-3 


4.4 


4.6 


4-7 


4.9 


5-o 


5-2 


5-3 


5-5 


5-6 


5.8 


5-9 


8.0 


4-3 


4.4 


4.6 


4 i 


4.9 


5.o 


5-2 


5-3 


5-5 


5-6 


5.8 


5-9 


6.1 


2 


4.4 


4-5 


H 


4.8 


5-o 


5-i 


5-3 


5-5 


5-6 


5-8 


5-9 


6.1 


6.2 


4 


4-5 


4.6 


4.8 


4.9 


5-i 


5-3 


5-4 


5-6 


5-7 


5-9 


6.1 


6.2 


6.4 


6 


4.6 


4-7 


4.9 


M 


5-2 


5-4 


5-5 


5-7 


5-9 


6.0 


6.2 


6.4 


6.5 


8 


4-7 


4.8 


5.0 


5-* 


5-3 


5-5 


5-7 


5-8 


6.0 


6.2 


6.3 


6.5 


6.7 


9.0 


4.8 


4.9 


5-i 


5-3 


5-5 


5-6 


5-8 


6.0 


6.1 


6-3 


6-5 


.6.7 


6.8 


2 


4.9 


5-i 


5-2 


5-4 


5-6 


5-8 


5-9 


6.1 


6.3 


6-5 


6.6 


6.8 


7.o 


4 


5-o 


5-2 


5-3 


5-5 


5-7 


5-9 


6.1 


6.2 


6.4 


6.6 


6.8 


6.9 


7-i 


6 


5-i 


5-3 


5o 


5-6 


5-8 


6.0 


6.2 


6.3 


6-5 


6.7 


6.9 


7-i 


7-3 


8 


5-2 


5-4 


5.6 


5.8 


5-9 


6.1 


6.3 


6.5 


6.7 


6.9 


7.0 


7.2 


7-4 


10.0 


5-4 


5-6 


5-8 


6.0 


6.2 


6.4 


6.6 


6.8 


7.0 


7-2 


7-4 


7.6 


7.8 


5 


5-7 


5-9 


6.1 


6.3 


6-5 


6.7 


6.9 


7-1 


7-3 


7-5 


7.8 


7.9 


8.2 


11.0 


6.0 


6.2 


6.4 


6.6 


6.8 


7.0 


7.2 


7-5 


7-7 


7-9 


8.1 


S.3 


8-5 


5 . 


6.2 


6.4 


6.7 


7.0 


7-i 


7-3 


7-6 


7-8 


8.0 


8.2 


8.5 


8.7 


8.9 


12.0 


6.5 


6.7 


7.0 


7.2 


7-4 


7-7 


7-9 


8.1 


8-3 


8.6 


8.8 


9.0 


J 


5 


6.7 


7.0 


7.2 


7-5 


7-7 


8.0 


8.2 


8.4 


8-7 


8.9 


9.2 


9.4 


9.6 


13.0 


7.0 


7-3 


7-5 


7-8 


8.0 


8-3 


8.5 


8.8 


9.0 


93 


9-5 


9.8 


10.0 


5 


7.2 


7-5 


7-8 


8.0 


8.3 


8.6 


8.8 


9.1 


9-3 


9.6 


9.8 


IO.I 


10.4 


14.0 

1 



EARTHWORK COMPUTATION TABLES 



241 



Table 37. — continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



41 


42 


43 


44 


45 


46 


47 


48 


49 


5o 


75 


100 




D'uble 
Areas 


0.8 


0.8 


0.8 


0.8 


0.8 


0.9 


0.9 


0.9 


0.9 


0.9 


1.4 


1.9 




1.0 


0.9 


0.9 


1.0 


1.0 


1.0 


1.0 


1.0 


1.1 


i.i 


i.i 


1.6 


2.2 




2 


I.I 


1. 1 


1.1 


1. 1 


1.2 


1.2 


1.2 


1.2 


1-3 


1-3 


1.9 


2.6 




4 


1.2 


1.2 


1-3 


1-3 


1-3 


1.4 


1.4 


1.4 


1-5 


i-5 


2.2 


3.0 




6 


1.4 


1.4 


1.4 


1-5 


1-5 


i-5 


1.6 


1.6 


1.6 


i-7 


2-5 


3-3 




8 


1. 5 


1.6 


1.6 


1.6 


1-7 


1-7 


1-7 


1.8 


1.8 


1.8 


2.8 


3-7 




2.0 


1.7 


1-7 


1.8 


1.8 


1.8 


1.9 


1.9 


2.0 


2.0 


2.0 


3-1 


4.1 




2 


1.8 


1.9 


1.9 


2.0 


2.0 


2.0 


2.1 


2.1 


2.2 


2.2 


3-3 


4.4 




4 


2.0 


2.0 


2.1 


2.1 


2.2 


2.2 


2.3 


2-3 


2.4 


2.4 


3-6 


4-8 




6 


2.1 


2.2 


2.2 


2-3 


2-3 


2.4 


2.4 


2-5 


2-5 


2.6 


3-9 


5-2 




8 


2.3 


2.3 


2.4 


2.4 


2-5 


2.6 


2.6 


2-7 


2-7 


2.8 


4.2 


5.6 




3-o 


2.4 


2-5 


2.6 


2.6 


2.7 


2.7 


2.8 


2.9 


2.9 


3-0 


4.4 


59 




2 


2.6 


2.6 


2.7 


2.8 


2.8 


2.9 


3-o 


3-0 


3-1 


3-2 


4-7 


6-3 




4 


2.7 


2.8 


2.9 


2.9 


3-0 


3-1 


3-1 


3-2 


3-3 


3-3 


5-0 


6.7 




6 


2.9 


3-0 


3-o 


3-i 


3-2 


3-^ 


3-3 


3-4 


3.5 


3-5 


5-3 


7.0 




8 


3-o 


3-1 


3-2 


3-3 


3-3 


3-4 


3-5 


3-6 


3-6 


3-7 


5.6 


7-4 




4.0 


3-2 


3-3 


3-4 


3-4 


3-5 


3-6 


3-7 


3-7 


3-8 


3-9 


5-9 


7-9 




2 


3-3 


3-4 


3-5 


3-6 


3-7 


3-S 


3-8 


3-9 


4.0 


4.1 


6.1 


8.2 




4 


3-5 


3-6 


3-7 


3-S 


3.8 


3-9 


4.0 


4.1 


4.2 


4-3 


6.4 


8-5 




6 


3-6 


3-7 


3-8 


3-9 


4.0 


4.1 


4.2 


4-3 


4.4 


4-5 


6.7 


8.9 




8 


3-8 


3-9 


4.0 


4.1 


4.2 


4-3 


4.4 


4-5 


4-5 


4.6 


7.0 


9-3 




5-o 


4.0 


4.1 


4.1 


4.2 


4-3 


4.4 


4-5 


4.6 


4.7 


4.8 


7.2 


9-7 




2 


4.1 


4.2 


4-3 


4.4 


4-5 


4.6 


4-7 


4.8 


4.9 


5-0 


7-5 


10.0 




4 


4-3 


4.4 


4-5 


4.6 


4-7 


4.8 


4.9 


5-o 


5-i 


5-2 


7-8 


0.4 




6 


4.4 


4-5 


4.6 


4-7 


4.8 


4.9 


5-o 


5-i 


5-2 


5-4 


8.1 


0.8 




8 


4.6 


4-7 


4.8 


4.9 


5.o 


5-i 


5-2 


5-3 


5-4 


5-6 


8.3 


i.i 




6.0 


4-7 


4.8 


4.9 


5.o 


5-2 


5-3 


5-4 


5-5 


5-6 


5-7 


8.6 


1.5 




2 


4.9 


5.o 


5-i 


5-2 


5-3 


5-5 


5-6 


5-7 


5-8 


5-9 


8.9 


1.8 




4 


5-o 


5-1 


5-2 


5-4 


5-5 


5-6 


5-7 


5-9 


6.0 


6.1 


9.2 


2.2 




6 


5-2 


5-3 


5-4 


5-5 


5-7 


5.8 


5-9 


6.0 


6.2 


6.3 


9-5 


2.6 




8 


5-3 


5-4 


5-6 


5-7 


5-8 


5-9 


6.1 


6.2 


6-3 


6-5 


9-7 


3-o 




7.0 


5-5 


5-6 


5-7 


5-8 


6.0 


6.1 


6-3 


6.4 


6-5 


6-7 


10.0 


3-4 




2 


5-6 


5-7 


5-9 


6.0 


6.2 


6.3 


6.4 


6.6 


6-7 


6.8 


0.3 


3-7 




4 


5-8 


5-9 


6.0 


6.2 


6.3 


6.5 


6.6 


6.7 


6.9 


7.0 


0.6 


4.1 




6 


5-9 


6.1 


6.2 


6.3 


6-5 


6.6 


6.8 


6.9 


7-i 


7.2 


0.8 


4.4 




8 


6.1 


6.2 


6.4 


6-5 


6.7 


6.8 


7.0 


7-1 


7.2 


7-4 


11. 1 


4.8 




8.0 


6.2 


6-3 


6-5 


6.6 


6.8 


7.0 


7-1 


7-3 


7-4 


7.6 


1.4 


5-2 




2 


6.4 


6.5 


6.7 


6.8 


7.0 


7.2 


7-3 


7-5 


7.6 


7-8 


1-7 


5-6 




4 


6-5 


6.7 


6.8 


7.0 


7.2 


7-3 


7-5 


7-7 


7-8 


8.0 


2.0 


6.0 




6 


6.7 


6.9 


7.0 


7.2 


7-3 


7-5 


7.7 


7-8 


8.0 


8.2 


2.2 


6.3 




8 


6.8 


7.0 


7.2 


7-3 


7-5 


7-7 


7-8 


8.0 


8.2 


8.3 


12.5 


6.6 




9.0 


7.0 


7.2 


7-3 


7-5 


7-7 


7-8 


8.0 


8.2 


8-3 


8-5 


2.8 


7.0 




2 


7-i 


7-3 


7-5 


7-7 


7-8 


8.0 


8.2 


8.4 


8-5 


8.7 


3-1 


7-4 




4 


7-3 


7-5 


7-6 


7-8 


8.0 


8.2 


8-3 


8.5 


8.7 


8.9 


3-3 


7-8 




6 


7-4 


7.6 


7-8 


8.0 


8.2 


8.4 


8.5 


8.7 


8.9 


9.1 


3-6 


8.2 




8 


7-6 


7-8 


8.0 


8.1 


8.3 


8-5 


8.7 


8.9 


9.1 


9-3 


13-9 


8-5 




10.0 


8.0 


8.2 


8.4 


8.6 


8.8 


8.9 


9.1 


9-3 


9-5 


9-7 


4.6 


9-5 




5 


8-3 


8-5 


8.7 


8.9 


9.2 


9.4 


9.6 


9.8 


10.0 


10.2 


5-3 


20.3 




11.0 


8.7 


8.9 


9.1 


9.4 


9.6 


9.8 


10.0 


10.2 


0.4 


0.7 


6.0 


1-3 




5 


9-i 


9-3 


9-5 


9.8 


10. 


10.2 


0.4 


0.7 


0.9 


i.i 


6.7 


2.2 




12.0 


9-5 


9-7 


10.0 


10.2 


10.4 


10.6 


10.8 


11. 1 


11.4 


11,6 


17.4 


23.2 




5 


9.9 


10.1 


0.4 


0.6 


0.8 


1.1 


1-3 


1.6 


1.8 


2.1 


8.0 


4.1 




13.0 


10.3 


0.5 


0.8 


1.0 


1-3 


i-5 


1.8 


2.0 


2.3 


2.5 


8.8 


5-o 




5 


0.6 


0.9 


1.2 


1.4 


1-7 


1.9 


2.2 


2.4 


2.7 


3-o 


9.4 


6.0 




14.0 , 



242 



OFFICE PRACTICE 



Distance Horizontal 



Table 37. — continued 
Sum of Areas Vertical Quantities in Cubic Yards 



2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


*4 ! 


D'uble 
Areas 


0.5 


0.8 


1.1 


i-3 


1.6 


1.9 


2.1 


2.4 


2.7 


3-o 


3-2 


3-5 


3.8 


14-5 


0.6 


0.8 


1.1 


1. 4 


1.7 


2.0 


2.2 


2-5 


2.8 


3-1 


3-3 


3-6 


3-9 


150 


0.6 


0.9 


1.2 


1-5 


i-7 


2.0 


2.3 


2.6 


2.9 


3-2 


3-4 


3-7 


4.0 


5 


0.6 


0.9 


1.2 


i-5 


1.8 


2.1 


2.4 


2.7 


3.0 


3-3 


3-6 


3-8 


4.1 


16.0 


0.6 


0.9 


1.2 


i-5 


1.8 


2. 1 


2.4 


2.7 


3.1 


3-4 


3-7 


4.0 


4-3 

1 


5 


0.6 


0.9 


1-3 


1.6 


1.9 


2.2 


2.5 


2.8 


3-i 


3-5 


3-8 


4.1 


1 
4.4 


17.0 


0.6 


1.0 


1-3 


1.6 


2.0 


2.3 


2.6 


2.9 


3-2 


3.6 


3-9 


4.2 


4-5 


5 


0.7 


1.0 


1-3 


1-7 


2.0 


2.3 


2.7 


3.o 


3-3 


3-7 


4.0 


4-3 


4-7 


18.0 


0.7 


1.0 


1.4 


1.7 


2.1 


2.4 


2.7 


3-i 


3-4 


3-8 


4.1 


4.4 


4-8 


5 


0.7 


1. 1 


1.4 


1.8 


2.1 


2.5 


2.8 


3-2 


3-5 


3-9 


4.2 


4-6 


4-9 


19.0 


0.7 


1. 1 


1.4 


1.8 


2.2 


2.5 


2.9 


3-2 


3-6 


4.0 


4-3 


4-7 


5-o 


5 


0.7 


1. 1 


1. 5 


1.9 


2.2 


2.6 


3-o 


3-3 


3-7 


4.1 


4.4 


4.8 


5-2 


20.0 


0.8 


1.2 


1.6 


2.0 


2.3 


2.7 


3-i 


3-5 


3.9 


4-3 


4-7 


5-1 


5-4 


1 


0.8 


1.2 


1.6 


2.0 


2.4 


2.8 


3-3 


3-7 


4.1 


4-5 


4.9 


5-3 


f' 7 l 


2 


0.9 


1-3 


1-7 


2.1 


2.6 


3-° 


3-4 


3-8 


4-3 


4-7 


5-1 


5-5 


6.0 

I 


3 


0.9 


1-3 


1.8 


2.2 


2.7 


3-1 


3-6 


4.0 


4.4 


4.9 


5-3 


5.8 


6.2 


4 


0.9 


1.4 


1.9 


2-3 


2.8 


3-2 


3-7 


4.2 


4.6 


5-i 


5-6 


6.0 


6-5; 


25.0 


1.0 


1.4 


1.9 


2.4 


2.9 


3-4 


3-9 


4-3 


4.8 


5-3 


5-8 


6-3 


6. 7 : 


6 


1.0 


i-5 


2.0 


2-5 


3-o 


3-5 


4.0 


4-5 


5-o 


5-5 


6.0 


6.5 


7-o' 


7 


1.0 


1.6 


2.1 


2.6 


3-1 


3-6 


4.2 


4-7 


5.-2 


5-7 


6.2 


6-7 


7-3 


8 


I.I 


1.6 


2.1 


2.7 


3-2 


3-8 


4-3 


4.8 


5-4 


5-9 


6.4 


7.0 


7-5 1 


9 


I.I 


1-7 


2.2 


2.8 


3-3 


3-9 


4.4 


5-o 


5-5 


6.1 


6.7 


7.2 


7-8, 


30.0 


1.2 


i-7 


2-3 


2.9 


3-4 


4.0 


4.6 


5-2 


5-7 


6.3 


6.9 


7-5 


8.0 


1 


1.2 


1.8 


2.4 


3-0 


3-6 


4.2 


4-7 


5-3 


6.0 


6-5 


7-i 


7-7 


8-3 1 


2 


1.2 


1.8 


2.4 


3-o 


3-7 


4-3 


4.9 


5-5 


6.1 


6.7 


7-3 


8.0 


8.6, 


3 


1-3 


1.9 


2-5 


3-1 


13.8 


4.4 


5-o 


5-7 


6-3 


6.9 


7-5 


8.2 


8.8 


4 


i-3 


1-9 


2.6 


3-2 


3-9 


4-5 


5-2 


5-8 


6.5 


7-i 


7-8 


8.4 


9.1: 


35-o 


L3 


2.0 


2.7 


3-3 


4.0 


4-7 


5-3 


6.0 


6-7 


7-3 


8.0 


8.7 


9-3 


6 


1.4 


2.1 


2.7 


3-4 


4.1 


4.8 


5-5 


6.2 


6.9 


7-5 


8.2 


8.9 


9.6 


7 


1.4 


2.1 


2.8 


3-5 


4.2 


4.9 


5-6 


6-3 


7.0 


7-7 


8.4 


9.2 


9-8, 


8 


1.4 


2.2 


2.9 


3-6 


4-3 


' 5-o 


5-8 


6-5 


7-2 


7-9 


8-7 


9.4 


io.r 


9 


1.5 


2.2 


3-o 


3-7 


4.4 


5-2 


5-9 


6.7 


7-4 


8.1 


8.9 


9-7 


0.4I 


40.0 


1.5 


2-3 


3-o 


3-8 


4-5 


5-3 


6.1 


6.8 


7-6 


S.3 


9.1 


9.9 


0.6 


1 


1.6 


2.3 


3-i 


3-9 


4-7 


5-4 


6.2 


7.0 


7-8 


8.5 


9-3 


IO.I 


0.9 


2 


1.6 


2.4 


3-2 


4.0 


4-8 


5-6 


6.4 


7-2 


8.0 


8.8 


9.6 


10.4 


1.2 


3 


1.6 


2.4 


3-3 


4.1 


4.9 


5-7 


6.5 


7-3 


8.2 


9.0 


9.8 


10.6 


XI J 


4 


i-7 


2-5 


3-3 


4.2 


5-o 


5-8 


6.7 


7-5 


8-3 


9.2 


10.0 


0.9 


i.7, 
1.9 


45o 


1-7 


2.6 


3-A 


4-3 


5-1 


6.0 


6.8 


7-7 


8.5 


9.4 


0.2 


1.1 


6 


1-7 


2.6 


3-5 


4-3 


5-2 


6.1 


7.0 


7-8 


8.7 


9.6 


0.5 


1-3 


2.2. 


7 


1.8 


2.7 


3-6 


4.4 


5-3 


6.2 


7-i 


8.0 


8.9 


9.8 


0.7 


1.6 


i 


8 


1.8 


2.7 


3-6 


4-5 


5-4 


6.4 


7-3 


8.2 


9.1 


10.0 


10.9 


11.8 


12.7 


9 


1.8 


2.8 


3-7 


4.6 


5-6 


6-5 


7-4 


8-3 


9-3 


0.2 


1.1 


2.1 


2.9 


50.0 


1.9 


2.9 


3-9 


4.8 


5-8 


6-7 


7-7 


8.7 


9.6 


0.6 


1.6 


2-5 


3-5 


2 


2.0 


3-o 


4.0 


5-o 


6.0 


7.0 


8.0 


9.0 


10.0 


1.0 


2.0 


3-o 


4-0, 


4 


2.1 


3-i 


4.1 


5-2 


6.2 


7-3 


8-3 


9-3 


0.4 


1.4 


2-5 


3.5 


4-5 


6 


2.2 


3-2 


4-3 


5-4 


6.4 


7-5 


8.6 


9-7 


10.7 


11.8 


12.9 


13-9 


1 

i5-o 


8 


2.2 


3-3 


4. J 


5-5 


6-7 


7-8 


8.9 


10.0 


1.1 


2.2 


3-3 


4.4 


5-5 


60.0 


2.3 


3-4 


4.6 


5-7 


6.9 


8.0 


9.2 


0.3 


i-5 


2.6 


3.8 


4.9 


6.1 


2 


2.4 


3-6 


4-7 


5-9 


7-1 


8.3 


9-5 


0.7 


1.9 


3-o 


4.2 


•5-4 


6.6 


4 


2.4 


3-7 


4.9 


6.1 


7-3 


8.6 


9.8 


1.0 


2.2 


3-4 


4-7 


5-9 


7,I i 


6 


2-5 


38 


5-o 


6-3 


7-5 


8.8 


10. 1 


11.4 


12.6 


13-8 


i5-i 


16.4 


17.6 


8 


2.6 


3-9 


5-2 


6-5 


7-8 


9.1 


10.4 


1.7 


3-0 


4-3 


5-5 


6.8 


8.2 


70.0 


2.7 


4.0 


5-3 


6.7 


8.0 


9-3 


10.7 


2.0 


3-4 


4-7 


6.0 


7-3 


8-6, 


2 


2.7 


4.1 


5-5 


6.9 


8.2 


9.6 


10.9 


2.3 


3-7 


5-i 


6-5 


7.8 


9.2 


4 



EARTHWORK COMPUTATION TABLES 



243 



Table 37. — continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


D'uble 
Areas 


4.0 


4-3 


4-6 


4.8 


5-i 


5-4 


5-6 


5-9 


6.2 


6.5 


6-7 


6.9 


7-3 


14-5 


4.2 


4.4 


4-7 


5-o 


5-3 


5-6 


5-8 


6.1 


6.4 


6-7 


6.9 


7.2 


7-5 


15.0 


4-5 


4.6 


4.9 


5-2 


5-5 


5-7 


6.0 


6-3 


6.6 


6.9 


7.2 


7-5 


7-8 


5 


4-5 


4-7 


5-o 


5-3 


5-6 


5-9 


6.2 


6-5 


6.8 


7-i 


7-4 


7-7 


8.0 


16.0 


4.6 


4.9 


5-2 


5-5 


5-8 


6.1 


6.4 


6.7 


7.0 


7-3 


7-7 


8.0 


8-3 


5 


4-7 


5-1 


5-3 


5-7 


6.0 


6.3 


6.6 


6.9 


7-2 


7-6 


7-9 


8.2 


8-5 


17.0 


4.9 


5-2 


5-5 


5-8 


6.2 


6-5 


6.8 


7-i 


7-5 


7-8 


8.1 


8.4 


8.8 


5 


5-o 


5-3 


5-7 


6.0 


6.3 


6.7 


7.0 


7-4 


7-7 


8.0 


8.4 


8-7 


9.0 


18.0 


5-i 


5-5 


5-8 


6.2 


6.5 


6.8 


7.2 


7-5 


7-9 


8.2 


8.6 


8.9 


9-3 


5 


5-3 


5-6 


6.0 


6.3 


6.7 


7.0 


7-4 


7-7 


8.1 


8-5 


8.8 


9.2 


9-5 


19.0 


5-4 


5-8 


6.1 


6-5 


6.8 


7.2 


7.6 


7-9 


8-3. 


8-7 


9.0 


9-4 


9.8 


5 


5-6 


5-9 


6.3 


6.7 


7.0 


7-4 


7.8 


8.2 


8-5 


8.9 


9-3 


9-7 


10. 


20.0 


5-8 


6.2 


6.6 


7.0 


7-4 


7-8 


8.2 


8.6 


9.0 


9-3 


9-7 


IO.I 


o-5 


1 


6.1 


6-5 


6.9 


7-3 


7-7 


8.1 


8.6 


9.0 


9-4 


9.8 


10.2 


0.6 


1.0 


2 


6.4 


6.8 


7.2 


7-7 


8.1 


8-5 


8.9 


9.4 


9.8 


10.2 


0.6 


1.1 


i-5 


3 


6.7 


7-i 


7-5 


8.0 


8.4 


8.9 


9-3 


9.8 


10.2 


10.7 


11. 1 


11.6 


12.0 


4 


7.0 


7-4 


7-9 


8.3 


8.8 


9-3 


9-7 


10.2 


0.7 


1. 1 


1.6 


2.1 


2.5 


25-0 


7.2 


7-7 


8.2 


8.7 


9.1 


9.6 


10.1 


0.6 


1.1 


1.6 


2.0 


2-5 


3-0 


6 


7-5 


8.0 


8.5 


9.0 


9-5 


10. 


0.5 


1.0 


i-5 


2.0 


2-5 


• 3-o 


3-5 


7 


7-8 


8-3 


8.8 


9-3 


9.8 


0.4 


0.9 


1.4 


1.9 


2-4 


3-o 


3-5 


4.0 


8 


8.1 


8.6 


9.1 


9-7 


10.2 


10.7 


H-3 


11. 8 


12.4 


12.9 


13-4 


13-9 


14-5 


9 


8.3 


8.9 


9-5 


10. 


0.5 


1.1 


1-7 


2.2 


2.8 


3-3 


3-9 


4-5 


5-o 


30.0 


8.6 


9.2 


9.8 


0.3 


0.9 


1-5 


2.1 


2.6 


3-2 


3-8 


4-3 


4.9 


5-5 


1 


8.9 


9-5 


IO.I 


0.7 


1-3 


1.9 


2-5 


30 


3-6 


4.2 


4.8 


5-4 


6.0 


2 


9.2 


9.8 


0.4 


1.0 


1.6 


2.2 


2.9 


3-5 


4.1 


4-7 


5-3 


5-9 


6-5 


3 


9-5 


10. 1 


10.7 


H-3 


12.0 


12.6 


13-3 


13-9 


14-5 


151 


*5-7 


16.4 


17.0 


4 


9-7 


0.3 


1.0 


1-7 


2-3 


2.9 


3-6 


4-3 


4.9 


5-5 


6.2 


6.9 


7-5 


35-0 


10. 


0.7 


i-3 


2.0 


2.7 


. 3-3 


4.0 


4-7 


5-3 


6.0 


6.7 


7-3 


8.0 


6 


0.3 


0.9 


i-7 


2-3 


3.o 


3-7 


4.4 


5-i 


5-8 


6-5 


7-i 


7-8 


8-5 


7 


0.6 


1-3 


2.0 


2.7 


3-4 


4.1 


4.8 


5-5 


6.2 


6.9 


7.6 


8.3 


9.0 


8 


10.8 


11.6 


12.3 


13.0 


13-7 


14-5 


15.2 


1 5 -9 


16.6 


17-3 


18. 1 


18.8 


195 


9 


1.2 


1.8 


2.6 


3-3 


4.1 


4.8 


5-6 


6-3 


7-i 


7-8 


8-5 


9-3 


20.0 


40.0 


1.4 


2.1 


2.9 


3-7 


4.4 


5-2 


6.0 


6.7 


7-5 


8.1 


9.0 


9-7 


o-5 


I 


1-7 


2.4 


3-2 


4.0 


4.8 


5-5 


6-3 


7-i 


7-9 


8-7 


9.4 


20.2 


1.0 


2 


2.0 


2.7 


3-5 


4-3 


5-1 


5-9 


6-7 


7-5 


8.3 


9.1 


9-9 


0.7 


i-5 


3 


12.2 


13. 1 


13-9 


14.7 


15-5 


16.3 


17. 1 


17.9 


18.7 


19.6 


20.4 


21.2 


22.0 


4 


2.5 


3-3 


4.2 


5-0 


5-9 


6.7 


7-5 


8-3 


9.2 


20.0 


0.8 


i-7 


2-5 


45.0 


2.9 


3-6 


4-5 


5-3 


6.2 


7-i 


7-9 


8.7 


9.6 


0.4 


1-3 


2.2 


3-o 


6 


3-i 


3-9 


4.9 


5.7 


6-5 


7-4 


8-3 


9.1 


20.1 


0.9 


1-7 


2.6 


3-5 


7 


3-4 


4.2 


5-1 


6.0 


6.9 


7.8 


8.7 


9.6 


0.4 


1-3 


2.2 


3-2 


4.0 


8 


13.6 


14-5 


15-4 


16.3 


17.2 


18.1 


19. 1 


20.0 


20.8 


21.8 


22.7 


23.6 


24-5 


9 


3-9 


4.8 


5-7 


6-7 


I 6 


8-5 


9-5 


0.4 


1-3 


2-3 


3-2 


4.1 


5.o 


50.0 


4-4 


5-4 


6.4 


7-4 


8.3 


9-3 


20.2 


1.2 


2.2 


3-2 


4.1 


5-i 


6.0 


2 


5-o 


6.0 


7.0 


8.0 


9.0 


20.0 


1.0 


2.0 


3-0 


4.0 


5-o 


6.0 


7.0 


4 


5-6 


6.6 


7-6 


8.7 


9-7 


0.8 


1.8 


2.8 


3-8 


4.8 


5-9 


6.9 


8.0 


6 


16.1 


17.2 


18.3 


19.4 


20.4 


21-5 


22.5 


23.6 


24.7 


25.7 


26.8 


27.8 


29.0 


8 


6.7 


7-8 


8.9 


20.0 


1.1 


2.2 


3-4 


4-4 


5-6 


6.6 


7-7 


8.8 


30.0 


60.0 


7.2 


8.4 


9-5 


0.7 


1.8 


2.9 


4.2 


5-2 


6-4 


7-6 


8-7 


9-8 


2.0 


2 


7-8 


8.9 


20.2 


1-4 


•2-5 


3-7 


4.9 


6.0 


7-3 


8.4 


9.6 


30.8 


4 


8.4 


9-5 


0.8 


2.0 


3-2 


4-4 


5-7 


6.8 


8.1 


9-3 


30.6 


1-7 


3-q 


6 


18.9 


20.1 


21.4 


22.6 


239 


25.2 


26.4 


27.7 


29.0 


30.2 


3i-5 


32.7 


34-0 


8 


9-4 


0.7 


2.0 


3-4 


4.6 


5-9 


7.2 


8-5 


9.8 


1.1 


2-4 


3-7 


5-0 


70.0 


20.0 


1.4 


2.6 


4.0 


5-4 


6-7 


8.0 


9-4 


oO-7 


2.0 


3-4 


4.6 6.0 


2 


06 


1.8 


3-3 


4-7 


6.0 


7-4 


8.8 


30.2 


i-5 


2.9 


4-3 5-7| 7-o; 


4 



244 



OFFICE PRACTICE 



Table $j. — continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



28 


29 


30 


3i 


32 


33 


34 


35 


36 


37 


38 


39 


40 


P'uble 
Areas 


7.5 


7-8 


8.1 


8.3 


8.6 


8.? 


9.3 


9./ 


1- 94 


' 9.9 10.2 10.5 


IO.' 


7 14.5 


7.8 


8.c 


8.3 


8.6 


8.g 


9.2 


95 


9-; 


' 10.0 10.: 


i 0.6 0.5 


I.I I5.0 


8.0 


S.3 


8.6 


8.9 


9.2 


9-5 


9-? 


IO.C 


> 0.3 


0.6 0.9 1.2 


1-5 5 


8.3 


8.6 


8.g 


9.2 


95 


9.8 


IO.I 


0.3 


0.7 


1.0 1.3 


i.e 


I.Qj 16.O 


8.5 


8. 9 


9.2 


9-5 


9.8 


IO.I 


0.4 


0./ 


I.C 


1-3 


1.6 i.g 


2.2 


5 


8.8 


9.1 


9.4 


9.8 


IO.I 


10.4 


10.7 


II. c 


H-3 


11. 7 


«•? 


► 12.3 


12.6 17.0 


g.i 


9.4 


9-7 


IO.I 


0.4 


0.7 


I.C 


i-3 


1-7 


2.C 


2-3 


2.6 


3-c 


5 


9-3 


9-7 


10.0 


0.3 


0.7 


1.0 


i-3 


1-7 


2.0 


2-3 


2.7 


3.0 


33 


18.0 


9.6 


9.9 


0.3 


0.6 


1.0 


1-3 


i-7 


2.C 


2.3 


2.7 


3-c 


3-3 


3-7 


5 


9.8 


10.2 


0.5 


0.9 


i-3 


1.6 


1.9 


2-3 


2.7 


3-c 


3-3 


37 


4.1 


19.0 


IO.I 


10.5 


10.8 


11. 2 


11.6 


11.9 


12.3 


12.6 


13.0 


13-3 


13.7 


14.1 


14.4 


5 


0.4 


0.7 


1.1 


1-5 


1.9 


2.2 


2.6 


2.9 


3-3 


3-7 


4.1 


4-5 


4.8 


20.0 


0.9 


1-3 


1-7 


2.1 


2.5 


2.8 


3-2 


3-6 


4.0 


4.4 


4-8 


5-2 


5-5 


1 


1.4 


1.8 


2.2 


2.6 


3-1 


3-4 


3.9 


4.2 


4-7 


5-1 


5.5 


5-9 


6.3 


2 


1.9 


2.4 


2.8 


3-2 


3-6 


4.1 


4-5 


4.9 


5-3 


5.7 


6.2 


6.6 


7-1 


3 


12.5 


12.9 


13-3 


13.8 


14.2 


14.7 


15. 1 


15.5 


16.0 


16.4 


16.9 


17.3 


17.8 


4 


2.9 


3-4 


3-9 


4-4 


4.8 


5-3 


5-7 


6.2 


6.7 


7-i 


7.6 


8.1 


8.5 


25.0 


3-5 


3-9 


4.4 


4.9 


5-4 


5-9 


6.4 


6.8 


7.3 


7-9 


S.3 


8.8 


93 


6 


4.0 


4-5 


5.o 


5-5 


6.0 


6-5 


7.0 


7-5 


8.0 


8.5 


9.0 


9-5 


20.0 


7 


4-5 


5-1 


5-5 


6.1 


6.6 


7-1 


7-6 


8.1 


8.7 


9.2 


9.7 


20.2 


0.7 


8 


15. 1 


15.5 


16.1 


16.6 


17.2 


17.7 


18.3 


18.8 


19-3 


19.9 


20.4 


20.9 


21.5 


9 


5-5 


6.1 


6-7 


7.2 


7-8 


8.3 


8.9 


9.4 


9.9 


20.6 


1.2 


1-7 


2.2 


30.0 


6.1 


6.6 


7.2 


7-8 


8.4 


8.9 


9-5 


20.1 


20.7 


1.2 


1.8 


2.4 


2.9 


1 


6.6 


7.2 


7-7 


8-3 


8.9 


9.6 


20.2 


0.6 


1-3 


1.9 


2-5 


3-2 


3-7 


2 


7-i 


7-7 


8-3 


8.9 


9-5 


20.2 


0.7 


1.4 


1.9 


2.6 


3-2 


3-8 


4-4 


3 


17.6 


18.3 


18.9 


19-5 


20.2 


20.8 


21.4 


22.0 


22.7 


23-3 


23.8 


24.6 


25.2 


4 


8.1 


8.7 


9-5 


20.1 


0.7 


i-3 


2.1 


2.7 


3-3 


3-9 


4-7 


5-3 


5-9 


35.o 


8.7 


9-3 


20.0 


0.7 


1.3 


1.9 


2.7 


3-3 


3-9 


4.6 


5-3 


6.0 


6.7 


6 


9.2 


99 


0.6 


1.2 


1.9 


2.6 


3-2 


39 


4-6 


5-3 


6.0 


6-7 


7-4 


7 


9-7 


20.4 


1. 1 


1.8 


2.5 


3-2 


3-9 


4.6 


5-3 


6.0 


6.7 


7-4 


8.1 


8 


20.2 


20.9 


21.7 


22.3 


23.2 


23.8 


24.6 


25.3 


259 


26.7 


27.4 


28.2 


28.9 


9 


0.7 


1.4 


2.2 


2.9 


3-7 


4.4 


5-2 


5-9 


6.6 


7-4 


8.1 


8.8 


9.6 


40.0 


1-3 


1.9 


2.8 


3-6 


4-3 


5-i 


5-7 


6-5 


7-3 


8.1 


8.8 


9.6 


30-4 


1 


1.8 


2.6 


3-3 


4.2 


4-8 


5-6 


6.4 


7.2 


7-9 


8.7 


9.6 


30.3 


1.0 


2 


2.3 


3-1 


3-8 


4-7 


5-4 


6.2 


7-1 


7-8 


8.6 


9.4 


30-2 


1.1 


1.8 


3 


22.8 


23.6 


24.4 


25.2 


26.1 


26.8 


27.7 


28.4 


29-3 


30.2 


30.9 


31.7 


32.6 


4 


3-3 


4.2 


5-o 


5-8 


6.6 


7-5 


8.4 


9.2 


9.9 


0.8 


1-7 


2.5 


3-4 


45.0 


3.8 


4-7 


5.6 


6. 4 


7.2 


8.1 


8.9 


9.8 


30.6 


i-5 


2.4 


3-2 


4.1 


6 


4-3 


5-2 


6.1 


6.9 


7-8 


8.7 


9.6 


30.4 


1-3 


2.2 


3.o 


39 


4.8 


7 


4.8 


5-7 


6.7 


7-6 


8.4 


9-3 


30.2 


1.1 


2.0 


2.8 


3-7 


4-7 


5-5 


8 


25-4 


26.3 


27.2 


28.2 


29.0 


29.9 


30.8 


31-7 


32.6 


33-6 


34-5 


35-4 


36.3 


9 


5-9 


6.8 


7-8 


8.7 


9.6 


30.5 


1.4 


2.4 


3-4 


4.2 


5-2 


6.2 


7-i 


50.0 


6.9 


7-8 


8.8 


9.8 


30.8 


1-7 


2.7 


3-7 


4.6 


5-6 


6.6 


7.5 8.5 


2 


7-9 


8.9 


9.9 


30.9 


2.0 


3-o 


4.0 


5-o 


5-9 


6.9 


8.0 


9.0: 40.0J 


4 


9.0 


30-1 


31. 1 


2.1 


3-2 


4.2 


5-2 


6.2 


7-3 


8-3 


9.4 


40.4 


1-5 


6 


30.1 


311 


32.2 


33-2 


34-4 


35-4 


36.5 


37-5 


38.6 


39-6 


40.8 


41.8 


42.9 


8 


1.1 


2.2 


3-3 


4.4 


5-6 


6.6 


7-7 


8.9 


40.0 


41. 1 


2.2 


3-4 


4.4 


60.0 


2.1 


3-2 


4.4 


5-6 


6.7 


7-8 


9.0 


40.1 


1.3 


2.4 


3-6 


4.8 


5-9 


2 


3-2 


4.4 


5-5 


6.6 


7.8 


9.1 


40.2 


1.4 


2.6 


3-8 


5.0 


6.2 


7-4 


4 


4.2 


5-4 


6.6 


7.8 


9.1 


40.2 


1.5 


2.7 


3-9 


5-2 


6.4 


7.6 


8.8 


6 


35-2 


36.4 


37-7 


39-o 


40.2 


41-5 


42.8 


44.0 


45-2 


46.5 


47-8 


49.0 5©-4 


8 


6.3 


7-6 


8.8 


40.1 


1.4 


2.8 


4.0 


5-4 


6.6 


8.0 


9.2 


50.5 1.8 


70.0 


7-3 


8.7 


9.9 


1-3 


2.6 


4.0 


5-3 


6.6 


8.0 


9.2 


50.6 


2-0, 3.3 


2 


8.4 


9-7 


41. 1 


2-5 


3-8 5-2 


6.6 


7-9 


9.4 


50.7 


2.1 


3.4; 4-8 j 


4 



EARTHWORK COMPUTATION TABLES 



245 



Distance Horizontal 



Table 37. — continued 
Sum of Areas Vertical Quantities in Cubic Yards 



41 


42 


43 


44 


45 


46 


47 


48 


49 


50 


75 


100 




D'uble 
Areas 


II.O 


n-3 


H.5 


11.8 


12. 1 


12.3 


12.6 


12.9 


I3-I 


13.4 


20.2 


26.8 





14-5 


1.4 


1-7 


1.9 


2.2 


2-5 


2.8 


3-0 


3-3 


3-6 


3-9 


0.8 


7-8 


— 


15-0 


1.8 


2.1 


2-3 


2.6 


2.9 


3-2 


3-5 


3-8 


4.1 


4.4 


i-5 


8-7 


— 


5 


2.1 


2.4 


2-7 


3-o 


3-3 


3-6 


3-9 


4.2 


4-5 


4.8 


2.2 


9.6 


— 


16.0 


2.5 


2.8 


3-1 


3-4 


3-7 


4.1 


4-3 


4-7 


4.9 


5-3 


2.8 


30.5 


— 


5 


12.9 


132 


13-5 


13-8 


14.2 


14-5 


14.8 


I5-I 


15-4 


15-7 


23.6 


31.4 


— 


17.0 


3-3 


3-6 


3-9 


4-3 


4.6 


4.9 


5-2 


5-5 


5-9 


6.2 


4-3 


2.4 


— 


5 


3-7 


4.0 


4-3 


4-7 


5-o 


5-3 


5-7 


6.0 


6.3 


6-7 


4.9 


3-3 


— 


18.0 


4.1 


4.4 


4-7 


5-i 


5-4 


5-7 


6.1 


6.4 


6.7 


7-1 


5-7 


4.2 


— 


5 


4.4 


4-7 


5-1 


5-5 


5-8 


6.1 


6.5 


6. 9 


7.2 


7.6 


6.4 


5-2 


— 


19.0 


14.8 


I5-I 


15-5 


15-9 


16.3 


16.6 


16.9 


17-3 


17.7 


18.1 


27.1 


36.1 


— 


5 


5-2 


5-5 


5-9 


6-3 


6.7 


7-1 


7-4 


7-7 


8.1 


8.5 


7.8 


7.0 


— 


20.0 


5-9 


6-3 


6.7 


7-1 


7-5 


7-9 


8-3 


8.7 


9.0 


9-5 


9.2 


8.8 


— 


1 


6-7 


7-i 


7-5 


7-9 


8.3 


8.7 


9.1 


9-5 


9.9 


20.4 


30.6 


40.7 


— 


2 


7.5 


7-9 


8.3 


8.7 


9.1 


9.6 


20.0 


20.4 


20.8 


1-3 


1.9 


2.6 


— 


3 


18.2 


18.6 


19.1 


19-5 


20.0 


20.4 


20.8 


21.3 


21.8 


22.2 


33-2 


44-4 


— 


4 


9.0 


9-5 


9.9 


20.3 


0.8 


1-3 


1-7 


2.2 


2.7 


3-2 


4-7 


6.2 


— 


25.0 


9.7 


20.2 


20.7 


1.2 


i-7 


2.2 


2.6 


3-1 


3-6 


4-1 


6.1 


8.2 


— 


6 


20.5 


1.0 


1-5 


2.0 


2-5 


3-0 


3-5 


4.0 


4-5 


5.0 


7-5 


50.0 


— 


7 


1-3 


1.8 


2.3 


2.8 


3-3 


3-8 


4-4 


4.8 


5-4 


5-9 


8.8 


1.8 


— 


8 


22.0 


22.6 


23.1 


23-7 


24.2 


24.7 


25.2 


25-8 


26.3 


26.8 


40.3 


53-7 


— 


9 


2.8 


3-3 


3-8 


4-4 


5-o 


5-5 


6.1 


6.7 


7.2 


7-8 


1.6 


5-5 


— 


30.0 


3-5 


4.1 


4-7 


5-2 


5-8 


6.4 


6.9 


7.6 


8.1 


8.7 


3-2 


7-3 


— 


1 


4-3 


4.8 


5-4 


6.1 


6.6 


7.2 


l* 


8.4 


9.1 


9.6 


4.4 


9.2 


— 


2 


5-0 


5-7 


6.3 


6.8 


7-5 


8.1 


8.7 


9-3 


9.9 


30.6 


5.8 


61.0 


— 


3 


25.7 


26.4 


27.0 


27.7 


28.3 


28.9 


29.6 


30.2 


30.8 


31.4 


47.2 


62.9 


— 


4 


6.6 


7-2 


7-8 


8.5 


9.2 


9.8 


30.4 


1.1 


1-7 


2.4 


8.6 


4-8 


— 


35-0 


7-3 


8.0 


8.6 


9.3 30.0 


30.6 


i-3 


2.0 


2.6 


3-3 


9.9 


6.7 


— 


6 


8.1 


8.8 


9.4 


30.1 


0.8 


1-5 


2.2 


2.8 


3-6 


4-3 


5i.4 


8.5 


— ! 


7 


8.8 


9.6 


30.2 


1.0 


1.6 


2.4 


3.1 


3-7 


4-5 


5-2 


2.8 


70.4 




8 


29.6 


30.4 


31.0 


31.7 


32.5 


33-2 


33-8 


34-6 


35-4 


36.1 


54-i 


72.1 




9 


30.4 


1.2 


1.8 


2.6 


3-3 


4.0 


4.8 


5.6 


6.3 


7.0 


5-5 


4.0 


— 


i 40.0 


1.2 


1.8 


2.6 


3-4 


4.2 


4.8 


5-6 


6.4 


7.2 


8.0 


6.9 


5.8 


— 


1 


1.8 


2.7 


3-4 


4.2 


5-o 


5-8 


6.6 


7-3 


8.2 


8.9 


8.3 


7-8 


— 


2 


2.6 


3-4 


4.2 


5.o 


5-8 


6.6 


7-4 


8.2 


9.0 


9.8 


9.6 


9.6 


— 


3 


33-4 


34-2 


1 35.o 


35-8 


36.7 


37-4 


38.3 


39-2 


399 


40.8 


61. 1 


81.5 


— 


4 


4.2 


4.9 


5-8 


6.7 


7-4 


8.3 


9.2 


9.9 


40.7 


1.6 


2.4 


3-4 


— 


45-0 


4.8 


5-7 


6.6 


7-4 


8.3 


9-1 


40.0 


40.9 


1-7 


2.6 


3-8 


5-i 


— 


6 


5-7 


6.6 


l 4 


8.3 


9.2 


40.0 


0.9 


1.8 


2-7 


3-5 


5-3 


7.0 


— 


7 


6.4 


7-3 


8.2 


9.2 


40.0 


0.8 


17 


2.6 


3-5 


4.4 


6.7 


8.9 


— 


8 


37-2 


38.1 


' 39.o 


399 


40.8 


41.7 


42.6 


43-5 


44-4 


45-3 


68.1 


90.6 


— 


9 


79 


8.8 


9.8 


40.7 


1.6 


2.6 


3-5 


4.4 


5-3 


6.4 


9-3 


2.6 


— 


50.0 


9-5 


40.4 


41-3 


2-3 


3-3 


4.2 


5-2 


6 o' 2 


7.2 


8.2 


72.2 


6-3 


— 


2 


41.0 


2.0 


3-o 


4.0 


5.o 


6.0 


7.0 


8.0 


9.0 


50.0 


5-0 


100. 




4 


2-5 


3-5 


4.6 


5-6 


6.6 


7-7 


8-7 


9-8 


50.8 


1.8 


7-8 


03.6 





6 


44.1 


45-2 


46.2 


47-3 


48.4 


49-4 


50.5 


51-5 


52.6 


53-7 


80.5 


107.3 


— 


8 


5.6 


6.7 


7.8 


8.9 


50.0 


5I 'o 


2.2 


3-3 


4.4 


5-5 


3-4 


II.O 


— 


60.0 


7-1 


8.2 


9.4 


50.5 


1.6 


2.8 


4.0 


5-1 


6.2 


7-4 


6.1 


14.8 


— 


2 


8.6 


97 


50.9 


2.1 


3-3 


4-5 


5-7 


6.9 


8.1 


9-3 


8.9 


18.6 


— 


4 


50.2 


5i.3 


2.5 


3-7 


5.o 


6.1 


7-4 


8.6 


9.9 


61. 1 


91.7 


22.1 


— 


6 


5i.6 


52.8 


54-i 


55-4 


56.7 


58.0 


59-2 


60.4 


61.7 


63.0 


94-5 


125.9 





8 


3-i 


4.4 


5-7 


7.0 


8.3 


9.6 


60.9 


2.2 


3-5 


4.8 


7.2 


29-5 


— 


70.0 


4-7 


6.0 


7-3 


8.6 


60.0 


1 61.3 


2.6 


4.0 


5-4 


6.6 


100. 


33-2 — 


2 


6.2 


7.6 


8.9 


60.3 


1.7 


3-1 


4.4 


5.8 


7.2 


8.61 02.9 


37-1, - 


4 



246 



OFFICE PRACTICE 



Distance Horizontal 



Table $1- — continued 
Sum of Areas Vertical Quantities in Cubic Yards 



2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


D'uble 
Areas 


2.8 


4.2 


H 


7.0 


8.5 


9.9 


n-3 


12.7 


14. 1 


15-5 


16.9 


18.3 


19.7 


76.0 


2.9 


4-3 


5-8 


7.2 


8.7 


IO.I 


1.6 


3-o 


4-5 


59 


7-4 


8.8 


20.2 


8 


3.0 


4.4 


5-9 


7-4 


8.9 


0.4 


i-9 


3-3 


4.9 


6.3 


7-8 


9-3 


0.8 


80.0 


3-o 


4.6 


6.1 


7.6 


9.1 


0.7 


2.2 


3-7 


5-2 


6.7 


8.2 


9.8 


1-3 


2 


3-i 


4-7 


6.2 


7-8 


9-3 


0.9 


2.5 


4.0 


5-6 


7-1 


8.7 


20.2 


i-7 


4 


3-2 


4.8 


6.4 


8.0 


9.6 


11. 2 


12.7 


14-3 


15-9 


17.5 


19.1 


20.7 


22.3 


6 


3-3 


4.9 


6.5 


8.1 


9.8 


1.4 


3-1 


4-7 


6.3 


7-9 


9-5 


1.2 


2.8 


8 


3-3 


5-o 


6.7 


8.3 


10. 


1-7 


3-3 


5-o 


6.7 


8.3 


20.0 


1-7 


3.4 


90.0 


3-4 


5-1 


6.8 


8-5 


0.2 


1.9 


3-6 


5-4 


7-i 


8.7 


0.4 


2.1 


3.8 


2 


3-5 


5.2 


7.0 


8.7 


0.5 


2.2 


3-9 


5-7 


7-4 


9.2 


0.8 


2.6 


4.4 


4 


3-5 


5-3 


7-1 


8.9 


10.7 


12. s 


14.2 


16.0 


17.8 


19.5 


21.3 


23.1 


24.9 


6 


3-6 


5-4 


7-3 


9.1 


0.9 


2.7 


4-5 


6.4 


8.2 


9-9 


1.8 


3.6 


5.4 


8 


3-7 


5-6 
5-8 


7 i 


9-3 


1.1 


3.o 


4.8 


6.7 


8.5 


20.4 


2.2 


4.1 


6.0 


100. 


3-9 


7.8 


9-7 


1-7 


3-6 


5-5 


7-5 


9-5 


1.4 


3-3 


5-3 


7.2 


05 


4.1 


6.1 


8.1 


10.2 


2.2 


4-3 


6.3 


8.4 


20.4 


2.4 


4.4 


6.5 


8.6 


10 


4-3 


6.4 


8.5 


10.7 


12.8 


14.9 


17.0 


19.1 


21.3 


23.4 


25-5 


27.7 


29.8 


15 


4.4 


6.7 


8.9 


1.1 


3-3 


5-5 


7.8 


20.0 


2-3 


4-4 


6.6 


8.8 


31.2 


20 


4.6 


6.9 


9.2 


1.6 


3-9 


6.2 


8-5 


0.8 


3-2 


5-4 


7-7 


30.2 


2.4 


125.0 


4.8 


7.2 


9.6 


2.1 


4-5 


6.9 


9-3 


1-7 


4.1 


6.5 


8.8 


1.4 


3-7; 


30 


5.o 


7-5 


10. 


2-5 


5-o 


7-5 


20.0 


2.5 


5-o 


7-5 


9.9 


2.5 


5.0 


35 


5-2 


7.8 


10.4 


12.9 


15.5 


18.2 


20.8 


23-4 


25-9 


28.5 


31. 1 


33-7 


36.4' 


40 


5-4 


8.0 


0.7 


3-4 


6.1 


8.8 


i-5 


4.2 


6.8 


9-5 


2.2 


4.8 


7-6 


45 


5-6 


8.3 


1.1 


3-9 


6.7 


9-5 


2-3 


5-o 


7.8 


30.6 


3-4 


6.2 


8.8 


150.0 


5-7 


8.6 


1-5 


4-3 


7.2 


20.1 


2.9 


5-8 


8.7 


1.6 


4-5 


7-3 


40.2' 


55 


5-9 


8.9 


1.9 


4.8 


7.8 


0.7 


3-7 


6.7 


9.6 


2.6 


5-6 


8.5 


'1 


60 


6.1 


9.2 


12.3 


15-3 


18.3 


21.4 


24.4 


27.5 


30.6 


33-6 


36.6 


39-7 


42.8 


65 


6.3 


9-5 


2.6 


5-8 


8.9 


2.1 


5-2 


8-3 


i-5 


4-6 


7-7 


40.9 


4.1J 


70 


6.5 


9-7 


3-o 


6.2 


9-4 


2.7 


5-9 


9.2 


2.4 


5-6 


8.9 


2.1 


5-5, 


i75-o 


6.7 


10. 


3-3 


6.7 


20.0 


3-3 


6.7 


30.0 


• 3-3 


6.7 


40.0 


3-3 


6.6, 


80 


6.9 


0.3 


3-7 


7-1 


0.6 


4.0 


7.4 


0.9 


4.2 


7-7 


1.2 


4.5 


8.0 


85 


7.0 


10.5 


14.1 


17.6 


21.2 


24.6 


28.2 


31.7 


35-2 


38.7 


42.2 


45-7 


49-3 


90 


7.2 


0.8 


4-5 


8.1 


1.6 


5-2 


8.8 


2.5 


6.2 


9-7 


3-3 


7.0 


50.5 


95 


7-4 


1.1 


4.9 


8-5 


2.2 


5-9 


9.6 


3-4 


7-1 


40.8 


4.4 


8.2 


1.9 


200.0 


7-8 


i.7 


5-6 


9-5 


3-4 


7.2 


3i-i 


5-0 


8.9 


2.8 


6.7 


50.5 


4-4 


10 


8.1 


2.2 


6.3 


20.4 


4.4 


8-5 


2.6 


6.7 


40.8 


4.8 


8.8 


3-o 


7-1 


20 


8-5 


12.7 


17. 1 


21.3 


25.6 


29.8 


34-1 


38.4 


42.6 


46.8 


5i. 1 


554 


59-6 


30 


8.9 


3-3 


7-7 


2.2 


6.6 


3I.I 


5-6 


40 


4-4 


a 8 


3-3 


7.8 


62.1 


40 


9.2 


3-9 


8.5 


3-i 


7.8 


2.4 


7.0 


1-7 


6.4 


50.9 


5.6 60.2 


4.8 


250.0 


9.6 


4-5 


9-3 


4.1 


8.9 


3-7 


8.5 


3-4 


8.2 


2.9 


7-8 2.7 


7-41 


60 


10. 


5.o 


20.0 


5-o 


30.0 


S.o 


9.9 


5.o 


50.0 


5.0 


60.0 


4.9 


70.0 


70 


10.4 


15.6 


20.7 


25.9 


31. 1 


36.3 


41.4 


46.7 


51-9 


57-o 


62.2 


67.4 


72.5 


80 


0.8 


6.1 


1-4 


6.8 


2.2 


7.6 


3-0 


8.3 


3-8 


9.1 


4.4 


9.8 


5-2 


90 


1.1 


6.7 


2.2 


7.8 


3-3 


8.8 


4-4 


50.0 


5-6 


61. 1 


6.8 


72.2 


7-9 


300.0 


i-5 


7.2 


2.9 


8.6 


4.4 


40.2 


5-9 


1.8 7-4 


3-i 


8.8 


4-5 


80.4 


10 


1.9 


7-8 


3.6 


9.6 


5-5 


1.4 


7-4 


3-3 9-3 


5-2 


71. 1 


7.0 


3-0 


20 


12.2 


18.3 


24.4 


30.6 


36.6 


42.8 


48.8 


55-0 61.2 


67.2 


73-3 


79-4 


8 5 .6 


30 


2.6 


8-9 


5-2 


1.4 


7-7 


4.1 


50.5 


6.7 2.9 


9.2 


5-5 


81.8 


8.2 


40 


3-o 


9-5 


5-9 


2.4 


8.8 


5-3 


1.8 


8.3 4-8 


71.3 


7.8, 


4.2 


90.8 


350.0 


3-3 


20.0 


6.6 


3-3 


9.9 


6.6 


3-4 


60.0 6.8 


3-3 


8o.o| 


6.8 


3-3 


60 


3-7 


0.6 


7-4 


4-3 


41. 1 


7-9 


4-8 


1.6 


8.5 


5-3 


2.1 


9.0 


6.0 


70 


14.1 


21.2 


28.2 


35-2 


42.2 


49-2 


56.3 


63.3 


70.3 


77-4 


84.3 


9i-5 


98.5 


80 


4-4 


1.6 


8.8 


6.1 


3-3 


50.6 


7-8 


5-o 2.3 


9.4 


6.6, 


3-9 


IOI.I 


90 


4.8 


2.2 


9.6 


7-1 


4.4 


1.8 


9.2 


6.7 4.1 


81.5 


8.9 


6.3 


3.6 


400.0 



EARTHWORK COMPUTATION TABLES 



247 



Table 37. — continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



15 


16 


17 


18 
25.3 


19 


20 


21 


22 


23 


24 


25 


26 


27 


D'uble 
Areas 


21.2 


22.5 23.9 


26.7 


28.2 


29.6 


31.0 


32.4 


33-8 


35-2 


36.6 


38.0 


76.0 


1-7 


3-i 


4-6 


6.0 


7-4 


8.9 


30.3 


1.8 


3-2 


4-7 


6.0 


7-5 


9.0 


8 


2.2 


3-7 


5-2 


6.7 


8.2 


9.6 


1.1 


2.6 


4.1 


5-6 


7.o 


8.5 


40.0 


80.0 


2.8 


4-3 


5-8 


7-3 


8.9 


30.4 


1.8 


3-4 


4.9 


6.4 


7-9 


9-4 


1.0 


2 


3-3 


4.8 


6.4 


8.0 


9.6 


1.2 


2.7 


4.2 


5.8 


7-3 


8.8 


40.4 


2.0 

I 


4 


23.8 


25.5 


27.1 


28.6 


30.2 


31.8 


33.4 


35.o 


36.6 


38.2 


39-8 


41.4 


43 -o 


6 


4.4 


6.1 


7-7 


9-3 


0.9 


2.6 


4.2 


5-8 


7-5 


9.1 


40.7 


2.3 


4.0 


8 


5.o 


6.7 


8.3 


30.0 


1-7 


3-4 


5.o 


6.6 


8.4 


40.0 


1.6 


3-3 


5.o 


90.0 


5-6 


7.2 


8.9 


0.6 


2-3 


4.1 


5-8 


7-5 


9.2 


0.9 


2.6 


4-3 


6.0 


2 


6.1 


7-8 


9.6 


1-3 


3-1 


4-8 


6-5 


8.2 


40.0 


1.8 


3-5 


5-2 


7.C, 


4 


26.7 


28.4 


30.2 


32.0 


33-7 


35-5 


37.3 


39.o 


40.8 


42.7 


44.4 


46.2 


48.0 


6 


7.2 


9.0 


0.8 


2.6 


4.4 


6-3 


8.0 


9.8 


1-7 


3-6 


5-4 


7.i 


9.o | 


8 


7-8 


9-6 


1-5 


3-3 


5-2 


7.o 


8.9 


40.8 


2.6 


4-4 


6.3 


8.1 


50.0 


100. 


9.2 


31.2 


3.0 


5.o 


7.0 


8.9 


40.8 


2.7 


4-7 


6.6 


8.5 


50.5 


2.5 


05 


30.6 


2.6 


4-6 


6.6 


8.7 


40.7 


2.7 


4-7 


6.8 


8.8 


50.9 


2.9 


S, °l 


10 


32.0 


34-1 


36.2 


38.4 


40.5 


42.6 


44.7 


46.8 


48.9 


51.0 


53-2 


55.4 


57.5! 


15 


3.3 


5-5 


7-7 


9.9 


2.2 


4-4 


6.6 


8.8 


51.0 


3-3 


5-5 


7.8 


60.0 


20 


4-6 


7.0 


9-3 


41.6 


3-9 


6-3 


8.6 


50.9 


3-2 


5.5 


7-8 


60.1 


2.5' 


125.0 


6.1 


8-5 


40.9 


3-3 


5-7 


8.2 


50.5 


2.9 


5-3 


7.8 


60.2 


2.6 


5.o 


30 


7-5 


40.0 


2-5 


5.o 


7-5 


50.0 


2.5 


5-o 


7.5 


60.0 


2.5 


5.o 


'I 


35 


38.8 


41.4 


44.0 


46.6 


49.2 


51.8 


54-4 


57.o 


59-6 


62.2 


64.8 


67.4 


70.0 


40 


40.2 


2.9 


5-6 


8.3 


51.0 


3-7 


6.3 


9.0 


61.7 


4.4 


7.0 


9.8 


2.5 


45 


1.6 


4.4 


7.2 


9-9 


2.8 


5-7 


8.2 


61.1 


3-9 


6.6 


9-3 


72.2 


5-o, 


150.0 


3.0 


5.9 


8.7 


51.6 


4-5 


7-6 


60.3 


3-1 


6.0 


8.8 


71.8 


4-6 


7-5 


55 


4.4 


7-3 


50.4 


3-3 


6.2 


9-3 


2.1 


5-1 


8.1 


71. 1 


4.0 


7.0 


80.0 


60 


45.8 


48.8 


52. 


55.o 


58.0 


61.0 


64.2 


67.1 


70.3 


73-4 


76.2 


79-3 


82.5 


65 


7.2 


50.5 


3-5 


6.6 


9.8 


3.o 


6.0 


9-2 


2.3 


5-5 


8.7 


81.8 


5-cj 


70 


8.6 


1.8 


5.o 


8.3 


61.5 


4.8 


8.0 


71.2 


4.6 


7-7 


81.0 


4.3 


7-5, 


i75.o 


50.0 


3-3 


6.6 


60.0 


3-3 


6.8 


9.9 


3-2 


6.7 


80.0 


3-2 


6.7 


90.0 


80 


1.4 


4.8 


8.1 


1.6 


5.o 


8.5 


71.9 


5-3 


8.8 


2.2 


5-6 


9.0 


2.5 


85 


52.8 


56.2 


59-8 


63.3 


66.8 


70.4 


73.8 


77-3 


80.9 


84.3 


87.9 


91.7 


95 -o. 


90 


4.0 


7-8 


61.3 


5-o 


8.7 


2.1 


5-7 


9-4 


3-o 


6.7 


90.2 


3-9 


7-5 


95 


5-5 


9.2 


2.9 


6.7 


70.3 


4.0 


7-7 


81.4 


5-1 


8.9 


2.8 


6.4 


100. o } 


200.0 


8.3 


62.1 


6.0 


70.0 


3-8 


7-8 


81.7 


5-5 


9.4 


93-4 


7.2 


101.2 


05.0 


10 


61.0 


5-1 


9-3 


3-2 


7-4 


81.5 


5-5 


9-5 


93-7 


7-8 


101.9 


06.0 


10.0 


20 


63-9 


68.0 


72.4 


76.6 


80.9 


85.2 


89.4 


93-7 


98.0 


102.2 


106.5 


110.8 


115.0: 

20.0 


30 


6-5 


71.0 


5-5 


9-9 


4-3 


8.9 


93-2 


7-8 


102.2 


106.8 


11. 1 


15.5 


40 


9.4 


4.0 


8.6 


83.2 


7-9 


92.5 


7-1 


101.9 


06.5 


11. 1 


15.9 


20.5 


25.0; 


250.0 


72.1 


7.0 


81.8 


6.5 


91.4 


6.5 


101.2 


06.0 


10.7 


15.5 


20.4 


25.3 


30.C 


60 


5.o 


80.0 


5-o 


90.0 


4-9 


100.0 


05.0 


10.0 


i.S-i 


20.0 


25.0 


30.0 


35.C 


70 


77-8 


82.9 


88.1 


93-2 


98.4 


103.8 


108.9 


114.1 


119. 2 


124-5 


129.5 


134.8 


140.0 


80 


80.6 


5-9 


91.2 


6-5 


102. 1 


07.4 


12.9 


18.1 


23.5 


28.9 


34-3 


39-8 


45.0 


90 


3-2 


8.9 


4-4 


100. 


05.7 


II. I 


16.8 


22.2 


29.7 


33-3 


38.9 


44.5 


50.C 


300.0 


6.0 


91.8 


7-5 


03 -3 


09.2 


14.8 


20.6 


26.3 


32.1 


37-9 


43-5 


49-3 


55.0 


10 


9.0 


4-7 


100.9 


06.8 


12.7 


18.6 


24.3 


30.3 


36.2 


42.2 


48.1 


54-1 


60.0 


20 


91.5 


97-7 


103.9 


IIO.O 


116. 1 


122.2 


128.3 


134.5 


140.6 


146.8 


152.8 


158.9 


165.0 


30 


4-5 


100.7 


07.1 


13.2 


19.6 


26.O 


32.2 


38.5 


44-9 


5ii 


57-2 


63.8 


70.0 


40 


7.2 


03.8 


10.2 


16.7 


23.2 


29.7 


36.2 


42.5 


49-1 


55-5 


62.0 


68.5 


75-q 
80.0 


350.0 


100.0 


06.6 


13.4 


20.0 


26.8 


33-3 


40.0 


46.6 


53-2 


60.0 


66.8 


73.4 


60 


02.8 


09.6 


16.4 


23.2 


30.2 


37-0 


43-8 


50.7 


57-5 


64-5 


71.2 


78.1 


85.0 


70 


105.6 


112. 5 


119. 6 


126.8 


133.8 


140.8 


147.8 


154.8 


161.8 


168.9 


175.9 


183.0 


190.0 


80 


08.2 


15-5 


22.9 


30.0 


37-2 


44-3 


51.7 


58.9 


66.1 


73-4 


80.5 


87.8 


95-o 


90 


II. I 


18.5 


25-9 


33-3 


40.7 


48.1 


55.6 


63.0 


70.4 77.8 


85.2 


92.6 


200.0 


400.0 



248 



OFFICE PRACTICE 



Table 37. — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



28 


29 


30 


31 


32 


33 


34 


35 
49-3 


36 

50.7 


37 


38 


39 


40 


D'uble 
Areas 


39-4 


40.8 


42.3 


43-6 


45-1 


46.5 


47-9 


52.1 


53-5 


54-9 


56.3 


76.0 


40.4 


1.8 


3-3 


4.8 


6.2 


7.7 


9.1 


50.5 


2.0 


3-5 


4.9 


6.4 


7-8 


8 


1-5 


3-o 


4.4 


5-9 


7-4 


8.8 


50.3 


1.8 


3-3 


4.8 


6.3 


7-8 


9.2 


80.0 


2-5 


4.1 


5-6 


7-1 


8.6 


50.1 


i-7 


3-2 


4-7 


6.2 


7-7 


9.2 


60.8 


2 


3-6 


5-2 


6.7 


8.2 


9.8 


1.3 


2.9 


4-5 


6.0 


7-5 


9.1 


60.7 


2.3 


4 


44.6 


46.2 


47.8 


49-3 


51.0 


52.5 


54-2 


55-7 


57-3 


58.9 


60.5 


62.1 


63.7 


6 


5.6 


7.2 


8.8 


5o.5 


2.1 


3-7 


5-4 


7.o 


8-7 


60.3 


1.9 


3-5 


5-2 


8 


6.7 


8.3 


50.0 


1-7 


3-3 


5.o 


6-7 


8.3 


60.0 


1.6 


3-3 


5.o 


6.6 


90.0 


7-7 


9.4 


1.1 


2.8 


4-5 


6.2 


7-9 


9.6 


1-3 


3.o 


4-7 


6.4 


8.2 


2 


8.8 


50.5 


2.2 


4.0 


5-7 


7-5 


9.2 


61.0 


2.7 


4.4 


6.2 


7-9 


9-7 


4 


49.8 


5i.5 


53.3 


55-1 


56.9 


58.7 


60.4 


62.2 


64.0 


65.8 


67.6 


69.4 


71. 1 


6 


50.8 


2.6 


4.4 


6.3 


8.1 


9.9 


1.7 


3-5 


5-3 


7.2 


8.9 


70.8 


2.6 


8 


1.8 


3-7 


5-5 


7-4 


9-3 


61. 1 


3-o 


4.8 


6.6 


8.5 


70.3 


2.2 


4.0 


1 00.0 


4.4 


6.4 


8.3 


60.3 


62.2 


4.2 


6.1 


8.1 


70.0 


72.0 


3-9 


5.8 


7-8 


05 


7.0 


9.1 


61.1 


3-2 


5-2 


7.2 


9-3 


71.3 


3-4 


5-4 


7.4 


9-5 


81.5 


10 


59-7 


61.8 


64.0 


66.0 


68.1 


70.4 


72.5 


74-5 


76.7 


78.8 


81.0 


83.1 


85.2 


15 


62.3 


4-5 


6.7 


8.9 


71. 1 


3-4 


5-5 


7-8 


80.0 


82.2 


4-5 


6.7 


9.0 


20 


4.8 


7.2 


9-5 


71.8 


4.1 


6.5 


8.8 


81.0 


3-4 


5-6 


8.0 


90.3 


92.7 


125.0 


7-3 


9.8 


72.1 


4-5 


7.0 


9.4 


81.8 


4.2 


6.6 


9.0 


91.4 


3-9 


6.1 


30 


70.0 


72.5 


5.o 


7-5 


80.0 


82.5 


5-o 


7-5 


90.0 


92.5 


5.o 


7-5 


100.0 


35 


72.6 


75-2 


77.8 


80.5 


83.0 


85.6 


88.1 


90.7 


93-4 


96.0 


98.5 


IOI.I 


103.7 


40 


5-2 


7-9 


80.5 


3-2 


5-9 


8.6 


9i.3 


4.0 


6.7 


9.4 


102.0 


04.8 


07.5 


45 


7-8 


80.6 


3-4 


6.1 


8.9 


91.7 


4-5 


7.2 


100. 


102.8 


05.6 


08.3 


II. I 


150.0 


80.4 


3-2 


6.2 


9.0 


91.9 


4-7 


7-6 


100.5 


03.4 


06.2 


09.1 


12.0 


14.8 


55 


2.9 


5-9 


8.8 


91.8 


4-7 


7-7 


100.8 


03.8 


06.7 


09.7 


12.6 


15.6 


18.5 


60 


85.5 


88.5 


91.6 


94.7 


97-7 


100.9 


103.9 


107.0 


110.0 


113. 1 


116. 1 


119. 2 


122.2 


65 


8.1 


9i.3 


4.4 


7-6 


100.8 


03-9 


07.1 


10.2 


13.3 


16.6 


19.7 


22.8 


26.O 


70 


90.8 


4.0 


7.3 


100.5 


03.8 


70.0 


10.2 


13.4 


16.7 


20.0 


23.2 


26.4 


29.6 


i75.o 


3-4 


6.6 


1 00.0 


03.3 


06.8 


in. 1 


13.4 


16.8 


20.0 


23-3 


26.7 


30.1 


33.4 


80 


6.0 


9.4 


02.8 


06.2 


09.6 


13.2 


16.5 


19.9 


23-4 


26.8 


30.2 


33-7 


37-1 


85 


98.6 


102. 1 


105.6 


109.2 


112.8 


116. 1 


H9-7 


123.2 


126.7 


130.2 


133.8 


1373 


140.8 


90 


101.2 


04.8 


08.4 


12.0 


15-6 


19.2 


22.9 


26.4 


30.0 


33-8 


37-2 


40.9 


44-5 


95 


03-7 


07.4 


11. 1 


14.9 


18.6 


22.2 


26.0 


29.6 


33-3 


37-0 


40.6 


44.4 


48.I 


200.0 


08.8 


12.8 


16.6 


20.6 


24.4 


28.4 


32.2 


36.2 


40.0 


44.0 


47.8 


51.6 


55-6 


10 


14.0 


18.2 


22.2 


26.4 


30.4 


34-4 


38.6 


42.6 


46.8 


50.8 


54-8 


59-o 


63.O 


20 


119.4 


123.6 


127.8 


132.0 


136.2 


140.6 


145.0 


149.0 


153.4 


157.6 


162.0 


166.2 


I70.4 


30 


24.6 


29.0 


33-4 


37-8 


42.2 


46.8 


51-0 


55-6 


60.0 


64.4 


69.0 


73-4 


78.O 


40 


29.6 


34-4 


39-o 


43-6 


48.2 


53-o 


57-6 


62.0 


66.8 


71.4 


76.0 


80.6 


85.4 


250.0 


34-6 


39-4 


44.2 


49.0 


54.o 


58.8 


63.6 


68.4 


73-2 


78.0 


82.8 


87.8 


92.5 


60 


40.0 


45.o 


50.0 


55-0 


60.0 


65.0 


70.0 


75.o 


80.0 


85.0 


90.0 


95-0 


200.0 


70 


145-2 


150.4 


155-6 


161. 


166.0 


171. 2 


176.2 


181.4 


186.8 


192.0 


197.0 


202.2 


207.4 


80 


50.4 


55-8 


61.0 


66.4 


71.8 


77.2 


82.6 


88.0 


93-3 


98.8 


204.0 


09.6 


I4.6 


90 


55-6 


61.2 


66.8 


72.2 


77-8 


83.4 


89.0 


94.4 


200.0 


205.6 


11. 2 


16.6 


22.2 


300.0 


60.8 


66.4 


72.4 


78.0 


83.8 


89.4 


95-2 


201.0 


06.8 


12.4 


18.2 


24.0 


29.6 


10 


65.8 


71.8 


77-6 


83.6 


89.4 


95-4 


201.6 


07.6 


13.6 


19.4 


25.2 


31.2 


37-0 


20 


171. 


i77.o 


183.2 


189.4 


195-4 


201.8 


207.8 


214.0 


220.0 


226.2 


232.2 


238.4 


244.4 


30 


76.2 


82.6 


88.8 


95.2 


201.6 


07.8 


14.2 


20.4 


26.7 


33-2 


39-4 


45-6 


52.0 


40 


81.6 


88.0 


94.6 


201.0 


07.6 


14.0 


20.4 


26.8 


33-4 


40.0 


46.4 


52.8 


59-2 


350.0 


86.8 


93-2 


200.0 


06.6 


136 


22.2 


26.8 


33-6 


40.0 


46.6 


53-4 


60.2 


66.8 


60 


92.0 


98.8 


05.6 


12.4 


19.2 


26.4 


33-0 


39-8 


46.8 


53-6 


60.4 


67.4 


74.2 


70 


197.2 


204.2 


211. 2 


218.4 


225.6 


232.2 


239-4 


246.4 


253-4 


260.4 


267.6 


274-6 


281.6 


80 


202.4 


09.6 


16.8 


24.0 


312 


38.4 


45-8 


52.8 


60.2 


67.6 


74-4 


81.8 


89.0 


90 


07.4 


14.8 


22.2 


29.6 


37.o 


44.4 


51.8 


59-2 


66.6 


*74-o 


81.4 


88.8 


96.2 


400.0 



EARTHWORK COMPUTATION TABLES 



249 



Table 37. — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



41 


42 


43 


44 


|45 


46 


47 


48 


49 


5o 


75 1 


100 




D'ubl 
Areas 


57-7 


59-2 


60.6 


61.9 


63-4 


64.8 


66.2 


67.6 


69.0 


70.4 


105.7 


140.7 


76.0 


9.2 


60.7 


2.1 


3-6 


5-0 


6. 4 


7.8 


9-3 


70.7 


2.3 08.4 


44-4 


— 


8.0 


60.8 


2.2 


3-7 


5-2 


6.7 


8.2 


9-7 


71.2 


2.6 


4.1 


11. 2 


48.1 


— 


80.0 


2.2 


3-8 


5-3 


6.8 


8-3 


9.8 


71.4 


2.9 


4-4 


5-9 


14.0 


51.8 


— 


2 


3-8 


5-4 


6.9 


8.4 


70.0 


71.6 


3-2 


4.7 


6.2 


7.8 


16.8 


55-5 


— 


4 


65.3 


66.8 


68.4 


70.1 


71.7 


73-3 


74-8 


76.4 


78.0 


79-6 


H9-5 


159.2 





6 


6.8 


8.4 


70.1 


17 


3-4 


5.o 


6.6 


8.3 


9.8 


81.5 


22.3 


63.0 


— 


8 


8.4 


70.0 


1-7 


3-3 


5-o 


6.7 


8.4 


80.0 


81.7 


3-4 


25.1 


66.7 


— 


90.0 


9.8 


1.6 


3-3 


4.9 


6.7 


8.4 


80.1 


1.8 


3-5 


5-2 


27.9 


70.6 


— 


2 


71.4 


3-2 


4.8 


6.6 


8.4 


80.2 


1.9 


3-6 


5-3 


7-i 


30.7 


74-1 


— 


4 


72.8 


74-7 


76.4 


78.2 


80.0 


81.8 


83.6 


85.3 


97-1 


88.9 


133-4 


177.7 


— 


6 


4.4 


6.3 


8.1 


9.9 


1-7 


3.5 


5-3 


7-2 


8.9 


90.8 


36.2 


81.6 


— 


8 


5.9 


7-7 


9-7 


81.4 


3-3 


5-2 


7.o 


8.8 


90.7 


2.6 


38.9 


85.1 


— 


100.0 


9.8 


81.7 


83.6 


5-6 


7-5 


9.4 


91.4 


93-4 


95-3 


7-2 


45-9 


94-4 


— 


05 


83-5 


5-6 


7-6 


9.6 


91.7 


93-7 


5-7 


7-8 


9.8 


101.9 


52.8 


203.7 


— 


10 


87.3 


89.4 


91.6 


93-7 


95-8 


97-9 


100. 1 


102.2 


104.4 


106.5 


159.8 


212.9 


— 


15 


91.2 


93-4 


5-6 


7-8 


100.0 


102.2 


04.5 


06.7 


08.9 


11.8 


66.7 


22.2 


— 


20 


5-o 


7-3 


9-7 


101.9 


04.2 


06.5 


08.9 


11. 2 


13-5 


15.6 


73-7 


31-4 


— 


125.0 


8.8 


101.2 


103.6 


05-9 


08.4 


10.7 


13. 1 


15.5 


17.9 


20.2 


80.5 


40.7 


— 


30 


102.5 


05.0 


07.5 


10.0 


12.5 


15-0 


17.5 


20.0 


22.5 


25.0 


87.5 


50.0 


— 


35 


106.3 


108.9 


111.5 


114. 2 


116. 7 


H9-3 


121. 9 


124.4 


127. 1 


129.8 


194.5 


259.2 


— 


40 


11. 2 


12.9 


15.5 


18.2 


20.8 


23-6 


26.2 


28.9 


31.7 


34-3 


201.5 


68.5 


— 


45 


14.0 


16.7 


19.5 


22.3 


25.0 


27.8 


30.6 


33-4 


36.2 


38.9 


08.5 


77-7 


— 


150.0 


17.8 


20.6 


23.5 


26.3 


29.2 


32.1 


34-9 


37-8 


40.8 


43-6 


15-4 


87.0 


— 


55 


21.5 


24-5 


27.4 


30.4 


33-4 


36.4 


39-4 


42.3 


45-2 


48.2 


22.4 


96.3 


— 


60 


25-3 


128.4 


I3I.5 


134-4 


137.6 


140.6 


143.8 


146.8 


149.8 


152.8 


229.3 


305.5 


— 


65 


129. 1 


32.3 


35-4 


38.5 


41.7 


44-9 


48.0 


51.2 


54-3 


57-4 


36.2 


14.8 


— 


7o 


32.9 


36.1 


39-4 


42.5 


45-8 


49.0 


52.2 


55-5 


58.8 


62.0 


43.o 


24.0 


— 


I75-0 


36.8 


40.0 


43-4 


46.8 


50.0 


53-4 


56.8 


60.0 


63-4 


66.8 


50.0 


33-3 


— 


80 


40. s 


439 


47-4 


50.8 


54-2 


57.7 


61.0 


64.5 


67.9 


71.4 


56.9 


42.6 


— 


85 


144.4 


147.8 


ISI.4 


154.9 


158.4 


161.9 


165.4 


168.9 


172.4 


176.0 


263.9 


351.8 


— 


90 


48.1 


51.8 


55-3 


58.9 


62.5 


66.2 


69.8 


73-4 


77.0 


80.5 


70.8 


61. 1 


— 


95 


51.8 


55.6 


59-3 


63.0 


66.8 


70.4 


74.1 


77-8 


81.4 


85.2 


77-7 


70.3 


— 


200.0 


59.5 


63.4 


67.3 


71.1 


75.o 


78.9 


82.8 


86.7 


90.5 


94-5 


91.6 


88.9 


— 


10 


67.0 


71.2 


75-2 


79-3 


83.4 


87.5 


91.5 


95-6 


997 


203.7 


305.5 


407.4 


— 


20 


174-7 


178.9 


183.3 


187.5 


191.8 


196.0 


200.1 


204.4 


208.8 


213-0 


319.4 


425.9 


— 


30 


82.2 


86.8 


91.1 


95-5 


200.0 


204.5 


08.8 


13.3 


17.8 


22.2 


33-3 


44.4 


— 


40 


89.8 


94-5 


99.0 


203.7 


08.3 


13.0 


17.5 


22.2 


26.8 


31-5 


47.1 


62.9 


— 


250.0 


97.4 


202.3 


207.0 


li.g 


16.6 


21.6 


26.3 


3I-I 


36.0 


40.8 


61.0 


81.5 


— 


60 


205.0 


10.0 


15.0 


20.0 


25.0 


230.0 


35-0 


40.0 


45 -o 


50.0 


75.o 


500.0 


— 


7o 


212.7 


217.8 


223.0 


228.2 


233.3 


238.6 


243-7 


248.9 


254-1 


259.2 


388.7 


5i8.5 


— 


80 


20.2 


25.6 


30.9 


36.3 


41.7 


47.1 


52.4 


57-8 


63.2 


68.5 


402.7 


37.o 


— 


90 


27.8 


33-4 


38.9 


44-5 


50.0 


55-6 


61. 1 


66.7 


72.3 


77-8 


16.5 


55-5 


— 


300.0 


35-4 


41.2 


46.9 


52.6 


58.3 


64.2 


69.8 


75-6 


81.3 


87.0 


30.4 


74.0 


— 


10 


43 -o 


49.0 


54-8 


60.8 


66.7 


72.7 


78.5 


84.4 


90.4 


96.3 


44-3 


92.6 


— 


20 


250.6 


256.7 


262.8 


268.9 


275.0 


281.2 


287.2 


293-3 


299-5 


305.5 


458.2 


611. 


— 


30 


58.2 


64-5 


7o.7 


77-1 


83.3 


89.7 


95-9 


302.2 


308.5 


14.8 


72.1 


29.6 


— 


40 


65.7 


72.3 


78.7 


85.2 


91.7 


98.2 


304.6 


11. 1 


17.6 


24.1 


85.9 


48.1 


— 


35o.o 


73-3 


80.1 


86.7 


93-4 


300.0 


306.8 


13-3 


20.0 


26.7 


33-o 


99.8 


66.0 


— 


60 


80.9 


87.9 


94.6 


301.5 


08.3 


15-3 


22.0 


28.9 


35-8 


42.6 


513.7 


85.2 


— 


70 


288.5 


295.6 


302.6 


309.7 


316.7 


323.8 


330.7 


337-8 


344-8 


351-8 


527.6 


703.6 


— 


80 


96.1 


303.4 


10.5 


17.8 


20.0 


32.3 


339-4 


46.7 


53-9 


61. 1 


41.5 


22.2 


— 


90 


303.7 


111 


18.5 


25-9 


33-3 


40.7 


48.1 


55-5 


62.9 


70.3 


55-5 


40.6 


~~ 


400.0 



250 



OFFICE PRACTICE 



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CONVERSION TABLE 251 

Overhaul. 

If dirt must be hauled more than a stated distance (free haul) 
to place it in fill, the additional distance is called overhaul and 
is paid for at an agreed rate; the amount of overhaul is estimated 
as the (number of cubic yards that have to be overhauled) X 
(the distance beyond the free haul expressed in stations, that is 
units of 100 ft.). That is, if 20 cu. yds. had to be hauled 3,000 ft. 
when the free haul was 2,000 ft., the overhaul would be expressed 
as 10 stations X 20 yds. 

Overhaul is to be avoided if possible, as it is a source of 
dispute between Contractor and Engineer. Where necessary 
it can often be computed from an inspection of the earthworks 
computation sheets. If the cut from which th£ dirt is drawn is 
short and well defined and the fill to which it is taken is likewise 
well defined, the position of the centers of gravity of both cut 
and fill can be located sufficiently close by inspection; however, 
if two or three cuts are hauled to one fill or one cut to more 
than one fill, the amount and length of overhaul can only be 
determined with accuracy by means of a mass diagram. 

In Fig. 64 an earthwork chart is given which was prepared 
for the Batavia-Buffalo road, State Route 6, Sections 10 and 11. 
This chart gives amount, location, direction, and length of haul 
for excavation at a glance, and as an example of overhaul. has 
been illustrated on the diagram this will indicate the method. 

Explanation of Fig. 64, page 253 . 

1. The horizontal scale represents stations along road: in 
this case 5 stations or 500 ft. to the inch. 

2. The vertical scale represents the algebraic sum of the exca- 
vation and embankment on whose vertical the amount is plotted. 
In this case 200 cu. yds. to the inch. 

3. Reading from left to right, all ascending lines indicate 
amount and location of excavation; all descending lines indicate 
amount and location of embankment. 

4. All embankment quantities in each balancing section were 
multiplied by the factor written above that section as " Balance 
Used." 

5. The excavation and embankment quantities at each station 
were added together algebraically, after the embankment 
quantities had been increased as specified; the algebraic sum so 
obtained was then added algebraically to the sum similarly 
obtained from previous sections. 

6. This diagram indicates the amount of material that should 
be excavated or deposited at each station. 

7. The diagram indicates the direction of haul. 

8. To compute overhaul consider the section A B C D E A. 
Suppose free haul is to be 500 ft. Find where a line 500 ft. long 
will fit the section. B D is such a line. The material above B D 
will be hauled free. 



252 



OFFICE PRACTICE 



On material A B there will be paid overhaul. The average 
distance the material A B will be hauled will be the distance 
between the centers of gravity of A B and D E respectively. 

Let X represent that distance. Then X minus 500 ft. equals 
the average length of overhaul. 

9. The overhaul can also be computed from the area of the 
section A B D E A; this area represents the product of the 
material excavated in yards and the distance hauled. Find the 
area of the section A B D E A by a planimeter or otherwise. 
This area will be expressed as yard stations, and when divided 
by the ordinate G B in cubic yards will give the length of haul in 
stations. 

Suppose the area A B D E A equals 2.5 square inches. Each 

square inch represents 200 cu. yds- X 5 stations, or 1,000 sta. yds. 

Therefore, an area of 2.5 square inches would represent 2,500 sta. 

yds. According to the diagram the total amount of dirt hauled 

equals 280 cu. yds. as measured on the ordinate GB. Therefore 

1 i r i • o 1 1 2,500 sta. yds. 

the average haul for this 280 cu. yds. equals -^—. — = 8.0 

280 cu. yds. 

stations. 

The free haul equals 500 feet, or 5 stations, therefore the overhaul 

equals 8.9 — 5 = 3.9 stations. The amount of overhaul equals 280 

cu. yds. X 3-9 = 1092 sta. yds. 

Table 39. * Giving the Number of Pounds of Stone per 100 

Feet of Road for Different Depths of Loose Spread 

and Different Weights of Stone 

12-foot road 



Weight of 

1 cu. yd. 

Stone, Loose 

Measure 


Depth of Loose Spread 


2\" 


?>\» 


3l" 


Si" 


6\» 


2250 
2300 
2350 
2400 

2450 
2500 
2550 
2600 


20,800 
21,300 
2 1 ,800 
22,200 

2 2 , 70O 
23,200 
23,600 
24,IOO 


26,000 
26,600 
27,IOO 
27,700 

28,200 
28,800 
29,400 
30,000 


32,300 
33,000 

33 , 7oo 
344oo 

35,2oo 
35,900 
36,600 
37,300 


43,700 
44,700 
45,7oo 
46,700 

47,700 
48,700 
49,600 
50,600 


54,200 
55,300 
56,600 
57,800 

59,000 
60,200 
61,400 
62,600 



1 Note. — The quantities in this table are figured by slide rule but are sufficiently 
close for the purpose to which the table is put. 



EARTHWORK CHART 



253 



OK 




254 



OFFICE PRACTICE 

Table 39. — Continued 



14-FOOT ROAD 


Weight of 




Depth of Loose Spread 




1 cu. yd. 
Stone, Loose 






















Measure 


2\» 


3i" 


3l" 


S\» 


6f" 


2250 


24,300 


30,400 


37,7oo 


51,000 


63,200 


2300 


24,800 


31,000 


38,500 


52,200 


64,600 


2350 


25,400 


31,700 


39,3oo 


53,300 


66,100 


2400 


25,900 


32,400 


40,200 


54,400 


67,500 


2450 


26,400 


33,000 


41,000 


55,6oo 


68,900 


2500 


2 7,000 


33,700 


41,800 


56,700 


70,300 


2550 


2 7,600 


34,4oo 


42,700 


57,800 


71,600 


2600 


28,IOO 


35,ioo 


43,5oo 


59,000 


73,ooo 






15-FOC 


)T ROAD 






2250 


26,000 


32,600 


40,400 


54,700 


67,700 


2300 


26,600 


33,2oo 


41,300 


55,900 


69,200 


2350 


27,200 


34,000 


42,200 


57,200 


70,800 


2400 


2 7,800 


34,7oo 


43,IOO 


58,400 


72,200 


2450 


28,400 


35,4oo 


44,000 


59,600 


73,800 


2500 


29,000 


36,100 


44,800 


60,800 


75,200 


2550 


29,500 


36,900 


45,800 


62,000 


76,700 


2600 


30,100 


37,600 


46,700 


63,200 


78,200 






16-FOC 


>T ROAD 






2250 


27,800 


34,7oo 


43,!oo 


58,400 


72,300 


2300 


28,400 


35,5oo 


44,000 


59,600 


73,900 


2350 


29,000 


36,300 


45,ooo 


60,900 


75,5oo 


2400 


29,600 


37,ooo 


45,900 


62,200 


77,200 


2450 


30,200 


37,800 


46,900 


63,600 


78,700 


2500 


30,900 


38,600 


47,800 


64,900 


80,300 


2550 


31,500 


39,400 


48,800 


66,200 


82,000 


2600 


32,IOO 


40,100 


49,800 


67,400 


83,600 



The computation of earthwork is the longest operation of the 
quantity estimate. When this is finished the quantity estimate 
is considered as practically complete. 







YARDS OF 


MACADAM 


PER 


100 FEET 


255 


Table 40 


Giving the Number of Cubic Yards 


of Macadam 




PER IOC 


> Feet of Road for Different Widths 


and Depths 






Depth 








Width 

of 

Macadam 






























2" 


2\» 


3" 


zh" 


4" 


5" 


6" 


r 


10' .... 


6.17 


7.71 


9.26 


10.80 


12.34 


15.43 


18.52 


21.61 




12' .... 


7.41 


9.26 


II. II 


12.96 


14.82 


18.52 


22.22 


25.93 




14' ... • 


8.64 


I0.80 


12.96 


15.12 


17.28 


2I.6l 


25.92 


30.25 




15' .... 


9.26 


11.58 


13.89 


16.20 


18.52 


23.16 


27.78 


32.41 




16' .... 


9.88 


12.35 


I4.81 


17.28 


19.76 


24.70 


29.63 


34-57 




18' .... 


11. 11 


I3.90 


16.67 


19.44 


22.22 


27.79 


33-34 


38-89 




20' .... 


12.35 


15.44 


18.52 


21.60 


24.70 


30.87 


37.04 


43.21 




22' .... 


13.58 


16.98 


20.37 


23.76 


27.16 


33.96 


40.74 


47-53 



The other quantities figured are: length of road in miles. Table 
38 converts lineal feet to miles. 

Quantities of macadam, sub-base, concrete paving foundations, 
square yards of resurfacing, which are simple computations involv- 
ing length, width, and depth: Tables 39, 40, and 41 can be conven- 
iently used. 

Quantities of oil or other surface or penetration treatments, which 
are usually specified as gallons, per square yard: Table 42 is developed 
with this in view. 

Concrete for culverts or retaining walls. Where a large amount 
of work is done it generally pays to compile a table of quantities 
for standard culverts of different sizes and lengths. The quan- 
tities can then be picked from these tables sufficiently close for a 
preliminary estimate. There would be no object in including in a 
book of this character any table suitable for certain culverts, as each 
department has a different standard. 

Expanded metal and reinforcing bars, Tables 15 and 16 cover 
these features. 

Weights of cast-iron pipe: Table 14 can be used. 

Incidentals requiring ordinary arithmetical computations only. 

The quantity estimated being completed, the estimate of cost is 
made. This is considered in chapter X. 



Final Design Report 

On the completion of the design a report of this nature is filed for 
reference. 



256 OFFICE PRACTICE 

Rochester, January 31, 19 16 
REPORT ON DESIGN AND ESTIMATE 
of the 
VARYSBURG-WARSAW PART II COUNTY HIGHWAY 

No. 1349 
WYOMING COUNTY 
(FORMERLY known as the Orangeville-Warsaw Road) 
Length, 4.74 Miles 

Type of Construction. Top: From Orange ville Center to 
Corporation line Village of Warsaw (Sta. 0+00 — 249 + 57) 3" 
waterbound macadam 14' wide. Imported limestone top and 
screenings, surface application of calcium chloride using 2^# per 
sq. yd. in two applications. 

Bottom: Orangeville Center Sta. 0+00 to corporation line Village 
Warsaw Sta. 249 = 57, 5" macadam 14' wide. Screened gravel local. 
Section 26' wide with 18" ditch. 

Estimated Cost $49,858.00 

Engineering and Contingencies 5,042.00 

$54,900.00 
Cost per Mile $11,600.00 

Survey. By H. TenHagen, rodman, Spring, 1915. Weather con- 
ditions favorable. 

Design. By F. W. Mills, Leveler. 

Field Inspection. By George A. Wellman, County Assistant; 

F. W. Mills, Leveler. 

Estimate. By George A. Wellman, County Assistant; George 

G. Miller, Chief Draughtsman. 

Status and Connections. This road is a section of the old Cherry 
Valley Trail which is claimed to be the shortest highway between 
Buffalo and New York. It is the beginning of a system of improve- 
ments to connect the western part of Wyoming County with Warsaw. 
At Halls Corners (Sta. 145 + 00) it will connect by a proposed 
County System road with the east end of C. H. 1267. With the 
proposed Varysburg- Warsaw Part I Road and proposed Route 19 it 
will connect with Route 16 already built. It will also connect with 
the proposed County System road south through Johnsonburg, 
North Java, to Arcade. 

Foundation Soil. Is for the most part clay loam and is very 
unstable when wet. This calls for an unusual estimate for sub-base. 

Traffic. The heaviest traffic is eastward and down hill. It con- 
sists principally of wagon hauled farm traffic. There is considerable 
automobile traffic both ways. This will greatly increase as the high- 
ways West towards Buffalo are improved. 

Grades. The ruling grade for eastbound traffic is 8% between 
Sta. 23+00 and 29+00. The ruling grade in the opposite direction 
is a short 8.54% at Sta. 149. 



FINAL DESIGN REPORT 257 

Alignment. The alignment is generally straight and curves easy. 
The minimum radius is 573' at Sta. 162+00. 

Right of Way. No land taking is necessary. 

Type of Metaling. The bottom course throughout the entire 
length of the road is to be of screened gravel as per B. R. sample 
G-2095 5" deep, to be obtained on the property of Henry Roth, one 
mile south of Sta. 145+00. 

Top course is to be 3" imported limestone from Buffalo Crushed 
Stone Co. with screenings from same source. 

Drainage. All existing culverts have been replaced by either 
concrete or cast-iron pipe structures. The former have been given 
preference wherever head room permitted. 

The bridge at Sta. 15+40 is to be rebuilt by the Town of Orange- 
ville and that at Sta. 175 + 19 by the Town of Warsaw. 

Materials 

The materials suitable to be used in the work have all been tested 
and accepted by the Department. The filler for the bottom course 
to be the fine material screened out at the pit. 

Sand for use in concrete has been accepted from the Roth pit, 
one mile south of Sta. 145+00. 

Unloading Points. Erie R. R. at Warsaw Station siding, 1200' 
from Sta. 249+57- Respectfully submitted, 

Perry Filkin, 

Division Engineer 

Construction Plans. The construction plans should give suf- 
ficient information to show the contractor what he is expected to do and 
to enable the constructing engineer to stake out and to build the road. 

A finished set of plans consist of a map, profile, and cross-sections 
showing the alignment in relation to the preliminary survey line, the 
proposed grade elevations, the shape of the finished road, the widths 



Fig. 65 

and depths of road metaling, the crowns to be used, the existing struc- 
tures and the proposed structures, and all the minor points of design. 
Each Department has its own method of giving this information, 
and it makes little difference how it is shown so long as it is complete 
and clear. In general it may be said that the scales used are the same 



258 



OFFICE PRACTICE 



as in mapping the preliminary survey and that the size of sheets 
or rolls must be convenient to handle in the field; sheets larger than 
24 ,/ X3o // are clumsy. 

Miscellaneous Points. A point often overlooked in lying a 
grade line is the proper approach to a railroad grade crossing where 
the track is on a curve and has a superelevated rail. Where the road 
grade is level, or nearly level, the solution is comparatively simple, 
as shown in Fig. 65; but where the grade of the road is in an opposite 
direction to the elevation of the rail it is more difficult and sometimes 
impossible to make an easy riding crossing. 



^ Edge of Macadam 




Fig. 66 

Also, where a road, on a steep grade, crosses the railroad track 
on a large skew angle, care must be taken to flatten the grade nea,r 
the track to avoid distorting the road section due to the difference 
in the rate of grade of the track and road. See Fig. 66. 

Grade Crossing Eliminations. In grade crossing elimination 
designs the following minimum clearances have been adopted, Div. 
5, N. Y. S. Dept. of Highways. 

Where a highway is to be built under a railroad the crown eleva- 
tion is made 13.5' below the bottom of the bridge girder, and the 
minimum right-angle distance between abutments is taken as 26 
feet. For solid floor railroad through girder bridges a clearance of 
1 3.5' below the bottom of the girder means a distance of from 16.5' 
to 1 7.0' below the top of the rail. 

The tables (pp. 259, 260) are taken from Spofford's " Theory of 
Structures," and a pamphlet issued by Heath & Milligan, of Chicago. 
They show the approximate weight of through girder railway bridges 
with the depth of floor system. They are useful for preliminary 
estimates of grade-crossing elimination. 

The weights given are for the steel only; the weight of the floor 
system must be added. For purposes of a rough prelim inary esti- 
mate of cost the superstructure can be assumed to cost $60.00 per 
ton in place including all erection costs. 

Where the highway crosses over the railroad a minimum clearance 
of 21.0' is used from the top of rail to the bottom of the highway 



GRADE CROSSING ELIMINATIONS 



259 



bridge; the span varies with the number of tracks. In determining 
the length required it is best to get in touch with the railroad engineers. 

Right of Way Computations. The form of traverse computa- 
tion and closure was shown on page 155. 

The areas of rights of way are generally figured by dividing the 
parcel into rectangles, trapezoids, triangles, sectors, or segments, 
and figuring these shapes from the formulae given in Table 57. These 
areas are checked by planimeter. They are usually figured to the 
nearest 0.01 acre. 




260 



OFFICE PRACTICE 



The method of double-meridian distances can, however, be used 
if desired. The following formula and example are given to illustrate 
this method. It is not often necessary and is a tedious computation : 

The rule is: 

Twice the area of the figure is equal to the algebraic sum of the products 
of the double-meridian distances of each course multiplied by its latitude. 

In which the double-meridian distance equals the sum of the 
meridian distances of the two ends of each course referred to the 



THROUGH PLATE GIRDER SPANS, STRINGER FLOOR. 
WEIGHTS, DIMENSIONS, ETC. 




1^ 



Base of Rail 



I I I I 



Low Iron 



771(77ZW7777777777777777777777777777} 
• Top of Masonry 

LOADING-COOPER'S E. 60 

Total end Shear is given in 
thousands of pounds per 
rail and includes both 
live and dead loads. 



230,000 
220,000 
210,000 

200,000 

190,000 




270,000 

260,000 

250,000 

210,000 



130,000 
120,000 
110,000 



90,000 
80,000 



Erector's Note. 
W= Total weight of one 
single track span with two 
light girders. 



45 



14L7 



50 



156.0 



55 



167.5 



3'4' 



3'11" 



60 



176 3 



65 '• 



191.1 



3'4^" 



70 



204.7 






75 



220.4 



5'0' 



80 



232.8 



85 



248.6 



c u 

o <u 

o t 

o bo 



2 ^ 

O T3 



© 

3 a 

cm +■> 

O « 

s * 

& O 

ID O 



90 



262.3 



3'5' 



30' to 50' 



.24 W 



.42 W 



.52 W 



95 



277 4 



100 



291.2 



3'6' 



55' to 80' 



25 W 



.46 W 



50 W 



110 



319 6 



85' to 110' 



:s w 



.51 W 



.44 W 



RIGHT OF WAY AREAS 



261 



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262 



OFFICE PRACTICE 



meridian drawn through the most westerly point of the parcel, 
and the latitude of each course is reckoned as plus if the course 
runs north and minus if it runs south. Take as an example the 
right of way parcel shown in Fig. 50, page 155, for which the traverse 
has been figured and refer the meridian distances to the meridian 
drawn through the corner 3.1' distant from station 194+ 71.7. 




Parabolic Crowns for . Pavements. 

It is often convenient to have the following data on parabolic 
crown ordinates in making templets for pavement work. 

Divide the distance from the center of the road to the curb or 
edging into ten equal parts and call the total crown 1.0; the dis- 
tance down to the surface of the pavement from the crown elevation 
at each of these ten points expressed in terms of the total crown will 
be 

Center of Road, point No. o o . 00 

1 0.01 

2 o . 04 

3 0.09 

4 0.16 

5 025 

6 0.36 

7 0.49 

8 0.64 

9 0.81 

Curb point 10 1 .00 



fointio 



Curb 







SUMMARY OF POINTS 



263 



Summary of Points to be Considered in Making an 
Economical Design 

Justifiable economy in grading is limited to the intermediate grades 
and to variations in the cross-sections. A well designed road in these 
particulars may easily save $700 to $900 per mile over a careless design. 

Economy in widths of hard paving is attained by the selection of 
a width suitable to each particular road or part of road. A uniform 
width of 16 ft. for all roads is unnecessary and a waste of money both 
in first cost and in maintenance and renewal. For class I and II. 
traffic nothing less than 15' to 16' should be considered; for class 
III and IV the widths may vary from io' up. The cost per ft. width 
per mile for different types is approx. as follows: 

Type of Road . f ir ^ ost P er .. 

J ^ foot width per mile. 

Brick $1200 

Asphalt 1 100 

Concrete 700 

Bituminous Macadam 600 

Waterbound " 500 

Economy in foundations is limited to utilizing local materials to 
their best advantage with short hauls. 

Economy in top courses lies in the selection of the cheapest type 
suitable to the traffic conditions and the use of the minimum thick- 
ness. 

Economy in maintenance is attained by preventing rather than 
by repairing damage. 

Table 41 

Square Yards per 100 Feet and per Mile eor Different Width 

of Surface 



Width 


Number of Square Yards 


Width 


Number of Square Yards 


Feet 


Per 100 Feet 


Per Mile 


Feet 


Per 100 Feet 


Per Mile 


8 


SS.S8g 


4,693 


26 


288.889 


15,253 


10 


in. in 


5,867 


28 


311.III 


16,427 


12 


*33-333 


7,040 


30 


333-333 


17,600 


14 


I55-556 


8,213 


32 


355-556 


^,773 


15 


166.667 


8,800 


34 


377-778 


19,947 


16 


177.778 


9,387 


36 


400.000 


21,120 


18 


200.000 


10,560 


3^ 


422.222 


22,293 


20 


222.222 


n,734 


40 


444.444 


23,466 


22 


244.444 


12,907 


42 


466.667 


24,640 


24 


266.667 


14,080 


44 


488,889 


25,813 



264 



OFFICE PRACTICE 



Q 

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lOO.OO 
I20.00 
I40.00 
I50.00 


160.00 
180.00 
200.00 
220.00 
240.00 


260.00 
280.00 
300.00 
320.00 
340.00 


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M tN tN tN tN 


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d 


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H H M M H 


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200.00 
211. II 

222.22 
233-33 
244.44 


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to •<+ tO\© O 


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GALLONS PER ioo FEET OF ROAD 



265 



9 

< 

>* 

w 
< 
0* 

C/3 

W 
M 

H 

O 
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1-) 

3 

< 
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w 

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00 


160.00 

200.00 
240.00 
280.00 
300.00 


O Q O Q O 

OOOOO 
dodo* 6 

MOO "tOO 

tO co t "* -t 


520.00 
560.00 
600.00 
640.00 
680.00 


720.0c 
760.00 
800.00 
840.00 

880.00 


N 


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CHAPTER X 

COST DATA AND ESTIMATES 1 

New methods of construction have so changed the cost of 
road improvements that engineers just going into this work, or 
those not familiar with present methods, are often handicapped 
in making estimates. 

The cost data given in this chapter has been gathered chiefly 
since 1907 and covers most of the items necessary for estimating 
the cost of any ordinary road improvement. Such data must be 
used intelligently or it will be misleading. Local conditions 
should always govern in making estimates, and in presenting 
costs it is best to describe the conditions under which the work 
was performed, leaving their special application to the one using 
the data. An engineer's estimate should represent the probable 
average bid price. In the following examples of actual cost 
those have been selected that are considered to be average cases. 
Contractors who have an unusually good plant and a well-or- 
ganized force can often do the work cheaper than is shown; on 
the other hand, those new to the work will spend more. 

Where machinery is used it is more satisfactory to include the 
items of depreciation, repairs, and interest in a lump-sum item 
for the whole contract than to try to reduce it to a yardage basis. 
These charges will be considered under the heading of " Plant 
and Pay Roll." 

BITUMINOUS AND WATERBOUND MADACAM CON- 
STRUCTION 

Cost of Earth Excavation. 

Table 43 shows the cost of earthwork on four roads in New 
York State, which represent easy, average, and difficult work. 
The cost per cubic yard includes excavation and placing in fill, 
shaping the subgrade for the stone, and trimming the shoulders 
and ditches. For heavy fills with short hauls wheeled scrapers 
were used, but the largest part of the work was done by wagons. 

Cost of Rock Excavation. 

The writer has no reliable personal data on ledge rock excava- 
tion. Rockwork on roads is usually a small item; the cuts are 
small and consequently expensive. Perhaps there is no item 
more variable in cost than small rock cutting. It is therefore 
safer to take as a basis of estimate the bids of experienced road 

1 Much of the data in this chapter was contributed by the author to the 
Engineering News and published July 13, 191 1. 

266 



EARTH EXCAVATION 



267 



to 

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268 COST DATA AND ESTIMATES 

contractors. The reports of the Massachusetts Highway Commis- 
sion and bids on New York State work show that prices for rock 
excavation range from $1.50 to $2 per cubic yard, for quantities 
up to 200 or 300 cu. yds., and $1.25 to $1.50 for larger quantities. 

Cost of Unloading Broken Stone. 

For making estimates of the quantity of stone required the 
following data on imported limestone used on Road 5,021 will 
be useful. The approximate sizes and actual weights of stone 
on this work were as follows: 

No. 1 Screenings, f inch screen 2,550 lbs. per cu. yd. 

No. 1 A Dustless screenings, f in. screen 

with dust jacket 2,350 " " " " 

No. 2, 1 in. screen 2,470 " " " " 

No. 3, 2 " " 2,350 " " " " 

No. 4, 3i" " •:•••: 2 ^ 2 ° " " " " 

For purposes of estimating the cost of handling imported 
crushed stone, the following weights for a cubic yard, based on 
railroad weights, will be used: No. 1, 2,600 lbs.; No. iA, 2,400 lbs.; 
No. 2, 2,500 lbs.; No. 3, 2,400 lbs.; No. 4, 2,400 lbs. 

Unloading Cars by Hand. 

On Road 5,021, with the author as engineer, a number of short 
time (10-hr.) estimates made the cost of unloading per ton $0.12 
to $0,135; and the cost per cubic yard $0.14 to $0.16. This 
work was in 1910, and labor cost $0,175 P er hour. The shoveling 
was done from a steel platform, where it was dumped from hopper- 
bottom cars. When shoveled from inside the cars the cost 
may run as high as $0.20 per cu. yd. The cost of shoveling is 
usually estimated at $0.15 per cu. yd. 

The time of loading 1^ cu. yd. wagons by hand shoveling will 
range from 8 to 12 minutes. 

Unloading Cars with Continuous Bucket Conveyor Elevator Plant. 

Where there is a large quantity of stone to be unloaded and it 
is not possible to install an elevator plant on the existing track, 
it often pays to put in a. switch. Six cars switches can be usually 
built for about $300.00. Where there are competing railroads no 
charge is usually made. 

The following data is from Road No. 5,046, season of 1910, 
with labor at $0,175 P er hour. The plant consisted of an 
ordinary continuous bucket conveyor operated by a 6 H.P. 
gasoline engine; the bin had a capacity of 100 tons. 

The average fuel consumption was five gallons of gasoline 
per day. Cost of fuel and oil averaged $1.00 per day. 

The average force at the elevator was one foreman and three 
helpers. 

A total of 4,670 tons, or 3,890 cu. yds., was unloaded at $0,084 
per ton, or $0,101 per cu. yd. 



UNLOADING 269 

The cost was divided as follows: 

Setting up elevator at Scottsville .... $ 60.00 

" Mumford 40.00 

" Wheatland .... 75-oo 

Labor of operation 194.00 

Gasoline and oil 25.00 

Total $394.00 

This method of unloading is not only cheaper than hand 
methods but also cheapens the cost of hauling, as no time is lost 
in loading the wagons. The time of loading a \\ cu. yd. wagon 
from bins ranges from 45 to 55 seconds. There is also a saving 
in car demurrage if the bin holds two or three car-loads. 

Elevator unloading saves about #0.04 per cu. yd. on team time 
and about #0.05 on the unloading, making a total saving per 
cubic yard of about #0.09. It usually costs about $150 to ship 
the plant and install it the first time, so elevator unloading is 
not adopted unless there are, at least, 2,000 cu. yds. of stone 
handled. 

Unloading Cars from Coal Trestle. 

This data is taken from the Scottsville road repair work, 
Mr. Harold Spelman, Engineer, season of 1910; labor at $0.20 
per hour; average force, two or three men. A total of 4,400 tons 
was unloaded. The cost divided as follows: 

Rent of trestle $125.00 

Labor 232.00 

Total $357.00 

Cost per ton 0.081 

" " cu. yd 0.098 

Unloading from Canal Boats. 

The plant used consisted of a portable bin and a horse-operated 
derrick; Road 5,014; Mr. James Anderson, contractor. The 
average amount of stone unloaded per day was 150 tons. The 
cost was $0,115 P er ton j or $0.14 per cubic yard, divided as 
follows : 

1 team and driver $ 4.00 (10-hour day) 

1 foreman 2.50 " 

6 laborers, at $1.75 per day .... 10.50 " 
Total $17.00 " 

Cost of Hauling Broken Stone. 

Table 44 shows the cost of hauling stone on good roads as for 
repair work. The wagons were loaded from bins, so no time was 
lost in loading. 



a 
a tt 



270 COST DATA AND ESTIMATES 

Table 44. — Haul of Stone on Good Roads for Repair Work 



Road 
No. 



Engineer in Charge 



Harold Spelman 
Harold Spelman 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 
G. G. Miller 



Price per 
Hour of 
Teams 


Length 

of Haul, 

Miles 


$0.50 


1.8 


0.50 

0.62 


1.2 

2.0 


0.62 


1-7 


O.62 


1.1 


O.62 


0.6 


O.62 


0.2 


O.62 


3-o 


. 0.62 


2-75 


O.62 


2-5 


0.62 


2.0 


0.62 


i.75 


O.62 


i-5 



Cost 

per Ton, 

Mile 



$0.20 
0.24 
O.20 
O.215 
0.23 
0.25 
0.50 
0.17 
O.I75 
O.I75 
O.19 
0.215 
O.23 



Cost 

per Yard, 

Mile 



$0.24 
O.288 
O.24 
O.26 
O.275 
0.30 
O.60 
0.205 
O.21 
0.21 
0.23 
O.26 
O.28 



Road No. 1, 10-hour day. 

Roads No. 2 and 3, 8 hours per day. 

Note. — Cost per ton mile on Roads No. 2 and 3 equals the 
cost per yard mile, for teams at $0.50 per hour. 

For hauling on bad roads for new construction I have the fol- 
lowing personal data: 

Clover Street Road, Section 1, season 1908; teams at $0.45 
per hour; dump wagons loaded from bins; no time lost. 
6,000 cu. yds., 0.6 mile haul cost 26 cts. per ton, or 31 cts. per 

yard mile. 
4,500 cu. yds., 0.6 mile haul, cost 24 cts. per ton, or 29 cts. per 

cubic yard mile. 

Scottsville-Mumford Road, season of 191 1; teams, $0.45 per 
hour. 300 cu. yds., 1 mile haul (including a 5 per cent sandy 

hill 1,200 ft. long) cost $0.30 per yard mile. 
500 cu. yds., 0.5-mile haul (level road in bad condition) cost 

$0.30 per yard mile. 

Hauling Field Stone and Filler. This material was hauled 
from fields and pits where it was loaded by hand, and considerable 
time thus lost. 

On the Clover Street Road, Section 1, season of 1908, with 
the author as Engineer, and teams at $0.45 per hour, 10,000 cu. 
yds. of field stone were hauled an average of one mile for $0.36 
per yard mile. 

On the Scottsville-Mumford Road, season of 191 1, with the 
author as Engineer, and teams at $0.45 per hour, 500 yds. of 
field stone were hauled 0.2 mile at $0.14 per cu. yd., or $0.70 
per yard mile. On the. same work 200 cu. yds. of filler was 
hauled 0.2 mile for $0.15 per cu. yd., or $0.75 per yard mile. 



COST OF SPREADING 271 

For all short hauls under J mile the cost is high and practically 
the same on account of the larger percentage of time lost in 
loading. 

Mechanical Hauling. This method has not come sufficiently 
into general use to be considered in estimating, in the writer's 
opinion, unless it is difficult to get teams. It rarely pays to 
use traction engines for less than a three-mile haul, even on a 
hard road. In case they are used a light engine or road-roller 
and a train of ordinary dump wagons are more satisfactory than 
a heavy engine and large 5 or 7 cu. yd. cars. For maintenance 
and repair work, however, some style of automobile truck will, 
doubtless, be used in the near future. Under favorable cir- 
cumstances mechanical hauling will cost about 12 to 15 cents 
per yard mile. 

Cost of Loading Local Fence Stone into Wagons. 

Road No. 5,046, W. G. Harger, Engineer, season of 191 1, 
Labor $0,175 P er hour. 
2,200 cu. yds., boulders loaded at a cost of $0.14 per cu. yd. 

A gang of six men will take from 9 to 13 minutes in loading i| 
cu. yds., depending upon the size of the stone. 

Road No. 495, E. E. Kidder, Engineer, season of 191 1, 
Labor, $0,175 P er hour. 
1080 cu. yds., boulders loaded at a cost of $0,184 per cu. yd. 

Road No. 492, E. E. Kidder, Engineer, season of 191 1, 
Labor $0,175 per hour, 300 cu. yds., loaded at $0,137 per cu. yd. 

COST OF SPREADING STONE AND BINDER 

Table 45, page 272, gives the cost of spreading broken stone 
on several New York State roads. 

The ratio of the loose to the rolled depths varies with the size 
of the fragments and the depth of the course. Table 46, page 
272, gives the averages of the results obtained from 1,000 test 
holes made by the writer on three separate roads. The last 
column of the table also gives the weights of No. 3 and No. 4 
stone required to make a cubic yard of rolled macadam. The 
amount of filler or binder per cubic yard of rolled macadam is 
given in Table 47, page 272. 

The excessive amount of filler required for the 2-inch bitumi- 
nous macadam, Table 47, was due to a layer of screenings placed 
under the No. 3 stone, all of which did not act as a filler. The 
small amount required for the 3-inch bituminous macadam was 
due to the fact that the bituminous binder partially filled the 
voids before the screenings were applied. 

The ratio of loose to rolled depth for boulder sub-base is 
variable. 

If the size of boulders is practically the same as the depth of 
the course, that is, if there is only one layer of stone, the loose 
depth and the rolled depth will be the same. Where there are 



272 



COST DATA AND ESTIMATES 



two or three layers of boulders the ratio is, approximately, 
1:1.25, i. e., a 12-inch, rolled depth would require 15-inch 
loose depth for boulder averaging 5 to 6 inches in diameter. 

Table 45. — Spreading Stone 



Refer- 
ence 
No. 


Engineer 


Labor 
Wage 


Depth of 
Loose 
Spread 


Amount 
Spread 


Cost 
per Ton 


Cost 

per Cu. 

Yd. 


1 


Harold Spelman . . 


$0.20 


4 in. 


7000 tons 


$0,066 


$0.08 


2 


W. G. Harger 


0.175 


5i in. 


6000 cu. yds. 


0.05 


0.06 


2 


W. G. Harger 


0.175 


4 in. 


4500 " " 


0.07 


0.083 


3 


W. G. Harger 


0.20 


6" 


1000 " " 


— 


0.05 






Placing sub-base stone 






3 


W. G. Harger 


0.175 


7 in. 


100 " " 


_ 


O.IO 


3 


W. G. Harger 


0.175 


10 " gravel 


200 " " 


— 


0.04 


4 


E.E.Kidder 


0.175 


6 " 


267 " " 


— 


0.07 


l 5 


E. E. Kidder 


0.175 


6 " 


1082 " " 


— 


O.I2 



Table 46. — Ratio of Loose to Rolled Depth 



Size of Stone 


Rolled Depth 


Loose Depth 


Ratio 


Weight per 

Cubic Yard 

Rolled Measure 2 


No. 4 

No. 4 

No. 3 

No. 3 


4 in. 

3 " 
3 " 

2 " 


5.2 in. 
3.8 " 

3-9 " 
2.4 " 


1-3 

I.27 

i-3 
1.2 


3120 lbs. 

3050 " 
3120 << 
2880 " 



Table 47. — Amount of Filler and Binder Required 



Kind of Course 


Kind of Filler 


Amount of Filler 

per Cu. Yd. of 
Rolled Macadam 


Weight of 
Screenings per 
Cu.Yd. of Roll- 
ed Macadam 


Bottom stone 

Waterbound top 3 . . . 
3-in. Bit. mac. top 3 . 
2-in. Bit. mac. top 3 . 
Sub-base 


Sand 

No. 1 

Nos. iA and 2 

No, iA 

Gravel 


0.35 cu. yds. 
0.50 " " 
0.37 " " 
0.60 " " 

o.33 " " 


1300 lbs. 
900 " 
1440 " 



1 Sub-base bottom course. The cost includes sledging of all large stone. 

2 Weight of cubic yard loose 2,400 lbs., as noted at the beginning of the chapter. 

3 Weight of cubic yard loose 2,400 lbs. Filler for top course includes wearing 
coat. 



COST OF SPREADING 273 

Cost of Loading Filler at Pit. On the Clover Street Road, 
Section 1, during the season of 1908, with the author as engineer 
and labor at $0.15 per hour, 400 cu. yds. of sand filler were loaded 
at a cost of $0.12 per cu. yd. On the Scottsville-Mumford 
Road, with labor $0,175 P er hour, 200 cu. yds. were loaded at a 
cost of $0.13 per cu. yd. 

Cost of Spreading Filler by Hand from Piles Spaced 20' to 30' 
Apart. On the Clover Street Road, Section 1, during the 
season of 1908, with labor at $0.15 per hour, 400 cu. yds. of 
sand filler were spread at a cost of $0.10 per cu. yd. On the 
Scottsville-Mumford Road, with labor at $0,175 P er hour, the 
cost of spreading 200 cu. yds. was $0.20 per cu. yd. This in- 
cludes some hand brooming, but most of the brooming was 
done by a broom attachment on the roller. 

Cost of Spreading No. iA and No. 2 Stone for Bituminous 
Macadam Top Courses and Brooming Same. A layer of No. 
iA, J inch deep, was spread over the bottom course. On this 
was spread 2^ inches of No. 3 stone. After rolling bitumen was 
poured over this course and a f-inch layer of No. 2 stone spread 
and rolled; the excess of No. 2 was broomed off and a f-inch 
wearing coat of No. iA placed. 

The cost of spreading for a 2-in. top was as follows: 

Cost of No. iA and No. 2 per cu. yd $0,282 

Cost per ton of No. iA and No. 2 0.210 

Eight hundred tons of this material were handled with labor 
costing $0,175 P er hour. 

For a 3-in. top course the procedure was the same, omitting the 
layer of No. iA under the No. 3 stone. The cost of handling 
400 tons for the 3-in. course was as follows: 

Cost per cu. yd of No. iA and No. 2 ... $0.31 
Cost per ton of No. iA and No. 2 0.26 

Cost of Spreading Screenings with Cross Dump Wagons. 
Wet dust screenings for waterbound macadam cannot be suc- 
cessfully spread in this manner. For spreading dry dust screen- 
ings, No. 2 stone or dustless screenings for bituminous macadam, 
this method has proved the cheapest and most satisfactory. 
On Road 5,046, season of 1910, a number of short-time estimates 
made the cost of spreading by this method about $0.06 per cu. yd. 
The cost of brooming is slightly increased over that required 
by the hand-spreading method, but not enough to counteract 
the advantage in the use of the wagon spreading. On the Clover 
Street Road, season of 1908, 1,000 cu. yds. of screenings were 
thus spread for about $0.07 per cu. yd. 

COST OF ROLLING 

In the following costs lubricating oil is not included, as no 
reliable data was obtained as to the quantity used. Gillette's 
" Handbook of Cost Data" gives this item as $0.30 per day; us- 
ing this amount would increase the costs given below from 0.2 to 
0.3 of a cent per cu. yd. The amount of coal used was variously 



274 COST DATA AND ESTIMATES 

estimated at from 450 to 500 lbs. per day. As before mentioned, 
items of depreciation, repairs of plant and equipment, and 
interest are not included in the cost per cubic yard of stone con- 
solidated. 

On Road 5,025, under Mr. E. E. Kidder, Engineer, during the 
season of 1910, the cost of rolling 3,400 cu. yds. of bottom stone 
and 1,700 cu. yds. of top stone, loose measure, was as follows: 

Rollerman, 4 months, at $90 $360.00 

Coal, J ton per day, at $2.70 per ton, 80 days . 55.00 

$415.00 

The time and cost were divided as follows: 

•§■ on subgrade . $ 69.00 

J on bottom stone 4" deep 138.00 

\ on bituminous top stone, 2" deep 208.00 

There was no cost for water. The roller worked 80 days in 
4 months. The cost of rolling per cubic yard of loose material 
was: bottom stone, $0.04, and top (bituminous macadam) $0.12. 

On Road 492, Mr. E. E. Kidder, Engineer, season of 1910, 
the cost of rolling 3700 cu. yds. of 4-in. bottom course was $0.03 
per cu. yd., and for 3,200 cu. yds. of waterbound top stone $0.05 
per cu. yd. Both quantities refer to loose measure. The roller 
worked 74 days in three months. The puddling was done by a 
pipe line and hose and brooms attached to the roller. The roll- 
erman's wages were $90.00 per month and coal $2.75 per ton. 

On Road 5,021 the cost of rolling a 3-in. bituminous top course 
per cubic yard of loose material was $0.09; for a 2-in. top $0.11. 

On Road 5,046 a roller working 111 days consolidated 
1,850 cu. yds. of field stone sub-base, 4,300 cu. yds. of bottom 
stone, and 2,150 cu. yds. of top stone, loose measure. The depth 
of the sub-base was 6 in. (rolled measure), the bottom course 4 in., 
and the top course 2 J in., bituminous macadam. The roller- 
man's wages were $90 per month and coal cost $2.75 per ton for 
J ton per day. There was no cost for water. The costs were 
divided as follows: sub-base, $0,035; bottom stone, $0,045; 
top stone, $0,105 P er cu - yd-, loose measure. 

COST OF CRUSHING STONE 

As a basis for all cost estimates for crushing, it is necessary to 
know something of the percentage of the different sizes of the 
crusher output. Table 48, page 275, gives the results of tests 
made by Mr. Archer White during the season of 1910 on or- 
dinary limestone and sandstone boulders composing the average 
field stone. The crusher used was the largest Acme portable 
crusher. The tailings were recrushed and the stone divided into 
four grades: No. 1, f-in. screen; No. 2, i|-in.; No. 3, 2^-in., and 
No. 4, 3^-in. From this data it may be seen that 1 cu. yd. of 
field stone makes 1 cu. yd. of crushed stone, and that it takes 
approximately 1.8 cu. yds. of field stone to make 1 cu. yd. 
rolled measure of sizes Nos. 3 and 4. The crusher toggle was 
set to produce both top and bottom stone sizes. 



SIZES OF CRUSHER RUN 



275 



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276 COST DATA AND ESTIMATES 

The cost. of labor was $0.20 per hour. The engineman of the 
crusher plant received $0.25 per hour and the foreman $0.30 
per hour. The field stone was loaded from a pile near the crusher 
into small dump cars running on a movable track. The loaded 
cars were drawn to the crusher by a small hoisting engine. The 
cost of bringing the field stone to the crusher pile is not included. 
The force loading consisted of one foreman, eleven laborers, and 
one engineman. The force crushing consisted of one foreman, 
four laborers, and one engineman. In eight days 1,500 cu. yds. 
were crushed. The cost of the entire output per cubic yard 
of loose measure was divided as follows: 

Loading stone for crusher $0,133 

Hauling to crusher 0.013 

Feeding to crusher 0.061 

Engineer to crusher 0.013 

Fuel and oil 0.030 

Loading crushed stone from bins 0.010 

Total $0,260 

Crushing Granite Hardheads and Sandstone. The following 
data is from the records of the Clover Street Road, Section 1, 
season of 1908. Labor cost $0.15 per hour and the engineman 
received $3 per day. The crusher used was a 10" X 20" Climax. 
A total of 5,000 cu. yds. of granite were crushed at a cost per 
cubic yard, loose measure, of $0.19; 7,000 cu. yds. of sandstone 
boulders were crushed at a cost of $0. 103 per cu. yd., loose measure. 
These figures are for the total output of the crusher and include 
the costs of feeding to the crusher, the pay of the engineman, 
coal, oil, but not the delivery to the crusher. On the Scottsville- 
Mumford Road under similar conditions the cost varied from 
$0.13 for granite and sandstone to $0.19 for granite hardheads 
per cubic yard of loose measure. 

Crusher force on the Clover Street and Scottsville-Mumford 
roads as follows: 

1 foreman $4.00 

5 men feeding crusher 2.00 each 

1 man tending screen 2.00 

1 engineer 3.00 

Fuel and oil 4-°° 

Where bottom stone alone is being crushed from local material 
the crusher is set to produce a larger amount of No. 4 stone, 
and the proportion of the screenings to the No. 3. and No. 4 size 
is different than given in Table 48. 

In the following data from Road 5,046, Scottsville-Mumford, 
mentioned above, the No. 3 and No. 4 and tailings _ were used 
as the bottom course stone, the tailings being broken into proper 
sizes after the stone was spread by knapping hammers. The 
cost of knapping will vary from $0.01 to $0.03 per cu. yd. of 



CRUSHING GRANITE AND SANDSTONE 277 

loose bottom stone, depending on the number of tailings pro- 
duced. When the crusher is set correctly to deliver a good grade 
of stone for bottom course, this charge should not amount to over 
$0.01 per cu. yd. of total output and is properly chargeable 
against crushing, which increases the crushing costs given above 
from $0.13 to $0.14 and from $0.19 to $0.20. 

The size of screens were f", i|", 2-|", and 3I". 

Crusher Set-up, No. 1. 60% Granite, 30% sandstone, 10% 
soft rock. 

Total screenings, No. 1 240 cu. yds. 

" No. 2 no record 

" No. 3, 4, and tailings i,5°o cu. yds. 

Crusher Set-up, No. 2. 50% granite, 40% sandstone, 10% 
soft rock. 

Total screenings 350 cu. yds. 

" No. 2 no record 

" No. 3, 4, and tailings 2,600 cu. yds. 

For this same road the amount of field stone required per 
loose yard of bottom stone is shown by the following figures. 
Approximately 1.5 yard loads were drawn to and from crusher. 



Date 


Number Loads of 
Field Stone Crushed 


Number Loads of 

No. 3 and No. 4 and 

Tailings Drawn from 

the Crusher 


1911 
April 24 


114 

86 

87 
104 
101 
106 

99 

86 

107 

no 

102 


93 
70 

69 
84 
82 

85 

78 
72 

95 

80 

83 


" 25 


^o 

" 26 


Mav c; 


" 6 


" 8 


" Q 


v 

" 10 


" 11 


" 12 


" IS--- 


Totals 


1 102 loads 
1653 cu.yds. 


891 loads 
1336 cu.yds. 



On this work 1.24 cu. yds. field stone produced 1 cu. yd. loose 
measure bottom stone, and 1.61 cu. yds. field stone produced 
1 cu. yd. bottom stone rolled measure. 



278 COST DATA AND ESTIMATES 

Table 48, page 275, gives 1.8 cu. yds. field stone to 1 cu. yd. 
rolled macadam, but this apparent difference is explained by 
the fact that the tailings were recrushed and the crusher set 
closer to produce top as well as bottom stone, consequently the 
per cent of No. 1 and No. 2 is higher than for the data just 
given. 

Data obtained by Mr. Frank Bristow, First Assistant Engineer, 
New York State Department of Highways, indicates that 1 cu. yd. 
of field stone produces 1.1 cu. yds. crushed stone when separated 
by screens of |" ', ij", 2'J", and 3J"; this is slightly more than the 
writer's experience has indicated. 

When local stone is crushed for bottom only, the screenings are 
used as filler for that course, and in a case of this kind it is neces- 
sary to know how much additional filler must be estimated. 
Take the case of the Scottsville-Mumford Road (crusher set-up 
No. 2) given above. Twenty-six hundred cubic yards loose 
measure will consolidate under the roller to approximately 
2,000 cu. yds. of rolled bottom stone. This will require 2,000 X 
o-35 = 7°° cu - yds. filler. The amount of screenings produced 
in crushing 2,600 cu. yds. of bottom was 350 cu. yds., showing 
that for cases similar to the one given, half of the total filler 
required must be obtained from other sources. 

Cost of Sledging Boulders. A certain percentage of the fence 
stone must be broken to reduce them to a proper size for crushing. 
This is done by blasting or sledging; where the boulders need to 
be broken only two or three times to reduce it to a usable size, 
sledging is the cheaper method. The cost of both of these 
methods is so variable that any cases cited would not be of much 
value. As given on page 260, under Standard Estimates, the 
author allows arbitrarily $0.40 per cu. yd. for all boulders actually 
sledged or blasted, and in making estimates the per cent to be 
treated in this manner is approximated roughly. 

As a matter of interest Gillette, in his cost data on rockwork, 
gives the cost of sledging small sandstone boulders as approxi- 
mately 0.05 per cu. yd., and the cost of mud capping at about 
0.35 per cu. yd. 

COST OF CRUSHING (continued) 

The following data is taken from the Report of the Massa- 
chusetts Highway Commission and refers to work done in 
Newton, Mass. The crushed stone was divided into the follow- 
ing sizes: 

Tailings 205 cu. yds 17-5% 

2\" stone 692 cu. yds 57 % 

Screenings and 1" . . 300 cu. yds 25.5% 

Totals 1197 100 % 

The material was cobblestones and labor probably cost $0.20 
per hour, teams, $0.45. The cost per cubic yard at the crusher 
was $0,445, or $0.33 per ton. 



CRUSHING GRANITE AND SANDSTONE 279 

The cost per cubic yard was divided as follows: 

Teaming to crusher $0.314 70.6% 

Feeding to crusher 0.033 7-4% 

Engineer of crusher ....... 0.029 6.5% 

Repairs, coal, oil, etc 0.045 10.1% 

Watchman 0.024 5-4% 

Total $0,445 100% 

Material. Conglomerate. 

Amount broken 1,288 cu. yds. 

Amount broken per hour 8.9 " " 

Divided as follows: Weight 

per cu. yd. 
loose 

Tailings, 378 cu. yds „ 29.3% 2,549 lbs. 

2\" stone, 668 cu. yds 5i-9%- • • • 2,368 " 

Screenings and 1", 242 cu. yds. . . . 18.8%. . . . 2,727 " 

Cost per cu. yd. in bins at crusher $1,112 

Cost of per ton in bins at crusher 0.885 

Divided as follows: Cost Per Cent 

Powder and repairs $0,018 1.6 

Labor drilling 249 22.3 

Sharpening drills and tools 023 2.1 

Breaking stone for crusher 420 37.8 

Loading stone for crusher 127 11.4 

Hauling stone for crusher 062 5.6 

Feeding crusher 053 4.7 

Engineer for crusher .038 3.5 

Coal, oil, and waste 050 4.5 

Moving and setting crusher 023 2.1 

Watchman .049 4.4 

Total $1,112 100 

Material. Greenish trap. 

Amount broken 3>*55 cu. yds. 

Amount broken per hour 7.7 " " 

Divided as follows: Weight 

per cu. yd. 
loose 

Tailings, 1,004 cu. yds 31-8% 2,457 lbs. 

2\" stone, 1,618 cu. yds $*•$% 2,383 " 

1" stone, 323 cu. yds 10.2% 2,277 " 

Screenings, 210 cu. yds 6.7% 2,585 " 

Cost per cu. yd. in bins at crusher $0,898 

Cost per ton in bins at crusher 0.745 

Divided as follows: 

Cost Per Cent 

Labor, steam, drilling $0,092 10.3 

Coal, oil, waste, powder, etc 0.084 9-4 

Sharpening drills and tools 0.069 7-7 



280 COST DATA AND ESTIMATES 

Breaking stone for crusher 0.279 31.0 

Loading stone for crusher 0.098 n.o 

Hauling stone for crusher 0.072 8.0 

Feeding crusher ' °-°53 5-9 

Engineer of crusher 0.031 3.4 

Coal, oil, waste, and repairs of crusher 0.079 8.8 

Other repairs 0.0 41 4.5 

Total $oT8o8 100 



W. E. McClintock, Engineer, Chelsea, Mass., season 1887: 

Labor $0. 20 per hour 

Teams 0.45 " " 

Material. Trap rock. 

Amount broken 1,718 tons 

Stone delivered at crusher bf subcontractor for $0.75 per ton. 

Cost. Tools $0,013 

Oil, waste, etc 0.016 

Fuel 0.050 

Stone at crusher 0.750 

Crushing (labor) 0.194 

Total per ton $1,023 

Dustless Screenings. The construction of bituminous mac- 
adams requires a dustless screening product referred o in 
the beginning of the chapter as No. iA; it is obtained by re- 
screening the ordinary screenings (f" product) to remove the 
dust; the percentage of dust in the ordinary screenings will vary 
according to the stone crushed and the setting of the crusher 
jaws. The author has no reliable data for small crushing plants, 
but through the courtesy of the Buffalo Cement Company the 
following data is given for their output of limestone screenings 
at Buffalo, N.Y. 

Size of screen opening for ordinary screenings f" 

Size of dust screen openings \" 

Cu. yds. of dust for 1 cu. yd. ordinary screenings 0.35 

" " dustless screening 1 cu. yd. ordinary screening. 0.65 

The same data from the Leroy plant of the General Crushed 
Stone Company gives: 

Size of screen openings for ordinary screenings f " to |£" 

" dust screen openings \" u T 5 g" 

Cu. yd. of dust per cu. yd. ordinary screenings 33% 

" " " Dustless screenings per cu. yd. ordinary screenings 67% 

Percentage of screenings to total output for Leroy limestone 
approximates 15%. 

The above furnished to the writer through the courtesy of the 
General Crushed Stone Company, of Easton, Pa. 



COST OF APPLYING BINDER 281 

COST OF STONE FILL BOTTOM COURSE 

The following data is taken from Road 5,021, season of 1910; 
labor cost $0,175 P er hour, teams $0.40 per hour. 

The amount placed was 10,000 cu. yds. rolled measure. The 
average rolled depth was 1.1 ft. The surface was carefully 
brought to line and grade, allowing a variation of 1 in. either above 
or below, which inequality was taken out with the top stone. 
A 3 in. bituminous top course was placed directly on this fill. 
The top layer of bottom stone was sledged to reduce all stones 
to 8 in. or under. Flint stone was used to "fill the top 6 in. and to 
surface the rough fill. The bottom course was of fence stone, 
hauled, on an average, about one-half mile. I estimate that 
one cubic yard rolled measure requires 1.25 cu. yds. loose. The 
cost of the bottom course per cubic yards rolled measure was 
$1.03, divided as follows: 

Loading 1.25 cu. yds $0.19 

Hauling 1.25 " " \ mile 0.20 

Placing 1.25 " " and rolling 0.24 

Sledging 0.15 

Flint * 0.10 

Cost of fence stone 0.15 

Total, per cu. yd $1.03 

Cost of Sub-base Bottom Course. Road 495, Parma Corners- 
Spencerport. E. E. Kidder, Engineer. 1,082 cu. yds. placed, 
average depth 6". Not much sledging required. 

Cost of stone, 1 cu. yd $0.10 

Loading, per 1 " " 0.184 

Hauling 1 mile • 0.30 

Laying, sledging and spreading filler . . . 0.136 

Rolling 0.02 

Superintendence 0.02 

Cost of filler in pit nothing (gravel used). 0.00 

Loading J cu. yd 0.04 

Hauling J cu. yd. 1 mile 0.10 

Total 0.90 

COST OF APPLYING BITUMINOUS BINDER 

The following data is taken from Road 5,021, season of 1910. 
Bituminous macadam, penetration method: 

Labor. 

Kettleman $0.20 per hour 

Spreaders 0.20 " " 

Plain labor 0.175" 

Teams 0.45 " " 

Apparatus. 

4 bbl. kettle (coal burner) Bitumen heated 

2 bbl. " (wood burner) to 400 F. 



282 COST DATA AND ESTIMATES 

1 2 ton Kelly roller 

Spreading pots having a vertical slot \" wide. 

Organization. 

Rollerman acting as foreman 

i Spreader 

i Kettleman 

3 Laborers 
Average speed 350 ft. of 16 ft. road, per day. 

Quantities. 

16,850 gals, laid in one coat covered 13,330 sq. yds., or 1.26 
gals, per sq. yd. 

Cost per gal. Unloading and hauling | mile $0.0015 

Heating 0.0032 

Spreading 0.0032 

Rolling and supervision 0.0051 

Total $0.0130 

Bituminous material f.o.b. Caledonia 0.0950 

Total per gal $0.1080 

Second quantity. 

Forty-two thousand gallons covered 24,000 sq. yds. in one 
coat, an average of 1.75 gals, per sq. yd. 

Cost per gal. Unloading and hauling if miles $0.0032 

Heating 0.0040 

Spreading 0.0039 

Rolling and supervision 0.0042 

Total $0.0153 

Bituminous material f.o.b. Caledonia , m 0.0950 

Total per gal $0.1103 

Cost of Applying Bituminous Binder. Road 5,046, Penetra- 
tion Method. 

18,890 gals, spread on 12,378 sq. yds. in one coat, of 1.52 gals. 
per sq. yd. 

Apparatus. 

5 2 bbl. kettles (wood burners) Fuel. Used bbl. staves 

and some extra wood. 
1 10- ton Buffalo Pitts Roller. 

Spreading hods. 

Organization. Per Hour 

1 Foreman $0.30 

2 Pourers, each 0.25 

5 Kettlemen, each 0.20 

2 Spreaders of No. 2, each ; 0.20 

4 Helpers, each , 0.175 

Labor of Placing. Cost per gallon. 

Fuel $0,001 

Kettlemen 0.005 

Pouring 0.003 



PUDDLING WATERBOUND ROADS 283 

Helpers 0.007 

Supervision 0.002 

Total $0,018 

Material f.o.b. Scottsville 0.093 

Total per gal $0,111 

Kentucky Rock Asphalt. I have the following data from 
the Clarence Center Road, Mr. John D. Rust, Engineer, col- 
lected during the season of 1910. In this work an 8-ton tandem 
roller was found to do better than a 6-ton tandem. The cost of 
handling, spreading, and rolling this material, from data of five 
days selected, varied from $0,033 to $0,036 per sq. yd. ; the average 
being $0,034. The following may be taken as a typical analysis 
of this cost: 

Abbreviations. L. Laborers. 

F. Foreman. 

T. Teams. 

E. Roller engineer. 

Asphalt $10.25 per ton f.o.b. unloading point. 

Run of July 20, 1909. 
69.22 tons hauled and placed. 
1,730 sq. yds. covered. 
80 lbs. asphalt per sq. yd. 

5 L. at cars, 10 hours, at $1.50 each $ 7.50 

\ F. at cars at $2.25 per day B . . 1.12 

5 T. haul 2 miles at $4.00 per team 20.00 

5 L. on wheelbarrows, n hours, each $0.15 per hour .... 8.25 

1 T. at shredding machine 4.40 

3 L. on rakes, 11 hours at $0.15 per hour ' 4.95 

3 L. shoveling, n hours, at $0.15 per hour 4.95 

1 F. at shredder, 11 hours at $0,225 P er hour 2.48 

1 E. on roller, n hours at $0.30 per hour 3.30 

Total , $56.95 

Cost per square yard, $0,033. 

PUDDLING WATERBOUND ROADS 

There are two methods of puddling : 
First, by Pipe Line and Hose. 
Second, by Sprinkling Carts. 

In the first method a i^-in. or 2-in. pipe line is laid along the road 
with taps every 200 to 300 feet. The road is wet down by a hose 
fastened to these taps and sprayed on by a nozzle, or the hose is 
fastened to a sprinkling attachment on the roller, which throws 
the water directly onto the wheels; this method is cheaper and 
more satisfactory than using sprinkling carts, but to work well 
a pressure of 125 lbs. should be maintained at the pump, which 
requires a better pumping apparatus than contractors usually 
have. A very satisfactory plant, used near Rochester, N.Y., 



284 COST DATA AND ESTIMATES 

consisted of a Gould Triplex Pump, operated by a 6-H.P. gasoline 
engine; the relief valve at the pump was set at 120 lbs. 

The cost of such puddling on Road 492 for 3,000 cu. yds. of 
top course was $0.05 per cu. yd.; on Road 294 for 4,000 cu. yds. 
of top course it was $0.06. This cost includes pumping, helper 
tending hose, and rollerman. Brooms on the roller were used 
which materially reduced the cost of brooming the screenings. 
No charge for water, no allowance made for laying the pipe line; 
this last charge is included in the lump-sum item of installing 
plant for a waterbound road, page 311. 

Gillette, in his handbook, gives sprinkling by carts approxi- 
mately $0.10 per cu. yd. of top course, which includes sprinkling 
the subgrade as well as puddling the top course. As the sub- 
grade is rarely sprinkled, his data reduced to the conditions cited 
on roads 492 and 294 would give approximately $0.06 per cu. yd. 
of top course. To this is added the cost of rolling, or about $0.04, 
which makes the cost of puddling by this method about $0.10 to 
$0.12, or about twice the amount of the first method. 

Mr. E. A. Bonney, on the Hamburg-Buffalo road, from a 
metered supply of water, states the amount required to first 
puddle a 3-in. top course varies from 50 gals, to 55 gals, per cu. yd. 
of top course, and the amount needed for the second puddle 
will be considerably less. 

Mr. H. P. Gillette states, in a monograph on the Economics 
of Road Construction, that 30 gals of water per cu. yd. will 
puddle a road. Mr. E. E. Kidder states that approximately 
80 gals, are required per cu. yd. of top course for two puddles. 
The author's experience agrees with the larger quantities. 

McClintock Cube Pavement. The general costs of this ex- 
perimental pavement were given in chapter V. We here give 
the detailed cost of the vitrified clay cubes and clay-ash cubes 
only, as the concrete cubes have not worn satisfactorily. 

Vitrified Shale Cubes. During 1909, 74,000 2|-in. vitrified shale 
cubes manufactured at Reynoldsville, Pa., were laid at a cost 
as follows: 

Teams at $0.50 per hour. 

74,000 cubes f.o.b. Reynoldsville $231.25 

Freight 68.41 

Carting 67.00 

Laying 20.00 

Total . $386.66 

Note. 331 sq. yds. were covered at a cost of $1.17 per sq. yd. 

Clay and Ash Cubes. In 19 10, cubes made of a local clay 
mixed with ashes and burned were tried in the effort to get a 
cheap, tough clay product. As far as known, this is the first 
time bricks made in this way have been used on roadwork. 

The ash-clay process has been worked out and patented by 
Karl Langenbeck, of Boston, Mass. Many local clays used for 
ordinary brick or farm tile will not stand up under vitrification 



PUDDLING WATERBOUND ROADS 285 

without the addition of expensive, imported refractory clays; 
but the substitution of coal ashes for the more expensive clays 
has a similar effect and the cost is materially reduced. Some of 
the local clay was sent to Mr. Langenbeck, who turned out a few 
cubes that compare favorably in toughness with the best paving 
bricks on the market. 

The Standard Sewer Pipe Company, of Rochester, N.Y., 
undertook to furnish 400,000 2-in cubes of this description for 
Mr. McClintock. It was necessary for them to experiment to 
determine a practical method of molding, the correct tempera- 
ture to use, and the best proportion of ashes, which naturally 
raised the price above ordinary practice. In molding they 
used a modification of the ordinary pipe-molding machine, 
which produced a hollow square of cubes, at the rate of 30,000 
cubes per hour. The scoring knives were so set that the cubes 
were nearly cut apart, leaving just enough uncut clay to hold 
them together during the burning, after which a light blow sepa- 
rated them cleanly. The toughness of the resulting cubes can 
probably be increased by further experiment; but the product 
was good, although not up to the standard of the sample cubes 
made by Mr. Langenbeck. 

The cost of the ash-clay cubes was as follows: 

400,000 cubes f.o.b. Rochester, N.Y. $1,200.00. . .$0,711 per sq. yd. 

Carting, six miles 247.75. • -0.147 " 

Filler 27.00. . .0.016 " 

Labor of laying 191.77. . .0.113 " 

Roller 12.9 4. . .0.008 " 

Total $1,679.46 $0,995 " 

Note. 1,688 sq. yds. covered 

Labor, $0.22 an hour I f j . and carti 

Teams, $0.50 an hour ) J to to 

Mr. McClintock has stated, in discussing the cost, that in 
large quantities he believes the cubes can be delivered f.o.b. at 
the plant for $1.50 per 1,000, which would reduce the cost as 
shown above to about $0.60 per sq. yd., and that the high cost 
of laying was due to the irregular shape of the first batch, due 
to not scoring the cubes deeply enough. 

Amiesite Cost Data. Road 1319, Honeoye Village, Season of 
1915. H. W. Baker, Eng. in charge. 4700 sq. yds. laid 16' wide i\" 
deep. Laid in two courses. Bottom course 2\" thick coarse ma- 
terial; surface \" thick fine material. 

Material 

588 tons @ $4.00 per ton f.o.b. plant $2352 .00 

588 tons freight $0.54 per ton 341 .04 



Total cost materials $2693.04 



286 COST DATA AND ESTIMATES 

Labor 

Force at cars unloading 

6 Laborers @ $2.00 per day $12 .00 

1 Foreman @ $2.50 per day 2 . 50 

1 Fireman @ $3 . 00 per day 3 . 00 

1 Night Fireman @ $2 . 50 per day 2 . 50 

$20.00 
Equipment at Cars 

1 boiler and pipe line per day 8 . 00 

\ ton coal and oil 2.50 

Total daily cost of unloading $30 . 50 

Hauling \ mile 

4 teams @ $5.00 per day $20 . 00 

Spreading and Compacting 

1 Asphalt raker 3 . 00 

4 Laborers @ $2 . 00 per day 8 . 00 

1 Rollerman 3 . 00 

per day $14 . 00 

Equipment 

1 roller (10 ton tandem) 10 . 00 

Coal, oil, etc o . 80 

Daily cost spreading and compacting $24.80 

Summary Daily Force Account 

Unloading 30 . 50 

Hauling 20 . 00 

Spreading and compacting * 24.80 

$75- 3o 
Number of days worked, 15 

Total labor 1 5 days $1129.50 

" materials cost. 2693 . 04 

Total cost $3822 . 54 

Cost per sq. yd 0.81 

Bid price sq. yd o . 85 

Conditions 

This work was done under bad weather conditions the night tem- 
perature being below freezing and only two days with an air temper- 
ature above 55 F. 

It was necessary to keep a night fireman at the cars to keep up 
steam and to move the steam pipes to different parts of the cars to 
insure the amiesite being in a condition to loosen and shovel in the 
morning. The material was loosened by bars and sledges to the 
bottom of the cars steamed 10 to 30 minutes and then shoveled 
into dump wagons, covered with canvas and hauled to the street. 

Under favorable weather conditions the cost of unloading from the 
cars would probably be reduced 40%. 

Table of Amounts of Amiesite required for different thicknesses and 
materials. 



DEPTHS AND WEIGHTS 



287 



«" s 








•8 A 








W U 




\0 NO to 


O O 


COO lOO x^. 


Cfl "-< 


m co ^ <N 


<N coO m 


rj- loco cn r^ 


CD 43 


00 p^ 


OnOO i>-0 O* 


06 r^-o' O* *o 


CO J>»0 O LO 


a 
8 J 


« A 








S3 *-* c 

s a 


Si 5; St 5; St 


St St St St St 


St St Si St St 


B £ 


ih|-*hmmI-* 


i-tl-^Hwcol-* 


i-iNMnmN< 





N N N N ro 


CN CN CN CN CO 


CN CN CN CN CO 


«4-l <4H 


Pcj 








J3 *& 










— ; r. 








• W-* "~ ' 




«H< ^1-* co|-* H-* «M 


m|->*Hoo ih|oo»h|th 


hMw!* w|oo«|-^ 


^1- 1— 1 


O O M t^ CS 


CO m O 00 O 


N't n ao 


iH|N 


CN rj- *>■ Qs CN 


^NO N 10 


coo an Tt 


4-J 
+-> CJ 


w O « W fO 


CN <N co co CO 


CN CN CN CO co 










' TO ^H 




















— J3 0> 








ss! 


*e a 

O (U 


Si St & Si St 


St S; St St St 


St St St St St 


i-i|-*»o!oo coloowl^ 


r-'-u-x eolaowJT* 


■H|Tj(m|oo «|aoco|-* 


-rB, a-> 


CO co -<t Tf Tf 


CO co ^t ^f- ^=f 


co co ^r tJ- ^j- 


m r ^ 










■a- 8 a 










iller 

Yds 
Ton 


On s On On On 


\^> \C> ~^o ^0 ^0 


"1" "1" 'I' "t "1" 

r^. j>. j>. r^. i>- 


2-6 * 


fe cr S 


CN CN CN CN <N 


CN CN CN CN <N 


CN CN CN CN CN 


T3 "., 


in a 








aj m trt 










w CA 

-CO 








a ^< 


tc c 


m]-4 m^n}^ «H< w|-* 






£ r^3 CU 

§«y 

u ^ 


*5 3 


t^ i>. r^ r^ r-» 


IO W0 1OIOIO 


co co co CO co 


O O O O O 


t^ J>- J>. t^. J^ 


N N J>. !>. N 










^•^ 










§3^ 




St St St St St 


St St St St St 


St St St St St 


JS PS 


to: 


M M M M M 


M M M M M 


M M 1— 1 M M 




fe^ 
















oj u d 










cn .-^ w 


miesite 
[j. Yds. 
erTon 


coco J>-00 
CO H OnOO *>» 

M M 


00 cn aaH 

M O CO J>- *^» 

M M 


CN -3- M M CO 

CN O On CO* *>• 

M M 


(U O > jT 


<ccAi 


















•cn^ TO M 


_ en 








.^ 3 co O 


,co 


He* H« 


«|-*}*t-|aO iH|QOiH|-^< 


i-<|-*irt|ao eo|aoeo|-* 


825* 

%£> O.C* 

O >% g N|» 


tc c 


COOO ^t" On lo 


CO O 10 co m 


tJ- m OnO co 




10 r^ O <n 1-0 


O O CN IOOO 


O On m Tf N 


M M CN CN CN 


M M CN CN CS 


(-1 M CN CN CS 










55 <£ 


St 


St St St St St 


St St St St St 


D O 


i-r-oao «laoeo|-<* 


1- — mjoo colooco!-* 


H , *'0|oo eo|oo«|^i 


1j 

< 


CN CN CO CO CO 


CN CN co co CO 


CN CN CO co CO 


















§0^8 >, 




W 


W 


w 


TO '^3 ^JD 




8 


u 






H 






c/3 

5 


< 


in 

< 


-2 «T73^ 

fl ifl C 3 




H 


in 


0^0 « 










H.^h^ 










^J J> 










4-> c 



288 



COST DATA AND ESTIMATES 



Hassam Concrete Pavement. 

Cost of Grouting. Road No. 5529. Lyell Ave., Spencerport. 
Season 1915. E. E. Kidder, Eng. in charge. Road 1 6' wide 5 " deep 
compacted measure and approx. 6 miles long. 9880 cu. yds. of Has- 
sam were grouted in 71 working days with the organization shown in 
Fig. 66 A. 

Inspectors 
Inquisitives Natives Vistors Etc. 
o °O0qO° o ocfto o o fc 



2g« 

Gas Engine g a 

Man on Top / _: 

Tongue .5* o? 



n 




I 1 Roller 

*f~at Rest 
1 '(as usual) 

Progress of Work 





Daily Force Account 


5 


Tamp & Broom-men 


$12.50 


1 


Spout-man 


2.00 


n 

8 


Operator 1 2.75 


Passers Etc. 


12.00 


l 


Roller-man 


3.50 


l 


Foreman 


3.50 




Total 1*36.75 



Fig. 66 a 

71 days @ $36.25 per day $2573-75 

Amount grouted 9880 cu. yds 

Cost of labor per cu. yd $0.26 

Conditions 

Administration and superintendence good. Temper of crew rather 
bad as they were not receiving the wages that they expected to get 
for the first half of the job. Could have made a better record. 
Speed of Work 
Averaged 450 lin. ft. per day. 



Materials 

Cement. 8500 bbls. used or an average of 0.86 bbls. per cu. yd. of 
Hassam. This varied from 0.75 in the beginning to 0.95 during the 
latter part of the work when a liberal spread of stone was used to 
compensate for rough grading and a desire to end the work before 
winter. 

Sand. Royalty on sand was $0.30 per load or $0,052 per cu. yd. 
of Hassam. Cost of haul corresponds to average costs given in 
previous cost data. 

Stone. 16050 tons of limestone ij" to 3 J" in size were used. This 
amounts to 3250 lbs. per cu. yds. compacted measure which is high 
for this grade of stone. This was due to a liberal use of stone over 
poorly shaped sub-grade and to excess depth where wet material was 
removed. 

Water. Metered supply. 70 gals per cu. yd of Hassam; this 
includes water for engines, leakage in a long line and considerable 
waste at the grout mixer. 

Concrete Roads. Cost Data. Rd. 5423, Hartland Medina Pt. 2. 
Season 1914. F. W. Bristow, Eng. in charge. 9550 cu. yds. 1: 
1^: 3 concrete pavement laid 16' wide 6" deep. 



CONCRETE PAVEMENT 289 

Materials and Equipment 

Cement. Knickerbocker @ $1.18 net bags returned f.o.b. siding. 
4 mile average haul. 

Sand. Excellent local sand, if mile haul. 

Stone. Local crushed stone (Medina Sandstone and granite \" to 
2\" in size) \ mile haul to crusher, 1 mile haul crusher to road. 

Concrete Mixer. Koehring with boom and bucket delivery | cu. 
yd. batch. 

Speed of Work. 500 to 550 lin. ft. of road or 148 to 165 cu. yds. 
mixed and placed per 10 hour day. 

Actual Amount of Materials Used 

Cement 1.85 bbls. per c. y. concrete 
Sand 0.4 c. y. per c. y. concrete 
Stone 0.80 c. y. per c. y. concrete 
Joints 

Wooden joints used for J the work. 

Steel and felt joints used for J the work. 

Labor Cost of Mixing and placing Concrete 
Labor $0,175 per 10-hour day. 
The force at the mixer comprised: 

1 Foreman. 

2 Laborers setting forms, 
shoveling stone. 

" sand, 
on stone wheelbarrows. 
" sand 

passing cement, 
emptying " 
1 Mixer runner. 

1 " fireman. 
4 Laborers placing concrete. 

2 " on screed. 
2 " floating. 
1 " preparing joints. 
1 " sprinkling, brooming, etc. 

The cost of setting forms, mixing, placing and finishing the concrete 
including coal ranged from 0.48 to 0.51 per cu. yd. 

This does not include overhead or plant charge. 

The water cost per cu. yd. concrete was approx. $0.04 and includes 
laying pipe line and pumping from creeks. 

The overhead charge per cu. yd. of concrete were approx. as follows: 

Bond $0,036 per cu. yd. 

Employers Compensation Insurance $2.92 per 

. $100 payroll 0.096 " " " 

Public Liability Insurance 0.016 " " " 

Machinery and tools, freight hauling, erection, 

interest, depreciation and repairs 0.600 " " " 

$.748 
Say $0. 75 per cu. yd. 




10 

3 
6 
2 

1 
1 



290 



COST DATA AND ESTIMATES 



MM 
u 
JO O 

-ft* 



£ 





5 


«! 


< 


hi 


« 




H 




w 


kr 





< 







« 


H 








Hi 


H 


m 


W 


H 


W 


H* 


« 


< 


<: 


111 


teH 


w 


rt 


< 






'I 



lunouiy 



J3A03 pu-Bg 



^unoray 



08 




o o 
o o 




o o 



10 000 00 
t^ 000 00 



o o 
o o 



Amj 



MOO CO 



limoray 



000 

O O to 



IPO 



00 OO ■<* 10 



^unoray 



SJ3H113 



000 

. O O to 



O tovO 
O f- o 

006 4 



%& 



o o 



o o 



lunoray 



S19A.VJ 



88 



O O 

o o 



88 8 



O O M 

o 000 



o o 



O O to <N 

^ Tf co m 



H3 



limoray 



000 
000 



o o 
o o 



o o 
o o 






•sq^ 



U9ui-p3 g 


00 


000 >t 


vO VO 


vOMD 


vO 


vO *=t 10 


s 

3 


^unoray 


O 

VO 


OOO 

OON 
6\ M <N 


O O 

q 


O O 

9 9 

CO CO 


O 

q 

CO 


O to^O 

9^9 


•sq-e^; 





■^ <SO0 
<N CO 


co fO 


O O 


O 


iH|0 
O IO <N 



•2u a 



00 00 00 <N O0O0 O0O0 OO 00 00 (N 



limouiy 



q 

to 




888 


O O 

9 9 

10 VO 


88 

10 10 






OOO 

9 9 9 

to VO 10 


•910 j sjnoH 


00 




00 00 00 


0000 


00 00 


00 


00 0000 


spiE^ araibg 





h. 

44 


O O "* 
vO O 00 
r^ cs cn 


LO O 
O O 
<N CO 


00 

83 


O 

HI 


">* ^-oo 

NCOM 



;99j {-egui^ 



GO 



C/I 



CO Otoji <N O O l ° l O<Uvo 

N^OOO O * 0+-> ^cob w 

<N CO U tOtOfl « rfjji ^ 

O g ^ 



o o 

CO M 






10 to O O O 

+++++ 

tj- co <0 CO co 




ASPHALT BLOCKS 



291 



00000000 

oqooooqo 
o'ddoidodd 



000000000 

■<too 't ^ "^ ■* "^" 



Tf (N rj" IO 



CN OO "^t" M 



OOOO 

o»oq q 

POO M 10 



O O <N 00 
Tj- <N CO "*t" 



00 rj-oo 00 



IT, 1^10 10 



<N O O M 

M ^00 "Sf 



<N <oO M 
CO M <N M 



+ + + + 



+++ + 



Q 



o 



t« cm 






10 f> 0» fO 

CM IO O >H 

OOOOO 

d d d 

11 II II II II 
10O moo 

NO ^100 
rf CS <N CO , ^ - 
II II H II II 

be 

rt c5 m 3 c-j 



rt i— 



<u o 
o~ 




55a^(3JS 






O CO £J J^N"^" 

C^ O O o o O 
6066666 



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11 11 11 11 11 11 



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Ph g 



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B-2 o 

"§-31 I S -| 

^5 ci J3 <u C ci 3 



292 COST DATA AND ESTIMATES 

COST, DATA, CONCRETE ROADS 

Materials 

Stone. Cost of stone varied greatly during the year, from 62^ to 
85^ per cu. yd. at the Blissville docks. To obtain a low voidage 
contractors ordered a mixture of No. 2 and No. 3 stone. This mix- 
ture weighed approximately 2700 lbs. per cu. yd.; therefore, cost 
of stone f.o.b. car at destination would be 

1 cu. yd. stone at Blissville (say) $0. 80 

Transfer (17^ per ton), 1.35 x .17 .23 

Freight (63ft per ton), 1.35 x .63, (rate to Patchogue). . . .85 

Total $1.88 

Note: Arrigoni paid $1.81 delivered f.o.b., on rate made in 19 14, 
before stone dropped. Freight rate to Patchogue then 60^. 

Haul varied from 12^ per yd. mile using tractor-roller and 5 cu. yd. 
trailers (3), to as high as 35^ per yd. mile with teams. 

Transfer from cars to wagons 15 c 7 to 20^ per cu. yd. dependent 
mostly on rate of wages; therefore, cost on job, with stone as per 
above, and a two-mile haul would be approximately $1.88 + .60+. 20 
= $2.68 per cu. yd. 

Gravel. Cost of same at bank, screened, and in bin varied from 
45^ to 85^ (dependent mostly on per cent of gravel). Haul: same 
as stone. 

Sand. Cost of same at bank (in wagons. Screening unnecessary) 
varied from 35^ to 60^. 

Haul: 25^ to 35^ per yd. mile. 

Note. When obtained from same pit as gravel I would consider 
its cost in bin as i the cost of all material leaving the plant, gravel 
in this case J of same total (say 25 ft [sand] and 50^ [gravel] 
where gravel would be 75^+ were all sand wasted). 

Cement. Cost of cement varied greatly during the year; a good 
average was $1.20 per bbl. net. Actual practice with graded stone 
has shown 1.75 bbls. per cu. yd. of concrete a safe factor. 

Haul varied from 3^ (truck) to 5^ (wagon) per bbl. mile. 

Handling: average 2^ per bbl. when handled direct from car to job. 
Plant. Exclusive of forms and water-line. 
1 Mixer — 4 bag mix, 1-1J-3, at least 20 cu. ft. capacity. 
1 Screed — 19' by 4" by 12", with J" iron plate. 
1 Bridge — 18' x 3" x 12". ' 
3 floats — (one split) ; and one trowel. 
1 doz. Forks — close tined for stone. 
10 Square Shovels. 
16 Wheel-barrows (2 or 2 J cu. ft. capacity). 

1 Canvass — 160' x 20' — with frame. 

2 Tampers. 

1 Template to test sub-grade. 

1 doz. Pins to hold expansion joints (or special template for that 
purpose). 
Small tools, other than noted. 



CONCRETE ROADS 



293 



I 
I 
I 

iff 



w 



w 



Straight-edge, 24 X 10" X 4", for extra width on curves. 
Total cost of above approximately $2300.00. 

Organization 
Concrete 1-1H-3, 4 bag batcil 
• H 



Jl Bridge 



Screed 



E 



*E 






T 
ixer 



P4-Mixe 



A" 

T ° ° T 

t t 



05 




"P 



CI 
<D 

G 
0) 

O 
• 
if 

^4 



Liett 


sr Position Number 


Rate 




Foreman 
Engineer 


2 

1 


$3.00 
4.00 
3.00 


a 


Fireman 


1 


2.50 


z> 


Chute 


1 


2.00 


s 


Placing cone 


3 


2.00 


F 


Screeding 


2 


2.00 


G 


Floating 


1 


2.50 


H 
J 


Brooming and 
general help 
Cement (to hopper) 


1 
2 


1.85 
2.00 


K 


Cement (getting 
ready ) 


1 


1.85 


L 


Stone (barrows) 


4 or 5 


1.85 


M 


Stone (shoveling) 


8 


.1.85 


N 


Sand (barrows) 


2 or 3 


1.85 


O 


Sand (shoveling) 


3 


1.85 


P 


Forms 


2 


2.00 


R 


Pump 


1 


2.25 


T 


Trimming grade 


3 


1.85 


W 


Watchmen, covering 
and wetting down 


2 


1.85 



Also charge X A Supt. and Va timekeeper 
Trimmers U T" place expansion joints 



Fig. 66 b 



Manipulation 

Exclusive of water, forms and trimming sub-grade. 

Supt. (J) . _ 3 . 

Time keeper {\) 

Foremen (2) (see Fig. 66 B) 

Engineer (1) ( " " " ) 

Fireman (1) ( " " " ) 

Mason (1) ( " " " ) 

Laborers (8 at 2 . 00) (see Fig. 66 B) 16 . 00 

Laborers (21 at 1.85) ( " " " ) 38.85 

Total ' $73-85 



00 
1 .00 
7.00 
3.00 
2.50 
2.50 



294 COST DATA AND ESTIMATES 

Based on an average day's work of 182 cu. yds. (10-hour day), the 
manipulation of a cubic yard of concrete would cost with the above 
organization, $.406. 

Note. The above organization has laid over 780 lin. ft. of 16^ 
ft. pavement (outside dimensions), in a 10-hour day. (The 182 cu. 
yds. is based on a length of 600' of pavement with a cross-section of 
8.2 sq. ft.) 

Water 

Plant should be capable of supplying 30 gallons per minute. 
Pipe: 10,000 (at least) lin. ft. 2" pipe, galvanized at 16 

cents $1600 . 00 

Black, at 14J cents,. .' 1450.00 

35 "Ts" for same (one each 300') at 50^ 17 .50 

Pumps: 3 to 25 H.P., dependent on conditions. For lower power, 
gas engine O. K.; for higher, steam the best (latter, best for surety 
of supply). 

Outfits $150.00 to $1000.00 

Where wells were necessary, 2" supply pipe. Driving same $1.40 
per ft. for depths not greater than 40'; $1.50 to 70' depth. This 
includes pipe and point. 

Shaughnessy paid a lump sum for water from Bay shore to I slip 
($300.00, I believe) from hydrants. On 5232A, water was bought 
from private parties for part of the work at $3.00 per day. 

Cost of running steam pump located at well or surface water 
supply, including operator, varies from $5.00 to $8.00 per day de- 
pendent on weather conditions. 

200' of rubber hose at $0 . 34 per ft. necessary for connection with 
mixer and sprinkling road. Of this a 15-foot section should be con- 
nected on intake pipe of mixer, with which to sprinkle sub-grade. 

Forms . 

1. 6" Channel forms (steel) 32^ per ft. including pins, 8' 
sections. 

2. Patent steel forms with bevel, 24^ per ft. Pins for same $1.00 
each, one necessary for each section. Sections 12' long. 

3. Wooden forms with bevel about 12 cents per lin. ft. 

Cost of placing same, 2 men at $2.00 per day, $4.00 per day (see 
"P," Fig. 66 B). 

At least 1200 ft. of forms necessary, so that 600 lin. ft. of road can 
be built without forms being moved. Based on (2) forms would 
cost 

1200' of forms, $288.00 

Say no pins 110.00 

Total $398.00 

Trimming Sub-grade 

Three men generally necessary at $1.85 per day (see T, Fig. 66 B). 






CONCRETE COST DATA 295 

General 

A steam roller ($2200.00) might justly be, partially at least, charged 
to concrete. Cost of operating same, including rollerman, not greater 
than $12.00 per day if owned by contractor. 

CONCRETE COST DATA 

Name of Road, Main Street, Sec. Ill, County Highway No. 130. 
(Erie County, New York State) 

Length, 3.68 miles. Thickness, average 7" parabolic crown. 
Width, 16'. Proportions of mix, 1-1^-3. 

Total No. Cu. Yds., 7038. 

1. Labor, exclusive of water supply, including supervision. .6818 

2. Plant forms and tools 3091 

f Steel plates .1782 ) 

3. Expansion joint material \ Tarred paper .0295 \ 2077 

I .2077 J 

4. Water supply, including labor 0625 

5. Cement placed on roadside ready for mixer 2. 3379 

6. Sand " " " " " " 8359 

7. Stone " " " " " " 1. 0518 

8. Reinforcement, if any 0000 



Total cost per cu. yd 5 .4867 

Labor, rate per hour, 16 J^; Teams, rate per hour, 50^; Hours in 

day worked, 10. 

Remarks: Work done by State day Labor. Materials unloaded 
by hand. Plant Charges included proportionate to life of plant. 
Seven-tenths mile average haul. 

Name of Road, Huntington- Ami tyville, Pt. 2, No. 12 19 (Suffolk 
County) . 

Length, 4.69 miles. Thickness, 4!" and 6f" = av. 5! ". 

Width, 1 6'. Proportions of mix, 1-1J-3. 

Total No. Cu. Yds., 7409. 

1. Labor, exclusive of water supply, including supervision ... $.52 

2. Plant forms and tools 58 

3. Expansion joint material 05 

10 
36 
23 
05 



4. Water supply, including labor 

5. Cement placed on roadside ready for mixer 2 

6. Sand " " " " " " 

7. Stone Gravel " " " " " 1 



Reinforcement, if any, 0000 

Total per cu. yd $4 . 89 

Contractor's Bid Price 5-3° 

Labor, rate per hour, 20^; Teams, rate per hour, 55^; Hours in day 
worked, 10. 



296 COST DATA AMD ESTIMATES 

Remarks: Auto truck for most of haul. Gravel furnished by large 

screening and washing plant accounts for high plant cost. Only 
proportionate part charged for this plant as it is to be used to produce 
commercial output. 

Road No. 1 20 1 — Nassau County 

(1) Sand: 

In bins Heling Bros, per cu. yd $.15 

Haul by auto (contractor owner) 2\ mi. at .15 .38 

Sand on road per cu. yd .53 

Gravel: 

In bins Heling Bros, per cu. yd , .85 

Haul by auto (contractor owner) 2\ mi. at .15. . . .7,8 

Gravel on road per cu. yd $1 . 23 

Cement: 

Cement stored at $1.00 per day for 150 days $150.00 

Approximately 11 70 bbls. stored. Storage per bbl. . 13 

F.o.b. Farmingdale (est.) 1 . 30 

Handling and hauling (.10 est.) double handling in 

most cases .10 

Cement per bbl. on road $1 • 53 

This price also approx. cost of cement bought from 
Parker, Hassam Co. 

Plant: 

(2) 1 auto truck (Sauer) $6,500.00 

1 Concrete mixer 1,200 . 00 

2 doz. shovels 2 1 . co 

2 teams at $700., 2 bottom dumpers at $400 2,200.00 

Forms (wooden) 800 lin. ft 40 . 00 

8 barrows 24 . 00 

2 doz. picks 42 . 00 

1 bucket conveyor, loader 600.00 

1 Screed 15.00 

Incidentals 20 . 00 

$10,672.00 

(3) Pressure water from fire plugs 

Pavement per cu. yd. cane. .10 $100.00 

1500 ft. (lin.) 2" pipe at .08 120.00 

100 ft. 2" rubber hose 50.00 

300 ft. 1" rubber hose 45.00 

$315 00 

(4) Manipulation per cu. yd. in place. This does not 

include covering, uncovering, sprinkling .92 

(5) Forms: 

Setting and re-setting forms per lin. ft. of road .... .03 

3X 1.75 X 20 days 

= .03 

3093 



CONCRETE COST DATA 297 

(6) Trimming: 

Per cu. yd. of concrete .28 

6 men @ $1 .75 20 days = $210 
roller @ 12. 6 " = 72 

990 

cu. yd. of cone. 
Expansion joints at 40^ apiece every 30 ft. 
Covering and uncovering and wetting concrete 
during curing season 

2 men to cover ©$1.75 $3 . 50 

2 men to uncover at $1 . 75 3-5° 

1 man to sprinkle 1 . 75 

8.75x20 R , ^^ 

.18 per cu. yd. cone. 

990 - 

Road No. 1203 — Nassau County 

(1) Sand: 

In Pit of Mr. Bennett per cu. yd $.15 

Screening and loading (estimated) .22 

Haul 2 mi. (auto truck) contractor owner @ .12. . .24 

Cost per cu. yd. on road $.61 

Trap Rock (Imported) 

F.o.b. Baldwin $1.59 per cu. yd $1.59 

Unloading 15^ .15 

Haul 1.6 mi. at 25^ teams and auto truck .40 

Stone per cu. yd. on road $2 . 14 

Cement: 

F.o.b. Baldwin per bbl $1 . 38 

Handling and hauling per bbl. .05 .05 

Cement per bbl. on road $1 . 43 

(2) Plant: 

1 Screed $ 20 . 00 

1 Concrete Mixer 1800.00 

1 Steam Roller 3000.00 

1 doz. Wheelbarrows 36 . 00 

2 doz. Shovels 21 . 00 

3 Teams at $700, 3 Bottom Dumpers at $400 3300.00 

1 Auto Truck 5000 . 00 

2 doz. Picks 42 . 00 

Forms (wooden $20.00; steel $126.00,) 146.00 

Incidentals 50 . 00 

Water Wagon 400 . 00 

$13,815.00 



298 



COST DATA AND ESTIMATES 



Water: 

Pressure line fire plugs, total. 

4000 ft. 2" pipe .06 

100 " " rubber hose 

3OO I 



(4) Manipulation: 

Includes all work, sprinkling, covering, uncovering, 
in place complete per cu. yd 

(5) Forms: 

Setting and resetting forms per lin. ft. of road 

(6) Trimming (Sub-grade) 

Per cu. yd. concrete in place 

Expansion Joints at 40^ apiece every 30 ft. 



$100.00 

240 . 00 

50.00 

45.00 

$435 00 



$.67 
•05 
.24 



Road No. 12 1 9 — Suffolk County 

(1) Sand: 

In bins Heling Bros, pit cu. yd 

Haul by auto (contract) 1.5 mi. est. .30. 

Cost per cu. yd. on road 

Gravel: 

In bins Heling Bros, pit cu. yd 

Haul by auto (contract) estimated .30. . 



Cost per cu. yd. on road 

Cement: 

Bbl. f.o.b. Farmingdale 

Handling and hauling 



Cement on road per bbl. 

(2) Plant: 

Same as on No. 1218 

(3) Water: 

Cost of water 

1 mile 2" pipe at .06 per. ft.. 

100 ft. 2" rubber hose 

400 ft. 1* 

1 pump and gas engine (est.), 



(4) Manipulation: 

Includes all work; sprinkling, covering, uncovering, 
in place complete per cu. yd 

(5) Forms, setting and reset ing per lin. ft. of road 

(6) Trimming: 

Per lin. ft. of road 

Expansion joints at 40^ apiece every 30 ft. 



$ 


. 10 




• 30 


$ 


.40 


$ 


•75 




•30 


$1 


•05 


$1 


.27 




08 


$1 


35 



$700 . 00 

320.00 

50.00 

60.00 
1,000.00 

$2,130.00 



$.50 

.02 

.06 



CONCRETE COST DATA 299 

Road No. 1218 — Suffolk County 

(1) Sand: 

In bins Heling Bros, pit cu. yd $.10 

Haul by auto (by contract) 1.7 mi. approx .40 

Sand per cu. yd. on road $ . 50 

Gravel: • 

In bins Heling Bros, pit cu. yd $ . 75 

Haul by auto (by contract) approx .40 

Cost per cu. yd. on road $1.15 

Cement: 

F.o.b. Farmingdale $1.27 

Handling and hauling .08 

Cement on road per bbl $1 . 35 

(2) Plant: 

Gravel and sand screening complete, including 

various set ups $15,000.00 

1 Concrete Mixer 1,800.00 

1 Roller 2,800 . 00 

1 Screed 20 . 00 

18 Wheelbarrows 54 . 00 

2 doz. Shovels 21 . 00 

3 teams @ $700, 3 bottom dumpers @ $400 3,300.00 

2 doz. Picks 42 . 00 

1 rd. Planer and Scarifier 600.00 

Forms (steel) 630 . 00 

Tarpaulins 100 . 00 

Incidentals 75 . 00 

$24,442.00 

(3) Water: 

Total paid for water approx $130.00 

1 mile 2" pipe at .06 320.00 

100 ft. 2" rubber hose 50.00 

400 ft. 1" " " 60.00 

$560.00 

(4) Manipulation: 

Includes all work, sprinkling, covering, uncovering, 

in place complete per cu. yd $ . 54 

(5) Forms: 

Setting and resettimg forms per lin. ft. of road. . . .02 

(6) Trimming: 

Per lin. ft. of road .06 

Expansion joints 40^ apiece every 30 feet. 



300 COST DATA AND ESTIMATES 



COST DATA 

Name of Road, Huntington Town Line-Farmingdale, Part i 
(Suffolk County) 

Length, 1.27 miles. Thickness, 5" & 7"= Av. 6". 

Width, 16'. Proportions of mix, 1-1J-3. 

Total No. Cu. Yds. 2051. 

1. Labor, exclusive of water supply, including super- 

vision $ . 56 

2. Plant forms and tools .61 

3. Expansion joint material .06 

4. Water supply, including labor .12 

5. Cement, Placed on roadside ready for mixer 2 . 13 

6. Sand, " " " " " " .22 

7. Stone, " " " " " " 1. 01 

8. Reinforcement, if any 0000 

Total per cu. yd $4.71 

Contractor's Bid Price 5 . 30 

Labor, rate per hour, 20^; Teams, rate per hour, 55^; Hours in day 

worked, 10. 

Remarks: Auto truck for most of haul. Gravel furnished by large 
screening and washing plant accounts for high plant cost. Only 
proportionate part charged for this plant as it is to be used to pro- 
duce commercial output. 

Road No. 1202 — Nassau County 

(1) Sand: 

Estimated at .10 per cu. yd. in bins $ . 10 

Haul (by contract) estimated at .40 per cu. yd. . . .40 

$.50 
Gravel: 

Stiff leg derrick set up (in bins) $2 . 00 

Haul (by contract) estimated at .40 per cu. yd. . . .40 

1st set up per cu. yd. on road $2 . 40 

Drag line set up per cu. yd $1 . 20 

Haul (by contract) estimated .40 per cu. yd .40 

2nd set up per cu. yd. on road $1 . 60 

Imported gravel per cu. yd. scow L. I. City .85 

Unloading from scow L. I. City .15 

Freight L. I. City to Central Park .78 

Unloading at Central Park .10 

Haul (by contract) at .20 per cu. yd .20 

Cost per cu. yd. on road $2 .08 

Average cost per cu. yd. on road $1 .92. 



CONCRETE COST DATA 301 

Cement: 

Bbl. f .o.b. Central Park ( P^ed ) $1 • 20 



\ by market 

Haul by contract per. Bbl .06 

Handling .02 

Per Bbl. on road $1.28 

(2) Plant estimated $12,000.00 

(3) Water: 

Cost of water $1,000 . 00 

4 mile 2" pipe at $0.06 per ft 1,270.00 

100 ft. 2" rubber hose at $0 . 50 50 . 00 

400 ft. 1" " " at $0.15 60.00 

1 pump, boiler, etc 1,000 . 00 

$3,380.00 

(4) Manipulation: 

Includes all work, sprinkling, covering and uncover- 
ing; in place complete per cu. yd $.64 

(5) Forms: 

Setting and taking up per lin. ft. of road .04 

(6) Trimming: 

Per lin. ft. of road . 075 

Expansion joints at 40^ apiece every 30 ft. 

COST DATA 

Name of Road, Little Valley-Cattaraugus, Part 1 (Cattaraugus 

County) 

T ,v ., / 3900 lin ft. 16 ft. \ 

Length, 5-35 miles. j ^ „ „ ^ ft j 

-,. , /6"&8" = Av. 7" -\ 

Thickness, | g. & f= Ay £ |r J 

2.575 miles completed. 

Width, 16 and 14. Proportions of mix. 1-1J-3. 

Total No. Cu. Yds. 8280 — This cost covers 4165 cu. yds. 

1. Labor, exclusive of water supply, including super- 
vision . 423 

2. Plant forms and tools. .662+ .158 for coal .820 

3. Expansion joint material .045 

4. Water supply, including labor .030 

5. Cement, placed on roadside ready for mixer 1 .984 

6. Sand, " " " " " " .522 

7. Stone, " " " " " " 1.505 

8. Reinforcement, if any 0000 

Total cost per cu. yd 5 . 324 

Contractor's Bid Price 6.30 



302 



COST DATA AND ESTIMATES 



Labor, rate per hour, i8|j£; Teams, rate per hour, None used; 

Hours in day worked, 10. 

Remarks: Industrial Ry. Plant delivering sand, stone and cement 
into hopper of concrete mixer, clam shell unloader used to take 
material off cars. Material delivered alongside mixer in buckets 
proportioned for one batch size. 

For plant layout see illustration 




Erie R.R.^ 1 
Plant Layout 



COST OF CONCRETE WORK 

The following data will help in estimating the cost of small concrete 
jobs, such as culverts, walls, etc. This data was collected by Mr. 
E. E. Kidder during the season of 1908. Table 49 contains the 
theoretical proportions of cement, sand, and stone required for the 
three ordinary mixtures of concrete. These values were found by 
experience to agree with actual proportions very closely for \" to 
(Continued page 304.) 



CONCRETE COST DATA 



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304 COST DATA AND ESTIMATES 

Table 49. — Materials Required for i Cu. Yd. of Concrete 



Mixture 


Cement 


Sand 


Stone 


1-2-4 

l-2|-5 

1-3-6 


1.5 bbls. 
1.2 " 
I.O " 


0.4 cu. yds. 
0.45 " " 
0.45 " " 


0.9 cu. yds. 

0.92 " " 

0.95 " " 


The amount of water used per cu. yd. of concrete will vary 
greatly. A plastic mixture usually requires about 30 gals, per 
cu. yd., according to Baker, 40 gals, according to Barnes. 

Where boulders are embedded in the foundations and side 
walls of small culverts similar to Plate 6, less cement, sand, and 
stone are required; our experience with work of this kind shows 
that only 0.8 to 0.9 bbls. of cement are needed per cu. yd. for 
the total amount of concrete in these culverts including cover 
and parapets. For all classes of work where boulders cannot 
be embedded these proportions are about right. 



Per Cu. Yd. 

Forms (labor) $0.58 

Lumber 0.50 

1 Labor, mixing, and placing 1.18 

1 Foreman 0.20 

1 Broken stone, at crusher 0.90 

1 Hauling stone, one mile 0.30 

Sand at pit at 65 cts. per cu. yd 0.32 

Hauling sand six miles 0.75 

1 Taking down forms o. 10 

Cement at culverts 2.00 

Total $6.83 

Labor, $0.15 per hour. 

Concrete, hand-mixed. 

200 cu. yds., placed in small culverts, averaging 12 to 15 cu. 
yds. each. 

Note. The labor of placing the concrete is customarily sublet to 
masons for $2.00 per cu. yd. 

Small Culverts. 

Java Center Road. George A. Wellman, Engineer. 

One hundred and sixty-one cu. yds. of concrete in culverts, 
averaging 12 to 20 cu. yds. each. 

Boulders were embedded in the third-class concrete. Water 
only had to be hauled for 30 cu. yds. of concrete. 

1 Items accurate; other items approximately correct. 



COST OF CONCRETE WORK 



3°S 



Materials 


Amt.PerCu.Yd. 


Unit Total 


of Concrete 


Cost Cost 


Material Costs 


$1.12. .$154.56. . 


0.86 bbls. . .$0.96 


1. 00 .... 60.00. . 


0.37 cu. yds.. .0.37 


. 1.55. . .201.50. . 


0.80 " " .1.24 


30.00 . . . .90.00. . 


0.56 


Totar . . . 


$3.13 



Item Total 

Quality 

Cement 138 bbls. . . 

x Sand 60 cu. yds. 

Crushed stone 130 " " . . 

Lumber 3 M 



Costs are f.o.b. unloading point; teaming of material included 
in the labor cost given below, except for sand, which cost $1.00 
delivered on the job. Concrete mixed and placed by hand. 

Cost of Labor and Teaming Per Cu. 

Item. Total Yd. of Con- 

crete 

Foreman $93-°° $0.58 

Labor, unloading stone from cars 20.00 0.12 

Mixing, placing concrete, and removing forms 204.00 1.27 

Carpenters, building forms 75-oo 0.47 

Teaming 182.00 . . . . . 1.13 

Total Labor. . . .$3.57 

Total Material . . . .3.13 

Total $6.70 

Labor $0,175 P er hour 

Teams 0.50 " " 

Carpenters 0.25 " " 

Foreman . 0.30 " " 

Small Span Concrete Arch. The following information of 
cost of 19-ft. span concrete arch was given by Mr. Charles M. 
Edwards, First Assistant Engineer, New York State Depart- 
ment of Highways. Arch was built at Pembroke, N.Y., by 
a contractor who was crushing stone at a quarry about one- 
half mile from the work. Cement was hauled three-quarters of a 
mile. For the concrete a mixture of one part Portland cement, 
two parts sand, and four parts stone was used. The old masonry 
abutments and wings were left in place and faced with 8 inches 
of concrete held by dowels. The quantities were: Concrete, 120 
cu. yds.; steel bars, 4,500 lbs.; pipe railing, 200 lin. feet. The 
cost of the work was as follows: 

Lumber, including arch centers . . .$156.00 on job 

Steel 106.00 " " 

Cement 137.00 on siding, f.o.b. 

Stone 240.00 on job 

Dust and sand 90.00 

Railing 78.00 f.o.b. siding 

Labor 300.00 



Total $ 



1,107.00 



1 The sand on this job cost practically nothing but we have placed the cost at 
$1.00 in order to avoid a misleading item. 



306 COST DATA AND ESTIMATES 

Omitting the cost of railing this figure gives a cost of $8.57 
per cu. yd. of concrete, including steel. This cost does not 
include salvage of lumber or overhead expenses of any kind. 
The contractor received $1,500.00 for the work, including the 
earth rilling, for which he used quarry strippings. This filling 
cost about $50.00. 

Guard-Rail. In the following data the labor cost alone is 
given, for the materials will vary so much at different times and 
places that any quotations would be of little value. 

The style of rail erected is similar to sketch, page 86. Road 
715, 9,760 lin. ft. were built at the following cost, according to 
S. O. Steere, engineer in charge: Post-hole auger-diggers and 
ordinary shovels were used; the holes were dug in medium 
hard clay; labor at $0.20 per 'hour, foreman $3.00 per day; 
unskilled labor used in painting fence. 

Digging post holes, setting posts, nailing on rails (erecting 
fence complete): 

Cost $0.0428 per lin. ft. 

Painting three coats 0.0094 " " " 

Total for erecting and painting ..$0.0522 " " " 

Road 5,046, W. G. Harger, as Engineer. 2,448 lin. ft. Built 
by subcontractor, Max Weller. 

Force: Max Weller acted as foreman. In this data he has 

been arbitrarily allowed salary of $4.00 per day $4.00 

1 helper 2.50 

1 helper 2.00 

1 helper 1.75 

Cost of erecting and painting complete, per lin. ft. $0,066. 

In Report of 1901 the Massachusetts Highway Commission 
gives the following costs for repainting guard-rail: 

Lineal feet of guard-rail painted 35°>33° 

Cost of paint per gal. (freight not included) $1.05 

Cost of paint per lin. ft. of guard-rail 0.0084 

Cost of paint and painting per lin. ft. of guard-rail 0.0165 

Lin. ft. of guard-rail painted per gal 134-4 

No. gals, of paint used per lin. ft. of guard-rail 0.0077 

Time required to paint one foot, in decimals of an hour . 0.0269 

Concrete Guard-Rail. Style of rail shown in sketch on page 
87, chapter on Minor Points. 

Labor, $0,225 per hour. 

Cost of manufacturing 1,233 lin. ft. of rail of the above de- 
scription. Taken from the Report of the New York State 
Highway Commission of 1910. 

Lumber $ 32.46. . . .$0,026 per lin. foot. 

Steel 139.64 0.114 " " 

Cement , 57.62 0.046 " " " 

Gravel 10.00 0.008 " " 

Metal cores 77.00 0.063 " " 



PRICES OF VITRIFIED PIPE 



307 



Labor 231.83, 



0.188 



Miscellaneous • 5-35- • • • -^004 

Total $553-9° °-449 

This data applies to small quantities; if manufactured on a 
large scale the cost should be reduced to about $0.30 per lin. ft. 

The cost of setting the above rail varied from $0.09 to $0,125 
per lin. ft: labor $0,225 per hour. This does not include haul- 
ing from the factory to the intended position on the road. 
Cobble Gutter. Road 5,046, W. G. Harger, Engineer. 

Labor, $0,175 P er nour - Foreman, $3.50 per day. 

Cobbles averaged 6 in. in size; no sand cushion required, as 
gutter was built in a sand cut. Gutter was laid by ordinary 
laborers using paver's tools; tamped with a paving rammer, and 
the top voids filled with No. 2 stone crushed on the job. 

430 sq. yds. were laid at the following cost per sq. yd.: 

Cobbles, free .$0,000 

Loading £ cu. yds. of cobbles 0.030 

Hauling | " " " J mile 0.024 

Laying and tamping . 0.080 

Filler. Cost of 0.05 cu. yds. No. 2 stone at crusher bin, 

approximately 0.030 

Hauling 0.05 cu. yds. 1 mile 0.015 

Spreading and brooming, 0.05 per cu. yd. No. 2 stone . . . 0.010 

Total $0,189 

PRICES OF VITRIFIED PIPE 

The discounts vary, but if no quotations of current prices 
are available the following list will serve for an approximate 
estimate: 

1 Eastern List 
Size Discount 

3* to 24" 88% 

24" and 30" 80% 

33" and 3 6* 75% 

At these discounts the net prices per foot in car-load lots f .o.b. 
factory are: 



Size 


Price 


Size 


Price 


a;, 


$0,024 


20" 


$0,270 


4" 


0.030 


21" 


0.325 


c 


0.036 


2 2" 


O.360 


6" 


0.048 


24" 


O.390 


8" 


0.066 


27" 


O.900 


10" 


0.096 


30" 


I. IOO 


12" 


0.120 


33" 


I.560 


15" 


0.162 


36" 


I-7SO 


18" 


0.227 


— 


— 



1 Engineering News, April 4, 191 2. 



3 o8 



COST DATA AND ESTIMATES 



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PLANT AND PAY-ROLL 



309 



PLANT AND PAY-ROLL 

Table 50, page 252, shows in a convenient form the value 
of plants and the largest weekly force account of two months' 
duration on fourteen roads in New York State. From this and 
other information it is reasonable to assume that a contractor has 
tied up, outside of money on plant and materials, from $5,000 
to $8,000 for the full length of time that the work is in progress, 
and for short periods he may have as high as $15,000 or $20,000 
invested. 

Interest, Depreciation, Repairs, etc. To the best of my 
judgment the following estimates show about the amount of 
money required on the different styles of construction noted. 
These data are based on an outfit which would be capable of 
a speed of about 0.7 mile per month, or five miles in a season. 

Adopted Value of Plant Items 



Item 



10-ton roller 

Brick roller 

Traction-engine 

Crusher 

Elevator 

Bin and screen 

5 H.P. gasoline engine 

Gas engine and pump 

6000 ft. of pipe 

Wagons 

Hand tools 

Plows 

Road machine 

Tar kettle 

Wheel scraper 

Slush scraper 

10-ton roller used for hauling 
Hauling traction-engine .... 



Value 



$1 



$2700 
1800 
1200 
900] 
200 \ 

500 J 
250 
200 
600 

115 

150 

100 

200 

25-200 

70 

6 

2700 

2200 



Life 



20 yrs. 
20 



5 

say 10 

6 

1 
3 
5 

5 

5 

10 



Annual 
Repairs 



$70.00 

40.00 

IOO.OO 

400.00 

50.00 
50.00 
10.00 
IO.OO 



10.00 
10.00 



IO.OO 



200.00 
200.00 



1 Including new tank every three years. 



310 COST DATA AND ESTIMATES 

6% Interest and Depreciation on Plant Items 



Item 



Roller 

Traction-engine 

Crusher 

Elevator 

Screen 

Bin 

Gasoline engine 

Gasoline pump 

6000 feet 1 1" pipe 

Wagons 

Hand tools 

Plows 

Tar kettle 

Concrete mixer 

Brick roller 

Wheel scrapers 

Slush scrapers 

Roller used for hauling 
Hauling engine 



Interest 



$162.00 

72.00 

54.OO 

12.00 

3.00 

30.00 

15.00 

12.00 

36.OO 

6.00 

9.00 

6.00 

I2.00 

I20.00 

108.00 

5.00 

162.OO 
132.OO 



Depreciation 



$135.00 

150.OO 

IOO.OO 

30.00 

50.00 

40.00 

30.00 

40.00 

60.OO 

20.OO 

150.00 

30.OO 

IO.OO 

IOO.OO 
15.OO 

270.OO 
300.OO 



Charge for bond \% total contract. 

PLANT FOR WATERBOUND MACADAM 

STONE 



IMPORTED 



Elevator unloading plant, provided more than 2,000 cu. yds. 
of stone is to be unloaded. 



Item 


Interest 


Depreciation 


Repairs 


Elevator 

Bin 


$12.00 
30.00 
15.OO 

162.OO 

36.OO 

12.00 

9.00 

6.00 

12.00 

5.00 

80.00 


$30.00 
40.00 
30.00 

135-00 
60.00 
40.00 

150.00 
30.00 
40.00 
15.00 

300.00 


$50.00 
50.00 
50.00 

70.00 
10.00 
50.00 

IO.OO 
IO.OO 

150.00 


5 H.P. gasoline engine 

1 roller with broom and sprink- 
ling attachment 


6000 ft. 1 \" pipe 

Gasoline engine and pump 

Hand tools 


Plows 


Road machine . . 


2 wheel scrapers 

2 slush scrapers 


1 <; wagons . 




Totals one season's work 5 miles 
Total per mile 


$379-°o 
76.00 


$870.00 
174.00 


$450.00 
90.00 



PLANTS FOR MACADAM STONE 



3ii 



Force account money out: Allow six weeks out continually for 
length of job at \% interest per month. 

Allow $6,000 out, or $40.00 interest per mile on force account. 

Bond charge: J of 1% contract price; approximately $25.00 
per mile. Insurance charge: $2.00 per $100.00 total force 
account, approximately $100.00 per mile. 

Allow for moving plant on job, $500.00 lump sum. 

Plant for Waterbound Macadam Local Stone 



Item 


Interest 


Depreciation 


Repairs 


1 traction engine 

1 crusher and bin 


$ 72.00 

IOO.OO 

IO.OO 

I2.00 

322.OO 


$150.00 

220.00 

50.00 

30.00 

770.OO 


$100.00 

400.00 

80.00 

20.00 

300.00 


1 steam drill and bits 


1 small boiler for drill 

Roller, pipe, gasoline engine and 
pump, hand tools, plows, road 
machine, scrapers and wagons 
as for imported stone plant. 
Total of these items 


Total for season, 5 miles .... 
Total per mile 


$516.00 
103.00 


$1220.00 
245.00 


$900.00 
180.00 



Force account slightly larger on local stone roads. Approxi- 
mately $7,000.00 out. 

Interest on force account $50.00 per mile 

Bond charge 20.00 " 

Insurance 120.00 " " 

Moving plant on job, $500.00 lump sum. 

Plant for Bituminous Macadam Imported Stone 



Item 


Interest 


Depreciation 


Repairs 


Elevator unloading plant 

2 rollers 


$60.00 

320.OO 

36.OO 

112.00 


$IOO.OO 
270.OO 

535-00 


$150.00 

140.OO 

30.OO 

170.OO 


3 tar kettles 

Hand tools, plows, road machine, 
scrapers and wagons as for 
waterbound macadam. Total 
of these items 




Total for season, 5 miles 

Total per mile 


$528.00 
106.00 


$905.00 
181.00 


$490.00 
98.OO 



Interest on force account $40.00 per mile 

Bond charge 30.00 " 

Insurance 100.00 " " 

Moving plant on job, $500.00 lump sum. 



312 COST DATA AND ESTIMATES 

Plant For Bituminous Macadam Local Stone 



Item 


Interest 


Depreciation 


Repairs 


i traction engine 


$72.00 

IOO.OO 

IO.OO 

I2.oo 

468.OO 


$150.00 

220.00 

50.00 

30.00 

805.00 


$100.00 

400.00 

80.00 

20.00 

340.00 


i crusher outfit 


i steam drill and bits 


i portable boiler for drill 

Rollers, hand tools, plows, road 
machine, scrapers, wagons, and 
tar kettles as for imported 
stone. Total of these items . . 


Total for the season, 5 miles . . 
Total per mile 


$662.00 
132.00 


$1255.00 
251.00 


$940.00 
188.00 





Interest on force account $50.00 per mile 

Bond charge 25.00 " 

Insurance 120.00 " " 

Moving plant on job, $500.00 lump sum. 

FORMS FOR ESTIMATES 

The following forms of estimate have proved very satisfactory. 
The item of 6% on materials is used to cover demurrage and 
interest on money tied up on freight and stone. The other 
items of profit are what we consider a reasonable return for 
the risk of such contract work. Mechanical hauling is not 
considered, because few contractors own plants that make it possi- 
ble. The total item of interest, depreciation, repairs, and inter- 
est on force account money for the whole job is charged against 
top and bottom stone, as the construction quantities of the 
macadam will vary less from the estimated quantities than any 
other classes of work. 

Standard Estimates. ( Figured on the basis of 20% profit on 
labor, 6% on materials, 6% on money invested, and an allow- 
ance made for depreciation on different plants, as previously 
given. 

Labor at $0,175 P er hour 
Teams at $0,450 " 



FORMS FOR ESTIMATES 



3*3 



Earth Excavation. 



Class 


Amount per Mile 


Price per Cu. Yd. 


Easy 

Easy 

Easy 

Average 

Average 

Hard 

Hard 


5,000-10,000 cu. yds. 
3,000- 5,000 cu. yds. 
i,5oo- 3,000 " 
3,000- 5,000 ' 
1,500- 3,000 " " 
3,000- 5,000 
1,500- 3,000 ' 


$0.40 

0.45 
0.50 
O.50 
O.60 
O.60 
0.70 





Rock Excavation. 

Large boulders (for which 10 cu. yds. a 

mile are allowed on all estimates) . . .$1.50 per cu. yd. 

( Steam drillwork, limestone 1.25 " " " 

I * \ " " " granite 1.50 " " " 

\ Hand " " limestone 2.00 " " " 

2 ' \ " " " granite 2.00 " " " 

1. Large quantities 

2. Small quantities 

Field Stone Sub-base. 

A sub-base course 6 in. deep made of the usual size fence stone 
requires 1 cu. yd. loose for 1 cu. yd. rolled; 12 in. deep requires 
1.25 cu. yds. loose. 

Cost of cobbles per loose cu. yd $0.10 

Loading cobbles per loose cu. yd 0.15 

'Hauling cobbles 1 mile per loose cu. yd. 0.35 
Placing cobbles per loose cu. yd 0.10 



Multiply these 
items by 1.25 for 
12-in. depth of 
sub-base. 



Rolling cobbles per loose cu. yd 0.05 

Filler (see below) . — 



Total 

20% profit 



$ — 



Estimate $ 



Filler. 

I cu. yd. per cu. yd. rolled sub-base. 

Cost J cu. yd. at pit or crusher $ — 

Loading J cu. yd 0.05 

Hauling f cu. yd. 1 mile 0.10 

Spreading J cu. yd 0.04 

Total $ — 



314 COST DATA AND ESTIMATES 

Sub-base Bottom Course. 

Same relation of loose and rolled quantities as for sub-base. 

Cost fence stone per loose cu. yd $0.10 

Loading fence stone per loose cu. yd. ... 0.15 

Hauling 1 mile per loose cu. yd 0.35 

Placing and sledging 0.20 

Rolling 0.05 

Filler (see below) — 

Total $ — 

20% profit 1 — 

Estimate — 

Filler. 

i cu. yd. per cu. yd. rolled sub-base. 

Cost J cu. yd. at pit or crusher $ — 

Loading 0.05 

Hauling 0.33 cu. yd. filler per mile 0.10 

Spreading and brooming 0.08 

Total $ — 

Imported Bottom Stone Materials. 

3" course, 3,05c 1 lbs. f.o.b. crusher. $ — 

4" " 3,i5o " " " — 

6% profit — 

Total $ — 

Freight on stone to delivery point — 

Total, No. 1 .$ — 

Labor. 

Unloading 

Under 2,000 cu. yds. (shoveling) $0.15 per cu. yd. 

Over 2,000 cu. yds. (elevator) 0.10 " " " 

Hauling (Teams) 

Bad conditions 0.35 " " " 

Average conditions 0.30 " " " 

Good conditions 0.25 

Mechanical hauling 0.15 " 

Spreading 

5I in. loose depth 0.06 " 

4 in. loose depth 0.08 

Rolling 0.05 

At this point total up and add 30% of the total to change the 
estimate from loose to rolled measure. 

Filler (see below) 

Labor, total $ — 

20% profit . — 

Total, No. 2 $ — 

1 These weights are for limestone. See pages 268, 272. 



iC u 



u a (c 
tt tt (C 

a (( u 



FORMS FOR ESTIMATES 315 



Filler. 



Cost of 0.35 cu. yd. at pit or crusher $ — 

Loading 0.35 " " 0.05 

Hauling 0.35 " " 1 mile @ $0.35 per yd. mile . . 0.12 
Spreading and brooming 0.35 cu. yd 0.07 

Filler, Total $ — 

Summary. 

Total No. 1 $ — 

Total No. 2 $ — 

Interest and depreciation $ — 



Estimate $ — 

Imported Top Stone Waterbound Macadam Materials. 

1 4,450 lbs. stone f.o.b $ — 

6% profit $ — 

Total $ — 

Freight on stone to delivery point $ — 



Total No. 1 $ — 

Labor. 

Unloading (same as bottom) $ — 

Hauling (same as bottom) $ — 

Spreading 0.08 

Rolling 0.04 

Puddling 0.06 

Total, loose measure $ — 

Add 30% .$ — 

Total rolled measure $ — 

Screenings. (See below) 

Total $ — 

20% profit — 

Total No. 2 JT~ 

Screenings. 

2 Unloading 0.5 cu. yd $0.07 

Hauling 0.5 " " 1 mile 0.15 

Spreading 0.5 " " by cross dump wagons 0.03 

0.5 " " " hand 0.07 

Total $ — 

Summary. 

Total No. 1 $ — 

Total No. 2 — 

Interest, depreciation, etc — 

Estimate $ — 

1 These weights are for limestone. See pages 268, 272. 

2 Screenings are usually unloaded by hand. 



316 COST DATA AND ESTIMATES 

IMPORTED TOP STONE BITUMINOUS MACADAM. 

PENETRATION METHOD 
Materials. 

2" course, 4,350 lbs. stone and screenings, f.o.b. crusher . .$ — 
3" " 4,050 " " " " " " . . . — 

gal. bituminous binder, f.o.b. plant — 

6% profit — 

Total . . $ — 

Freight on materials to delivery point — 

Total No. 1 .$ — 

Labor. 

No. 3 stone. 

Unloading 1 cu. yd. (same as given) . . . .$ — 
Hauling 1 cu. yd. " " " .... — 
Spreading 1 cu. yd. " " " .... — 
Rolling 1 cu. yd 0.09 

Total $ — 

Add 20% for 2" course, 30% for 3" course — 

Total No. 2 $ — 

No. iA, No. 2, and Bitumen. 
Unloading 0.6 cu. yd. for 2" course (same as given) $ — 

(( n a z u il ct i" li u li tl 

Hauling at the rate of $0.30 per yd. per mile — 

Hauling bitumen at rate of $0,002 per gal. per mile — 

Spreading and brooming No. iA and No. 2 at rate of $0.30 

per cu. yd — 

Manipulation of heating and spreading bitumen at $0,015 

per gal — 

Total No. 3 $ — 

Total No. 2 — 

Total $ — 

Add 20% profit — 

Total No. 4 $ — 

Summary. 

Total No. 1 $ — 

Total No. 4 — 

Interest, depreciation, etc — 

Estimate $ — 

Local Stone Macadam. 

Field stone. 
1 cu. yd. field stoAe = 1 cu. yd. crushed. 
1.8 cu. yds. field stone = 1 cu. yd. No. 3 and No. 4 rolled. 

Cost of field stone $0.10 per cu. yd. 

Blasting or sledging, per cu. yd. actually blasted 

or sledged 0.40 " " " 



LOCAL STONE MACADAM 



317 



9 — 



Loading field stone 0.15 per cu< yd 

Hauling field stone 1 mile 0.35 

Crushing 

Sandstone (soft) 0.10 

Limestone 0.15 

Granite and trap rock 0.20 

Total cost in bins (loose including Nos. 1, 2, 3, 

and 4 stone) $ — 

Quarried Stone. 

Limestone, quarrying, small quarries $0.50 

Conglomerate, " " " 0.75 

Trap, " " " 0.65 

Crushing (same as above) — 

Total cost in bins $ — 

The crushing does not include repairs to crusher. 
The crushing is taken from previously given data. 
The item of quarrying includes delivery to crusher. 

Estimate of Bottom Stone. 

Cost in bins $ — 

Loading, per cu. yd 0.01 

Haul (same as bottom) — 

Spread (same as bottom) — 

Rolling (same as bottom) — 

Total (loose measure) $ — 

Add 30% — 

Total rolled measure $ — 

Filler (same as bottom) — 

20% profit — 

Total, No. 1 $^^~ 

Interest and depreciation — 

Estimate $ — 

Local Top Stone. 

Cost in bins $ — 

Manipulation same as for imported stone — 

Total $ — 

20% profit — 

Total No, 1 

Interest and depreciation . , 

Estimate 



Material. 



Imported No. 2 Stone, Estimated Loose 

2,400 lbs. stone $ — 

6% profit — 



Total No. 1 $ — 



318 COST DATA AND ESTIMATES 

Unloading (same as bottom) — 

Haul (same as bottom) — 

Spreading o.io 

Total $ — 

20% profit — 

Total No. 2 $ — 



Total No. 1 $ — 

Total No. 2 — 

Estimate $ — 



Local No. 2 Stone. 

Cost per cu. yd. in bins $ — 

Haul same as above — 

Spreading same as above — 

Total $ — 

20% profit — 

Estimate $ 

The following is an example of the method of using these standard 
forms. 

Estimate for Local Fence Stone Bottom Course 

Assume that stone will cost $0.10 per cu. yd. in the fences. 
" I mile average haul to crusher. 
" 20% of the stone has to be sledged or blasted. 
" f of a mile average haul from the crusher. 
" that filler costs $0.15 per cu. yd. in the pit. 
" average haul of J mile for filler. 

" that the interest and depreciation charge for the total 
job, say 4 miles, is distributed over 6,000 cu. yds. of macadam. 

Use Standard form for Local Bottom Stone, given on page 261. 

Cost 1 cu. yd. field stone $0.10 

Blasting and sledging \ cu. yd. stone 0.08 

Loading 1 cu. yd. field stone 0.15 

Hauling 1 cu. yd. field stone \ mile " 0.18 

Crushing 1 cu. yd. (Mixed granite and sandstone) 0.15 

1 cu. yd. Total cost in bin $0.66 

Cost 1 cu. yd. crushed stone in bins $0.66 

Loading on wagons 0.01 

Haul to road, average conditions, f of a mile ... 0.22 

Spreading 5 \" loose 0.06 

Rolling 0.05 

Total $1.00 






EXAMPLE OF METHOD 319 

Add 30%. . , .30 

Per. cu. yd. rolled measure $1.30 

Filler (see below) 0.31 

Labor, total $1.61 

Add 20% profit 0.32 

Total, No. 1 $1.93 

Interest, depreciation, etc. (see below) 56 

Estimate per cu. yd. rolled in place $2.49 

say $2.50. 

Filler. As mentioned on page 240, the screenings produced in 
crushing bottom only, as in this case, will amount only to 50% of 
the required filler, therefore two estimates must be made for filler 
as below: 

Screenings for Filler. 

Cost of 0.35 cu. yds. screenings in bin @ $0.66 per cu. yd. . . $0,230 

Loading 0.35 " " from bin 0.003 

Hauling 0.35 " " " f of a mile 0.077 

Spreading and brooming 0.35 cu. yds 0.070 

Total ; $0,380 

Sand Filler. 

Cost of sand in pit 0.35 cu. yds $ 0.052 

Loading 0.35 cu. yds 0.050 

Hauling 0.35 " " \ mile (short-haul figures) 0.060 

Spreading and brooming 0.35 cu. yds 0.070 

Total $0,232 

Average these costs as the screenings must be utilized to use up 
the total output of the crusher. Average filler $0.31. 

Interest, Depreciation, etc. 

From page 255, using value adopted for, say, waterbound macadam 
roads, the following charge for a 4-mile road is figured: 

Interest on plant 4X 103.00 . . . $412.00 

Depreciation on plant 4X245.00 .... 980.00 

Repairs on plant 4X180.00 .... 720.00 

Interest on pay-roll 4X 50.00 .... 200.00 

Bond charge 4X 20.00 .... 80.00 

Insurance 4X 120.00 .... 480.00 

Moving plant on job 500.00 

Total $3,372.00 

to be spread over 6,000 cu. yds. of macadam. 

3,372 

~~ = 0.56 cents 

6.000 



320 COST DATA AND ESTIMATES 

The cost of an improved highway generally depends on the item 
of top and bottom stone in place complete. Many of the minor 
items have standard prices. Such items as cast-iron pipe, the vari- 
ous sizes of tile, pipe railing, mesh reinforcement steel, etc., will 
hardly vary in price throughout the Eastern States. A table of 
these standard prices as used by the New York State Highway Com- 
mission is given below. 

It will be noted that all of these items have little bearing on the 
total cost, and that the items of Earth Excavation, Sub-base, or 
Sub-base Bottom Course, Macadam Bottom and Top Course, Con- 
crete Foundation, Brick Pavement, etc., which of necessity are not 
standard in price, determine whether or not the road is to be expen- 
sive. 

Unit Prices Minor Items 



Overhaul on excavation $ o.oi per yd 



sta. 
yd. 



sq 
a 




ft 

lin. 


ft 

ft. 
it 


a 


n 


ton 
lin. 


ft. 

a 



Third-class masonry cement joints . . 6.00 per cu 

Second-class concrete 9.00 " " 

Third-class concrete (stone ) 7.00 " 

" " " (gravel) 5-50 " * 

Pointing old masonry 0.75 " sq 

Riprap 1.50 " cu 

Paving cement joints 1.50 

Cobble gutter 0.50 

Expanded metal 0.08 

Guard-rail 0.30 

2" pipe rail 1.50 

Concrete guard-rail 1.00 

Cast-iron pipe in place 35-oo 

6" V. T. P. in place 0.30 

12" V. T. P. " " 0.60 

15" V. T. P. " " 0.90 " " " 

18" V. T. P. " " 1. 10 " " " 

24" V. T. P. " " 2.00 " " " 

Relaying old pipe 0.10 " " " 

4" farm tile under drain in place .... 0.10 " " " 

Steel in place 0.05 " lb. 

Oak timber in place 50.00 " M.B.M. 

Hemlock timber in place 40.00 " M.B.M. 

Danger signs 2.00 each 

Guide-board posts 6.00 " 

Highway No. signs 1.00 " 

Guide signs per letter 0.15 " 

The item of Earth Excavation as shown in Table 36 may vary 
between 40c and 65c. In extreme cases where material is difficult to 
handle, it may be estimated still higher. A particular instance of 
costly excavation where 70c was estimated occurs on a road near 
the Lackawanna Steel Plant at Buffalo. This road had been filled 
with slag from time to time. 

In the remaining variable items the length of haul is a governing 
factor and three actual conditions of determining the average haul 
are given here before proceeding farther with the estimate data. 



EXAMPLE OF METHOD 321 

The following cases 1, 2, and 3 show also the present method of 
estimating where interest and depreciation are not directly considered. 

Case I 

The simplest possible conditions. Perry Village County Highway, 
Wyoming County, N.Y. Imported stone, delivery at middle of 
road — coal trestle available for unloading — no dead haul to road. 
Road 16 feet wide throughout. 

Railroad at Station 60 Station 0+00 = beginning of contract 

106+ 23 = end of contract 

For ease of computation, say stone runs 10 yds. to mile. 

Station o + 00 to 60 

1.1 miles average .55 miles ,55milesXn yds. = 6.05 yd. miles 

Station 60 + 00 to 106 + 23 

., .. .44 miles X 8. 7 yds. = 3.83 yd. miles 

.87 miles average .44 miles J/ , — ; —* ^ , r, — ^ — r 

1 6 Total yds. 19.7 9.88 yd. miles Total 

9.88 yd. miles „ . . 

■ = = 0.50 miles average haul 

19.7 yds. J & 

Completion of Perry Village Estimate. 

Stone from Rock Glen Quarries Stone $0.65 per ton f.o.b. 

Cu. yd = 2400 lbs. Freight .40 " " " 

Sub-base Stone .50 " " " 

Bottom Top Screenings Sub-base 

Stone 78 .78 .78 .60 

Unloading 15 .15 .15 .15 

Average haul § mi. at 

•35 ••••; 175 .175 -175 .175 

Manipulation 30 .25 .20 .20 

1.305 
Consolidation (plus \). .468 .451 .4 + \ .22 

.5220 

Filler (^ cu. yd. sand Screen- 

at $1.00) 50 ings .522 Sand .50 

Profit (20%) 474 .465 .369 

Freight (40 + .08 + (40+. 08+ (40+08 

.16) 64 .16+192) .832 +.096 ) .576 

6% interest on freight 
to cover demurrage, 
etc 038 .05 .034 

Manipulation of Bi- 
tuminous Material . . .60 

S3.525 $4,275 te.824 

Use $3.55 Use $4.30 Use $2.80 

Case II 

The Walker-Lake Ontario Road, Monroe County, N.Y. Road 
extends from Station o + 00 to Station 197 + 45. . 



322 COST DATA AND ESTIMATES 

Local stone — mostly fences. Because of location of stone as 
determined by engineer's inspection, it was determined to make 
three set-ups of crusher, at Station 40, 104 + 50 and at Station 157. 
The hauls from stone piles to these crushing points were figured 
in the regular manner. From the crusher to road, the hauls were 
arranged, 

From Station 40 — haul stone o + 00 to 77 + 00 

" " 104 + 50 haul stone 77 + 00 " 130 + 00 

" " 157 " " 130 + 00 " 197 + 45 

Care was taken to see that enough stone was available near each 
crushing point to furnish macadam between stations supplied from 
that set-up. 

The widths of road were as follows: 

o + 00 to 40 + 00 — 12' wide 
40 + 00 " 66 + 60 — 16' wide 
66 + 60 " 129 + 50-14' " 
129 + 50 " 197 + 45-12' " 
Use 10 yds. per mile for 12' road 
proportionally 11.7 yds. mile for 14' road 
" 13.3 " " " 16' " 

Haul on road from Station 40 + 00 

12' wide o + 00 to 40 + 00 

0.76 miles average .38 .38 miles X 7.6 yds. = 2.89 yd. miles 

16' wide 40 + 00 to 66 + 60 

.50 miles average .25 .25 miles X 6.6 yds. = 1.65 yd. miles 

14' wide 66 + 60 to 77 + 00 

.20 miles average .1 

plus dead haul .5 

.6 .6 miles X 2.3 yds. = 1.38 

16.5 5.92 yd. miles 

Haul on road from Station 104 + 50 

14' wide Station 77 + 00 to 129 + 50 (say 130) 

77 + 00 to 104 + 50 

.52 miles average .26 .26 miles X 6.1 yds. = 1.59 yd. miles 

104 + 50 to 130 

.48 miles average .24 .24 miles X 5.6 yds. = 1.34 yd. miles 

1 1.7 yds. 2.93 yd. miles 

Haul on road from Station 157 

12' wide Station 129 + 50 (say 130) to 197 + 45 
130 to 157 

.51 miles average .26 .26 miles X 5.1 yds. = 1.33 yd. miles 
157 to 197 + 45 

.76 miles average .38 .38 miles X 7.6 yds. = 2.89 yd. miles 

12.7 yds. 4.22 yd, miles 



EXAMPLE OF METHOD 323 

Average haul for entire road 

From Station 40 16.5 yds. 5.92 yd. miles 

104 + 50 n.7 " 2.93 " " 

157 1^7 " 4.22 " " 

40.9 13.07 

13.07 -7- 40.9 = .32 miles 

say .3 miles average haul 

Sub-base Bottom Course 

Stone $ .15 

Sledging, blasting, and sorting 30% of stone at .35 per yd. . . .105 

Loading into wagons 15 

Haul to crusher at Stations 40, 104 + 50 and 157. One 

mile at .35 35 

Haul on road. 3 mile at .35 105 

Manipulation 20 

Consolidation (plus i) 212 

Filler (J cu. yd. sand at .80) 40 

Profit (20%) -334 

$2,006 
Use $2.00 

Local Stone Top Course — Bituminous Binder 

Top Course Screenings 

Stone 15 .15 

Sledging, blasting, and sorting 60% of 

stone at .35 .21 .21 

Loading into wagons .15 15 

Haul to Crusher at Stations 40, 104 + 50 

and 157. 1.1 miles at .35 385 .385 

Crushing 35 .35 

Haul on road .30 miles at .35 .105 .105 

Manipulation .20 .20 

Consolidation (plus f ) .517 1.55 

Filler (.401. yd. of screenings) .620 .620 

Profit (20%) 537 

Manipulation Bituminous Material .60 

$3-824 
Use $3.85 

Case III 

The Obi-Cuba Highway, #965, Allegany County, N. Y. 
9.93 miles long. 

From a field inspection of this road, it was found that stone was 
available at both ends of road, but not in the middle. An ample 
supply of good gravel was found in the middle section, and it was 
determined to build a concrete base with bituminous top, this type 
of road being the only one which could be built using local material. 



324 



COST DATA AND ESTIMATES 



The hauls and freight charges on imported material would make the 
cost prohibitive. 

The road was divided into three sections as follows: 
Station o + oo to 330 local field stone concrete 

Station 330 + 00 " 460 " gravel " 

Station 460 + 00 " 524 + 14 " quarry stone " 

Haul on stone + 00 to 330. Crusher at 146, 220, and 285. 
These crusher set-ups were determined upon more by reason of 
nearness of stone supply and grade of haul than to equalize the haul- 
ing distance. The haul to the crusher was figured for the separate 
sources of supply and found to average i| miles. 

Haul from crusher on road, Station 146 to Station + 00 
(12' wide use 10 yds. per mile) 2.76 miles, average 1.38 miles. 

38 miles X 27.6 yds. = 38.09 yd. mi. 



25 



25 



43 



X 


5 


X 


10 


X 


5 


X 


8 


X 


8.6 



tl _ 



1.25 



5-o 



= 1.25 



= 3-2 



= 3-7 



64.2 yds. 52.49 yd, 



mi. 



Station 146 to 170 
0.5 miles, average .25 miles 
Station 220 to 170 

1.0 miles, average 0.5 miles 
Station 220 to 245 

0.5 miles, average .25 miles 

Station 285 to 245 
0.8 miles, average 0.4 miles 

Station 285 to 330 
0.86 miles, average .43 miles 

Total for 1st section 
52.49 -r- 64.2 = 0,82 mile, average haul for 1st section. 

Haul from gravel pit to road. Station 330 to 460. 

Bank station 385 at side of road — no dead haul great enough to be 
figured. 
Station 385 to 330 

1.1 miles, average haul .55 miles .55 miles X n yds . = 6.05 yd, miles 
Station 385 to 460 

1.4 miles average haul .7 miles .7 " X 14 " = 9-8 " 

Total 25 yds. 15.85 yd. miles 
15.85 -S- 25 = .63 miles Say .65 average haul 

Haul from quarry in Village of Cuba § mile from end of road. 

Station 460 to 524 + 14 

Station 460 " 500 14' wide (use 11.7 yds. per mile) 

Station 500 " 524+14 16' wide (use 13.3 yds. per mile) 

Station 460 to 500 

0.8 miles, average .4 mi. 

Station 524 + 14 to 500 dead haul .5 " 

Quarry to 524 + 14 " " _ 1 75 " 

1.65 " 
1.65 miles X 9.36 yds. = 15.44 yd- mi. 
Station 500 to 524 + 14 
0.5 miles, average haul .25 mile 
Quarry to 524+14 dead haul .75 mi. 1 mile X 13.3 yds. = 13.3 y d. mi. 

i.oomi. Total 22.66 28.74 " " 



XS7-6 " 


= 165.89 


X io. 4 " 


= 54 


X i4.o " 


= 9 .8 



EXAMPLE OF METHOD 3 2 5 

28.74 -S- 22.66 = 1.27 Say 1.3 miles average haul . 

Haul on Sand Pits at Stations 26 and 385 

Station 26 to + 00 
.5 miles, average .25 mi. .25 miles X 5 yds. = 1.25 yd. mi. 

Station 26 to 330 
5.76 miles, average 2.88 mi. 2.88 

Station 385 to 330 
1.04 miles, average .52 mi. .52 " 

Station 385 to 460 
1.4 miles, average .7 mi. .7 " 

Station 460 to 500 
0.8 miles, average .4 mi. 

385 to 460 dead haul 1.4 mi. 

Total 78 " 1.8 " X 9-36 " = 16.8 " " 

Station 500 to 524 + 14 
0.5 miles, average .25 mi. 
460 to 500 dead haul .8 mi. 
385 to 460 " " 1.4 mi. 

Total "245 mi. 2.45 " X 6.65 yds. = 16.3 " " 

103.01 215.44 

215.44 -£- 103.01 = 2.1 miles average haul. 

Hani on Cement 

Cement delivered at Cuba and Portville. 

Station o + 00 to 160 Say 10 bbls. to mile 

3 miles, average 1.5 mi. 7.5 miles X 30 bbls. = 225 bbl. mi. 

dead haul, Portville 6.0 mi. 

to o + 00 7.5 mi. 

Station 160 to 460 

5.68 miles, average 2.84 mi. 

460 to 524 -+- 14 dead 1.3 mi. 

Penn. R.R. to 524 +14 .2 mi. 

4.34 mi. 

4.34 mi. X 56.8 bbls. = 246.5 bbl. mi. 
Station 460 to 500. 
.8 miles, average 0.4 mi. 

500 to 524 + 14 dead .5 mi. 

Penn. R.R. to 524 + 14 .2 mi. 

1.1 mi. 

1.1 mi.X9.36 bbls. = 10.3 bbl. mi. 
Station 500 to 524 + 14 
.5 average .25 mi. 

Penn. R.R. to 524 + 14 .2 mi. .45 mi.X6.65 bbls.= 3.0 bbl. mi. 

.45 102.81 484.8 bbl. mi. 

484.8 -r 102.81 =4.7 miles, average haul. 

Having the haul figured for stone, gravel, cement, and sand, it was 
decided to obtain a composite price for the aggregate of the concrete 
instead of presenting an estimate with three prices for concrete 
foundation. This was done as follows: 



326 COST DATA AND ESTIMATES 

Field Stone. 

Stone $.10 yd. royalty 

Blasting 35 " 

Loading 15 " 

Haul to crusher 1.5 @ 40c . . .60 " 40c. yd mile used as haul 

1 Crushing 30 " was off steep hills and 

Haul to road .8 mi. @ 35c.. . .28 " hard grades 

$1.78 yd. 
Gravel. 

Gravel (royalty) $.50 

Stripping 05 

Loading (by hand) .15 

Haul to Station 385, 0.1 mile @ 35c .03 

Haul on road, .65 miles @ 35c .23 

I96 
Stone at Cuba Quarry. 
This stone bought from quarry owner at flat rate of 75c. in bins: 

Stone $.75 

Haul 1.3 @ 35c 455 

$1,205 Say $1.21 

Sta. 0+00 to 330 = 6.25 miles @ 10 yds. = 62.5X$i.78 = $iii.25 

330 " 460 = 2.46 " "10 " =24.6X .96= 23.62 

460 " 500 = .8 " " n. 7 " = 9.36X1.21= 11.33 

500 to 524+14= .5 " "13.3 " = 6.65 X1 21= 8.05 

103. 11 ^ $154-25 

$154.25 -T- 103. 1 1 = $1.49 composite price 
Sand 

Sand (screened) $1.00 yd. royalty 

Loading .10 " 

Haul to road 0.1 @ 40c 04 " 40c. used because of 

Haul on road 2.1 miles @ 35c. . .735 steep hard grade 

$1,875 Say $1.88 
Cement 

Delivered at Cuba or Portville $1.05 per bbl. 

Haul .188 tons X 4.7 miles X .29 per ton mile . . . .25 " " 

$1.30 
Concrete 
Inasmuch as gravel must be screened and sharp sand supplied, the 
proportions for stone concrete, ratio 1 — 2\ — 5, were used in place 
of standard gravel proportions. This is Fuller's rule for proportions 
of cement, stone, etc., for one cubic yard of concrete. A table of 
these ratios for different mixtures is found on page 248. 

Stone $i-49X .92 = $1.3708 

Sand 1.88X .46 = .8648 

Cement 1.30X1.21 = 1.573 

$3.8086 

1 This item is higher than noted in the previously given cost data, as this esti- 
mate is made according to the N. Y. S. method, which does not consider interest 
and depreciation as a separate item. 



EXAMPLE OF METHOD 3^7 

Mixing $ .40 

Spreading 20 

Profit 20% .8817 

$5-2903 
Say $5.30 per cu. yd. 

Note : — This method of estimating does not consider deprecia- 
tion directly. See other method of estimating following. 

The method of estimating the top course for a Concrete Bitumin- 
ous Top road does not vary from an ordinary bituminous top course, 
except that under the present New York State specifications the 
course is figured for loose measure. Therefore the items for con- 
solidation and filler would be omitted. 

Brick Cost Data on Country Roads. 

The cost of brick pavements on country roads differs somewhat 
from similar work on city streets. There is not much data avail- 
able for this class of work, but through the courtesy of Mr. Wm. C. 
Perkins, First Assistant Engineer, New York State Department of 
Highways, the author is able to give some unusually reliable data 
obtained from fifteen miles of brick paving averaging 14 ft. wide, 
built near Buffalo, N.Y., in 19 10. Mr. Perkins' method of estimating, 
as given on page 331, assumes that 20% profit on both materials and 
labor will take care of the plant and pay-roll charges and give a reason- 
able profit. The method of estimating is different from that given 
on macadam roads. His results are good. 

Excavation. Where brick pavement is built on an ordinary unim- 
proved country road, the excavation is of the same class and will 
cost the same as given for macadam roads. 

Where pavements are built over macadam roads and the old sur- 
face must be cut into two or three inches and reshaped, the excava- 
tion is much more expensive. For this class of work see page 335 
(scarifying and reshaping). 

Labor Manipulation for Different Items of Brick Pavement Laid 
During 1910, in the Buffalo Residency. 

These items figured from force accounts kept by the different 
engineers in charge of roads. 
Labor averaged $0,175 per hour. 
Concrete Base, 5" thick (exclusive of edging). 
Machine-mixing, laying same in place, including labor of tamping, etc. 
Road No. 2-R, Buffalo-Hamburg.. $0.0853 per sq. yd. 

" 128, Buffalo- Aurora 0.0991 " " " (gravel 

concrete) 
" 863, Blasdell Village. ... 0.1228 " " " 
" 87, Main Street, Sec. 2. 0.1129 " " " (3" base) 
" 862, Hamburg Village . . 0.0655 " " " (28' and 

30' wide) 

The excessive cost on Blasdell Village due to a poor concrete 
mixer (gasoline) which was constantly breaking down. 



328 COST DATA AND ESTIMATES 

On Main Street, Sec. 2, poor organization and too high priced 
men; also, lack of water, causing delays. 

On Hamburg Village low price due to width of base 28' and 30', 
allowing work to progress faster. 

On Road No. 69, Main Street, Sec. 1, edging and base were 
laid in one operation; gasoline mixer; plenty of water; cement, 
$1.12; sand $1.40; labor, $1.90 per day; stone, $1.12 per cu. yd.; 
base 3" thick; 8" edgings; cost in place, including edging $4,696 
per cu. yd., or $0,506 per sq. yd., or $0,886 per lin. ft. of road. 

Assumption. If we assume, $0.09 per sq. yd. as an average cost 
for 1 6' road (exclusive of edging) the manipulation would be 
$0,648 per cu. yd. 

If we assume $0.0655 P er S Q- yd- for street work (Hamburg 
Village) the manipulation would be $0,472 per cu. yd. 

Concrete Edging. 8" thick. 

Hand-mixed; placing same, including erecting of forms, and 
removing same; tamping, placing steel, and all labor necessary. 
Road No. 2-R, Buffalo-Hamburg, $0.0730 per lin. ft. of edging 

0.0821 " sq. yd. of pavement 
(Road 16' wide) 
Road No. 128, Buffalo- Aurora, 0.0555 " nn - ft. of 5" edging 

0.0713 " sq. yd. pavement 
(Road 14' wide) 
Road No. 863, Blasdell Village, 0.0826 " lin. ft. edging 

0.0929 " sq. yd. pavement 
(Road 16' wide) 
Road No. 87, Main Street, Sec. 2, 0.0748 " lin. ft. edging 

0.0842 " sq. yd. pavement 
(Road 16' wide) 

On Road No. 862, Hamburg Village, concrete curb 6" top, 
10" bottom, 15" deep; hand-mixed, exposed curbing, all labor, 
including erection and removal of forms, $0.1294 per lin. ft. 

Assumptions- If we assume $0,082 per sq. yd. of paving as' 
cost of edging and $0.09 per sq. yd. cost of base, the total cost 
per sq. yd., 16' road (including edging) would be $0,172 per 
sq. yd., or the manipulation would be $1,238 per cu. yd. 

If we assume $0,073 P er ^ n - ft- of &" edging io|" deep, the 
manipulation would be $3,379 per cu. yd. of the edging in place. 
(This high cost due to forms, etc., and the small amount of con- 
crete per lin. ft.) 

Sand Cushion. 

Spreading sand, rolling, and making bed ready for work. 
Road No. 2-R, Buffalo-Hamburg, $ 0.0102 per sq. yd. 
Road No. 128, Buffalo- Aurora, 0.0082" " " 
Road No. 863, Blasdell Village, 0.0187 " " " 
Road No. 87, Main St., Sec. 2, 0.0151 " " " 
Road No. 862, Hamburg Village, 0.0160 " " " (28' and 30' 

wide) 

On Main Street, Sec. 1, Road No. 69; sand, $1.40; labor, 
$1.90; cost per sq. yd. 2" thick, $0.0838, including material. 



BRICK PAVEMENT 329 

Assumption. From the above I would assume $0,013 P er 
sq. yd. as cost of preparing sand cushion. 

Brick Pavement. 

Laying brick, including all labor of handling from the piles, 
removing all culls, and the rolling of the brick. 
Road No. 2-R, Buffalo-Hamburg, $0.0611 per sq. yd. 
Road No. 128, Buffalo-Aurora, 0.0544 " " " 
Road No. 863, Blasdell Village, 0.0969 " " " 
Road No. 87, Main St., Sec. 2, 0.0965 " " " 
Road No. 862, Hamburg Village, 0.0700 " " " (28' and 30' 
Road No. 69, Main St., Sec.i, 0.0983 " " " wide) 

Assumption. 

I consider Blasdell and Main Street, Sec. 1 and Sec. 2, too 
high and the engineer claims that the force was cut up and 
wasted time. 

I would assume $0,070 per sq. yd. as cost of laying brick, etc. 

Grouting. 

Necessary grouting to obtain flush joints, scoop method, in- 
cluding the placing of the protecting sand covering. 

Road No. 2-R, Buffalo-Hamburg,$o.o2i9per sq. yd. 

Road No. 128, Buffalo- Aurora, 

Road No. 863, Blasdell Village, 

Road No. 87, Main St., Sec. 2, 

Road No. 69, Main St., Sec. 1, 

Road No. 862, Hamburg Village, 

On Main St., Sec. 1, Road No. 69; sand, 
labor, $1.90; actual cost $0.0848 per sq. yd., including materials. 
Assumption. 

From the above I would assume $0,028 per sq. yd., as the cost 
of applying grout. 

Expansion Joints. 

Removing strips, cleaning joints, and pouring tar. 
Road No. 2-R, Buffalo-Hamburg, $0.0067 P e r tin. ft. of joint 

0.0076 " sq. yd. pavement 
(Road 16' wide) 
Road No. 128, Buffalo-Aurora, $0.0057 per lin. ft. of joint 

0.0073 " sq. yd. pavement 
(Road 14' wide) 
Road No. 863, Blasdell Village, $0.0115 per lin. ft. of joint 

0.0129 " sq. yd. pavement 
(Road 1 6' wide) 
On Main Street, Sec. 1, Road No. 69, the expansion joints cost 
$0.0296 per lin. ft., or $0,033 P er sq. yd. (Road 16' wide), in- 
cluding material, labor, etc. 
Assumption. 

From the above I would assume $0.0075 P er sq. yd. as the cost 
of expansion joints. 



0.0211 


k a 


a 


0.0322 


cc a 


a 


0.0321 


ct tt 


u 


0.0285 


a 11 


it 


0.0273 


it u 


" (28 and 30' 
wide) 


}; sand, 


$1.40; 


cement, $1.12; 



33° 



COST DATA AND ESTIMATES 



Unloading. 

Data for unloading not reliable. 
Road No. 2-R Buffalo-Hamburg 
Road No. 863, Hamburg Village 



.$0,014 per sq. yd. 

.Contract taken for $1.50 per 
1,000 brick; unloaded, haul 
i mile, and pile; this would 
be $0.06 per sq. yd. 

.$0,019 P er S Q- yd. 



Road, No. 69, Main St., Sec.i . . 
Assumption. 

I would assume $0,028 per sq. yd. as on and off. 

Hauling. 

No reliable data. 

If we allow 600 brick per load, $5 per day for teams, 10 loads 
per day, haul 1 mile costs $0,034 per sq. yd. 

Summary, Labor Cost of Brick Pavement. 

Manipulation of Concrete 

Pavement 16' wide; edging 8" X 10J". 

* Concrete base $0.09 per sq. yd. . . $0,648 per cu. yd. 

edge ■ 0.082 " " " .. 3.378 " " " 

Concrete base and edging. . .$0,172 " " " . . 1.238 " " " 



Brick Work Labor 

Preparing sand cushion $0.0130 per sq. yd. 

Laying brick 0.0700 

Grouting 0.0280 

Expansion joints 0.0075 

On and off 0.0280 

Haul one mile 0.0340 

Cost of labor $0.1805 

Useful Data for Brick Roads. 

6" X 10J" edging per lin. ft. of edging 0.016203 cu - yd. 

8" X 10J" " " " " " 0.021605 " " 

5" X 16' concrete foundation per lin. ft. 16' 

road 0.24691 " "■ 

2" sand cushion loose per sq. yd o»°555 

1 barrel of cement will grout 36 sq. yds. of pavement. 

1 barrel of paving pitch will fill 130 lin. ft. of joints 1" wide. 

Amount of Grout Required for Stone Block Paving. 

For blocks similar to Medina sandstone blocks, running about 
26 to the sq. yd., Gillette states that 0.6 cu. ft. of joint filler are 
required per sq. yd. of pavement with joints averaging \" wide. 
Second quality blocks with wider joints require proportionally 
more. 

* Recent cost data indicates that $0.35 per cu. yd. is ample. 



a 

tt 



STANDARD ESTIMATE 331 

STANDARD ESTIMATE, BRICK SURFACING, EXCLUSIVE 
OF FOUNDATION 

Materials. 

Per Sq. Yd. 

Cost of brick, f.o.b. unloading point $ 

" " sand for sand cushion, on job 

' grout, on job 

cement for grout, on job 

" " paving pitch for expansion joints, on job 

Labor and Teaming. 

Unloading brick and piling along road $0,035 

Hauling brick per mile 0.040 

Preparing sand cushion 0.020 

Laying brick 0.070 

Grouting 0.028 

Expansion joints 0.007 

Total $ — 

Add 20% profit — 

Estimate $ — 

SAMPLE — Standard Estimate, Brick Pavement — 
Wm. C. Perkins 

Brick: $22.50 per 1,000 f.o.b. cars at Road siding, 

bricks lay 40 to the sq. yd. 
Labor, $0,175 P er hour, 10 hours. 
Sand, 1. 00 per cu. yd. on cars at siding. 
Stone, 1.25 per cu. yd. on cars at siding. 
Cement, 1.30 per bbl. delivered on work. 
Sand: 

f.o.b. cars $1.00 

Unloading 15 

Haul 1 mile @ $0.30 30 

Cost cu. yd. sand $1.45 

Stone: 

f.o.b. cars $1.25 

Unloading 15 

Haul 1 mile @ $0.30 30 

Cost cu. yd. stone $1.70 

Concrete: 1 - 2 J - 5. 

Use any standard mixing tables, stone 1" and under, dust 
screened out. 

Cement, 1.19 bbls. X $1.30 = $1.55 

Sand, 0.46 cu. yds. X 1.45 = 0.67 

Stone, 0.91 " " X 1.70 = 1.55 

* Manipulation = 0.50 

$4.27 
20 % profit ...85 

Total $5.12 

* Recent cost data indicates that $0.35 is ample with labor at $0,175 per hour. 



332 COST DATA AND ESTIMATES 

The manipulation is based on machine-mixing and is for base 
alone laid 5" thick. The concrete edging is estimated separately 
and runs from $0.13 to $0.15 per lin. ft. 

Material per Square Yard 

Brick f.o.b. cars , . . . .$0,900 

Sand cushion and cover 0.080 

Grout (sand and cement) 0.042 

Material expansion joint 0.008 

$1,030 
Labor per Square Yard 

Unloading and piling $0,035 

Haul 1 mile 0.040 

Laying and rolling 0.070 

Making sand cushion 0.020 

Grouting 0.028 

Expansion joints 0.007 

Culling, replacing, etc 0.005 0.205 

$I - 2 35 
20 % profit .247 

Total $1,482 

Therefore, standard 16' road is estimated to cost, per square 
yard (exclusive of edging) : 

Concrete base $0,711 

Brick 1.482 

Total $2,193 P er S Q- yd. 

Say, $2.20 per sq. yd. 

In the above estimate I have allowed 20% profit on material 
and freight. I do this so as to cover all interest charges, inci- 
dentals, contingencies, etc. I consider this one of the fairest 
ways to take care of all general expenses. 

MAINTENANCE AND REPAIR COSTS 

Cold Oiling. The following data is furnished by Mr. Frank 
Bristow, Supt. of Repairs, Division No. 5, New York State 
Department of Highways. The work was done in 19 10. Labor 
averaged $0.20 per hour; teams, $0.50 per hour. 

Oiling. Actual Cost Data. No. 6 stock or 65% aspnaltic 
base oils applied cold by Studebaker Oiler upon macadam road 
which had been swept by horse sweeper, oil being broomed 
by hand where necessary and then covered by a thin coat of 
dustless screenings, or gravel, spread by hand. 

The labor costs include pumping oil from the car tank, hauling 
same to road, applying same, sweeping road and spreading 
screenings; also, demurrage on cars and moving tools and re- 
pairs, but not cost of the plant. 



MAINTENANCE AND REPAIR COSTS 

Table 51 



333 







Average cost of 
materials 


Average 

Quantities of 

Materials Used 


Average Cost 


>> 

-4-> 

3 

6 


j3 <u 

tc 

£ > 

7 
4 
12 

3 


> 3 


O.B 

55 

S3 

O 




«- 
. 


rtCO 

O M 


t- . 

§*■ 

U ft 


M 

O . 

M 


Total Labor 
and Material 
per Sq. Yd. 


Orleans 

Niagara 

Erie 


2.48 
2.24 
2.00 

4-43 


$0.0435 
0.0425 

0.0437 
0.0455 


$1.82 

i-57 
1.88 
1.83 


0.42 
0.43 
0.34 
0.42 


0.016 
0.016 
0.012 
0.015 


$O.OI3 
O.OI4 
0.007 
O.Oig 


$0,057 
0.057 
0.045 
0.066 


Erie 





Other information would show that cost per mile to sweep average 
road is $8.33; cost per gallon applying oil $0.0075; cos t ah labor 
sweeping, hauling, applying oil and cover about $0.25 per gal. used. 

Tasle 51 A 
Division 7 N. Y. S. Dept. Highways 

H. G. HOTCHKISS SUPT. MAINTENANCE 





Cost Data for Oiling, 


Surface Treatment 191 5 






No. 


Kind 


Gals. 


No. Tons 


Total Cost 


Total Av. 


Cost per 


Miles 


Sq. Yds. 


Bit. Mat. 


per 


of Cover 


per 


Cost per 


Mile 16' 








Sq. Yd. 


per Mile 


Sq. Yd. 


Sq. Yd. 


Surface 


20.54 


158144 


CO. 


0.25 


62 


0.0344 


1 




23-63 


188208 


CO. 


0.25 


41 


0.0250 




17-75 
19.94 


146734 
172775 


CO. 
CO. 


0.24 
0.19 


37 
43 


0.0237 
0.0189 


} 0.026 


244.06 


21.47 


200995 


C 0. 


0.19 


59 


0.0264 






16.22 


199925 


CO. 


0.28 


74 


0.0287 






22.51 


188601 


L. C 0. 


0.20 


3i 


0.0195 


\ 0.0183 


171.78 


41.09 


382330 


L. C. 0. 


0.20 


27 


0.0177 


15-44 
13.42 


126657 
126056 


H. C T. 
H. C T. 


0.25 

0.25 


40 
40 


0.0323 
0.0337 


J 0.0330 


309.77 


17.19 


143846 


L. C T. 


0.25 


47 


0.0319 


0.0319 


299.45 



C O. = Cold Oil. See Specifications, page 386. 
L. C. O. = Light Cold Oil. 

H. C T. = High Carbon Tar. See Specifications, page 388. 
L. C T. = Low Carbon Tar. See Specifications, page 389. 
Cover Material; Slag or Stone Screenings and Pea Gravel. 

Cost of Applying Oil (Mechanical Spreaders) 

Cost of Applying Cover approx 

Cost of Oils on Switch C. O. $0.03 

L. C. O. 0.03 

H. C T. 0.07 

L. C T. 0.06 



$0.01 per gai. 
0.25 " ton 



334 



COST DATA AND ESTIMATES 



Table 51 B 

Division 7 N.- Y. S. Dept. Highways 
Cost Data Repainting and Rebuilding Guard Rail 19 14 



No. Lin. Ft. 
Painted One Coat 


Cost 
per Lin. Ft. 


No. Lin. Ft. 
Painted Two Coats 


Cost 
per Lin. Ft. 


15325 
79925 
17486 
42027 


$.0212 
•0233 
.0251 
.0264 


26428 

8433 
12824 
13160 


$.0425 
.0360 
•0352 
.0442 


Rebuilding Wooden 
Guard Rail 


Rebuilding Concrete 
Guard Rail 


No. Lin. Ft. 


Cost per Ft. 


No.. Lin. Ft. 


Cost per Ft. 


160 

554 
360 

272 


$.219 
.189 
.200 
.141 


100 
335 


$0,896 
0.764 



Hot Tar Flush Coats. The cost of applying hot tar flush coats by 
hand is practically the same as given for applying Bituminous Binder 
penetration method. 

The writer has no reliable data on the cost of machine application. 

Calcium Chloride. The cost of applying calcium chloride as 
a temporary dust layer on ten miles of road in Monroe County, 
N.Y., as given by Mr. Frank Bristow, First Assistant Engineer, New 
York State Department of Highways, is as follows: 

The material was applied by an ordinary agricultural drill. The 
force used was, 1 horse and driver, $0.30 per hour; 1 helper, $0.20 
per hour. No preliminary work of sweeping was done; the material 
was spread on the middle 12 feet of macadam, using, approximately 
0.75 lbs. to the sq. yd., the average speed being 0.5 miles, or 3,500 
sq. yds., per day, at a cost of $0.0015 per sq. yd. 

Cost of calcium chloride at plant $13.00 net ton 

Freight 1 .60 per ' 

Unloading from cars, approximately. . . o. 15 

Hauling three miles, . . 09° 

Total, delivered on road. ... $15 • 65 

Total per sq. yd. delivered on road. . . . 0.0059 

Labor of spreading 0.0015 

Total per sq. yd. in place. . . $0.0074 

Total per mile 12' wide, approximately $52.00 



COST DATA ON RESHAPING ROAD 335 

Cost of Applying Calcium Chloride 

Road No. 5507 Scottsville — Canawagus. Season 1915. W. G. 
Harger, Eng. in charge. 

15 tons were applied at the rate of 1^ lbs. per sq. yd. on a 16' road 
for $22.00 or at the rate of $1.50 per ton. 

Force used, 1 team hauling agricultural plaster spreader. 2 laborers 
helping driver. Calcium Chloride in metal drums had been previously 
distributed along the road. 

Wages: Team, $5.00 per day; Laborers, $2.00 per day. 

Recapping The cost or recapping with any style of macadam 
is practically the same as original construction for that style of work 
except the item of scarifying and reshaping the old road. 

Scarifying. The cost of scarifying, as given by Mr. E. A. Bonney 
on the Erie County repair work for the season of 1907, is as follows: 

COST DATA ON RESHAPING ROAD 

Work was done on Main Street Road, No. 69, Erie County, N.Y., 
between July 15 and Sept. 13, 1907. 

The road had been built as a waterbound macadam. It was worn 
out, particularly in the center. There were few ruts, but the road 
was nearly level; in some stretches the center was lower than the 
sides. It was proposed to reshape the road and to lay a new top 
course treated with tarvia. 

The work of reshaping was done by loosening the old surface with 
spiked wheels of roller; this separated the crust into chunks of various 
sizes which were broken up by men with picks. The stone was then 
raked from the sides to the center, brought to the required crown, 
and rolled ready for the new course of stone. 

The cost of the complete operation included the number of men 
picking and the rollerman's salary. 

Labor $0. 175 per hour 

Rollerman 0.300 " " 

The roller was rented at a flat rate of $5.00 per day, and a portion 
of the time it was used on other parts of the work. This cost plus 
the coal and oil is not included. 

The data was compiled daily, and as the work was performed prac- 
tically every working day between the dates named an average of 
the square yard price should be nearly correct. The highest cost on 
any one day was $0.06 per sq. yd., the lowest cost $0,016, and the 
general average $0.03 per sq. yd. 

1 Through the courtesy of Mr. Halbert P. Gillette, author of 
''Handbook of Cost Data," we are able to publish the following: 

Cost of Resurfacing old Limestone Macadam. "In Engineer- 
ing News, June 6, 1901, I gave the following data to show that the 
intermittent method of repairing macadam is the most economic. 

1 Gillette's Handbook of Cost Data, Myron C. Clark Publishing Company, edition 
of 1907, page 147. Pages 288 and 289, edition of 1910, in slightly different form. 



336 COST DATA AND ESTIMATES 

The data were taken from my timebooks and can be relied upon as 
being well within the probable cost of similar work done by contract 
under a good foreman. It will be noted that the cost of operating 
the roller is estimated at $10.00 per day. This includes interest 
and depreciation as well as fuel and engineman's wages. 

"The road was worn unevenly, but^as it still had sufficient metal 
left, very little new metal was added. 

"The roller used was a 12-ton Buffalo Pitts, provided with steel 
picks on the rear wheels. It required eighty hours of rolling with 
the picks in to break up the crust of a surface 19,400 sq. yds. in area, 
240 sq. yds. being loosened per hour. The crust was exceedingly 
hard, and, at times, the picks rode the surface without sinking in, 
so that a lighter roller would probably have been far less efficient. In 
fact, a ten-ton roller had been used a few years previous for the same 
purpose at more than double the expense per square yard, I am told. 
The picks simply open up cracks in the crust of a depth of about four 
inches, and it is necessary to follow the roller with a gang of laborers 
using hand picks to complete the loosening process. The labor of 
loosening and spreading anew the metal was 1.880 man-hours, or 
a trifle more than 10 sq. yds., per man-hour. About 60% of this 
time was spent in picking and 40% in respreading with shovels and 
potato hooks. 

"After the material had been respread, the short section was 
drenched with a sprinkling cart, water being put on in such abundance 
that when the roller came upon the metal the screenings which had 
settled at the bottom in the spreading process were floated up into 
the interstices. The roller and sprinkling cart were engaged only 
63 hours in this process, 300 sq. yds. being rolled per hour; an excep- 
tionally fast rate. The rapidity of rolling was due to four factors: 
1. The great abundance of water used, the water being a very short 
haul. 2. The unyielding foundation (telford) beneath. 3. The 
abundance of screenings and fine dust, the road not having been 
swept for some time. 4. The great weight of the roller, which was 
run at a high rate of speed. I am not prepared to say that longer 
roiling woule not have secured a harder surface, but I doubt very 
much whether it would. The metal, I should add, was hard lime- 
stone. Summing up, we have the cost of resurfacing the road per 
square yard to have been as follows: 

Cents per sq. yd. 

Picking with roller at $1 per hour $0.40 

Picking by hand labor at $0.20 per hour . 1 . 20 

Respreading by hand labor at $0.20 per hour 0.80 

Rolling with roller at $1 per hour 0.33 

Sprinkling with cart at $0.40 per hour 0.13 

Foreman, 143 hours at $0.30 for 19,400 sq. yds 0.44 

Total 3.30 

"At this rate a macadam road sixteen feet wide can be resurfaced 
for a little more than $300 per mile. The frequency with which such 
resurfacing is necessary will, of course, depend upon several factors, 



COST DATA ON RESHAPING ROAD 337 

chief of which are the amount of traffic and the quality of the road 
metal. I should say that five years would not be far from the aver- 
age for a country road built of hard limestone. Unless the road has 
had an excess of metal used in its construction, new metal should be 
added at the time of resurfacing to replace that worn out. 

"I am unable to see how any system of continuous repair with its 
puttering work here and there can be as economical as work done 
in the manner above described. I would not be understood, how r ever, 
as favoring an entire neglect of the road between repair periods. 
At times of heavy rains and snows, ditches and culverts need attention 
and there should be some one whose duty it is to look after such 
matters. What I do question is the economy of having a man con- 
tinuously at work putting in patches upon the road." 

1 NEW YORK STATE PATROL MAINTENANCE, 1910 

The standard Patrol distance is five miles. 

The standard Patrol distance, brick roads, is twelve miles. 

Patrolman's wages $78 per month, including horse and cart. Patrol 
is operated eight and one-half months in a year. 

The cost of this system of maintenance per mile for 19 10 was, 
approximately, $250 exclusive of administration charges. 

Patrolman's wages $125 .00 

Materials 125.00 



$250.00 

These costs do not include surface treatments. Such a treat- 
ment of a road every two years would amount to about $375 a mile 
per year on waterbound roads. 

Automobile Truck Repair System. The tendency on minor 
repair maintenance work seems to be towards lengthening the patrol 
distance; confining the duties of the patrolman to cleaning culverts 
and ditches, trimming shoulders, and reporting the necessity of 
minor repairs. It is believed that these repairs can be handled more 
economically from a central point by the use of an automobile truck 
specially equipped for such work and which can operate within a 
radius of 20 to 30 miles. Special trucks have been devised with 
facilities for heating and applying bituminous materials as well as 
carrying materials. 

Conclusion. In conclusion the author desires to again call the 
attention of the reader to the fact that while cost data is valuable 
it must be used with discretion and not figured too closely. 

1 Data obtained from Mr. Frank Bristow, Supt. of Repairs, N.Y.S. Dept. of 
Highways. 



33& 



COST DATA AND ESTIMATES 



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CHAPTER XI 



NOTES ON CONSTRUCTION 

No matter how well a road is designed, unless the constructing 
engineer uses good judgment, and the inspection is conscientious 
and intelligent, the results will not be satisfactory. This chapter 
emphasizes the importance of the different stages of the work and 
gives a few suggestions as to the manner of meeting common 
difficulties. 

Staking out for Construction. The construction survey picks 
up the center line shown on the plans and by means of offset 
stakes driven to a certain elevation marks the position and ele- 
vation of the road conveniently for building. Any arrangement 
of stakes that shows the position of the proposed center line 
and the elevation of the proposed grade is satisfactory. These 
stakes may be set on one or both sides of the road at intervals 
of 50 or 100 feet. The offsets to the center line may be marked to 
the nearest one-tenth foot, or the stakes may be so set that the 
offset is an even foot, and they may be driven so that the ele- 
vation of the proposed grade is above or below them an even 
foot, one-half foot, or an odd tenth. A satisfactory method in 
general use in western New York is to set the construction 
stakes on both sides every 50 feet, with an even foot offset and 
driven to such elevation that they are either an even foot or 
one-half foot above or below grade. 



r Stak'ing Ou+ ^ 


r 




No+es 


y 


Sta. 


Offsets 


Cut or Fill 


Levels 




Grade 


Grade 
Hod 

Readmg 


Rod Readinq on Stakes 


L. 


R. 


L. 


R. 


B.S. 


F.S. 


Elev. 


H.I. 


Elev. 


L. 


R. 


B.M*5 














526.42 












JO 


25 


23 


FOB 


FLO 


4.17 






530.59 


524.2 


6A 


• 6.9 


7.A 


t50 


25 


22 


F0.B 


FI.S 








V? 


524.G 


6.0 


6.5 


7.5 


II 


24 


25 


FOB 


FI.5 








97 


525.0 


5.6 


6.1 


7.1 


+50 


21 


26 


COS 


Fl.0 








?? 


525.4 


5.2 


4.1 


0.2 


12 


22 


25 


C0.5 


F/.S 








ft 


525.8 


4.8 


4.5 


6.3 . 


tso 


23 


24 


C1.0 


F2.0 








ft 


526.2 


4.4 


3.4 


6A 


13 


24 


24 


Gr. 


Gr 








9f 


526.6 


4.0 


4.0 


4.0 


+50 


25 


23 


Gr. 


F0.5 








It 


527.0 


3.6 


3.6 


4.1 


14 


30 


17 


Or. 


COS 




3.20 


527.33 


ft 


527.8 


2.8 


2.8 


2.3 


+50 


25 


26 


Gr 


C/.O 


7.41 






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528.6 


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25 


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FI.S 








99 


529 A 


5A 


4-.e 


6.9 


+50 


25 


26 


FLO 


Fl.0 








ft 


560.2 


A 6 


5.6 


5.6 


16 


25 


26 


Gr. 


c/.o 








11 


56). 


3.8 


3.8 


2.8 


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25 


23 


FI.S 


Cf.O 








it 


531.8 


3.0 


4.5 


2.0 


17 


24 


24 


F1.5 


Gr. 








It 


532.6 


2.2 


3.7 


2.2 


+50 


18 


2& 


FLO 


F3.0 








tt 


533.4- 


1.4- 


2A 


6A 


















tf 










\__ 














J 


v 








J 



Fig. 67 
339 



340 



NOTES ON CONSTRUCTION 



Such stakes can be readily explained to the ordinary grading 
foreman so that he has no difficulty in working from them without 
the assistance of an inspector. The 50-foot interval is convenient 
for fine grading, as the lines can be stretched this distance with 
no apparent sag, while if a 100-foot interval is used the sag is ob- 
jectionable. With stakes on both sides of the road the elevation 
of the proposed grade can be readily transferred to the center 
by stretching a line between them and measuring down or up 
the required amount. This is a much simpler and more accurate 
method than transferring by straight-edge where two or three 
lengths of straight-edge must be used from the stake to the center. 




Grade Stake 
Marked C 4.0 
Offset 26.0' 
K 

brad? Stake 

Marked C 1.0 
Offset 24.0' 

Fig. 68. — Showing Suggested Method of Staking out 

The left stake marked C 4.0' offset 28.0' means that the crown 
grade of the finished road is 4.0 feet below the top of this stake and 
that the proposed center line of macadam is 28.0' from the face of 
the stake. 

To transfer the proposed grade to the center by the string method. 
Fasten chalk line to top of left stake; measure up 3.0' above top of 
right stake and draw line taut at this elevation. The string is level 
and 4.0' above crown grade. Pull as tight as possible, allow about 
\* for sag and measure down 3' \\\" for finished grade. 



Cost of Staking Out. The speed and cost of staking at 50-foot 
intervals will, of course, vary with the experience of the men and 
the character of the road. A party of four men should pick 
up the proposed center line and set offset stakes on both sides at 
a speed of 1.5 to 2 miles a day; a party of three men should grade 
these stakes at a speed of 1.0 to 2.0 miles a day, and the cost of 
staking out for construction, including livery and board, would 
be from $20 to $30 per mile. 

It is common for new men to spend an unnecessary amount of 
time in setting the grade stakes. They will often attempt to have 
the elevation of the grade stakes correct to within 0.01 foot. For 
all practical purposes, for work of this character, stakes correct to 
within 0.1 foot in elevation and 0.1 foot in alignment are satisfac- 
tory. Curb stakes for village work, however, should be carefully 
set to within 0.02 foot in elevation and line. 



CONSTRUCTION 



341 



CONSTRUCTION 

Rough Grading. By rough grading is meant all of the work pre- 
liminary to the finished shaping, and includes moving practically all 
the dirt that is to be handled. It is particularly important to 
supervise this stage of construction, as it is here that the construct- 
ing engineer regulates the placing of the best material in the center 
(under the metalling) and the poorer materials on the sides. 

In order to grade economically, the contractor and inspector 
should each be furnished with lists similar to those given below, 
showing, in a convenient form, the amount of excavation station 
by station and within what bounds it is to be placed. 



Excavation 
Summary 


Lists 


Sta.toSta. 


Exc. |Emb. 


Waste 


Borrow 


Remarks 


123 


134 


476 


375 






Quantities in cu. yds. 


134 


/40 


286 


240 








140 


157 


642 


662 \ r- 


W05 


Maul from Sfa.l79foI50 


157 


178 


766 \ 629 \ \ 






17 & 


179 


23/ 




Z3l-> 






179 


186 


238 


244 








Detail Quantities 










Sta. to Sta. | Exc. 


Emb. 




123 


123+50 


575 


225 


Quantifies in cu. ft- 


123+50 


124 


150 


900 




124 


1 ■ 24+501 — 


1450 




/24+50 


125 150 


300 




125 


/25+50 


320 


20O 




125+50 


126 


170 


500 




126 


126+50 


30 


925 




126+50 


127 


30 


850 




127 


121+50 


260 


410 




I27t50 


128 


350 


250 




128 


128+50 


635 


160 




/28+50 


129 


635 


75 




v., 






J 


^ y 



Fig. 69 

Cuts. For cuts over 3 feet deep slope stakes are placed and care 
taken that the slopes are properly carried down. If excavated beyond 
the finished lines it is practically impossible to make a back-fill that 
will hold and the resulting irregularities are unsightly. 

Fills. For fills slope stakes are set in the same manner as for 
cuts. 1 The earth should be deposited in thin layers, six to eight 
inches deep, extending from slope to slope, and each layer well 
compacted either with a roller or by driving over it with wagons 
in the process of building. Where the old surface has a steep slope 
it must be plowed to give a good bond with the new fill and prevent 
slide. 

It is bad practice to build the center of the fill and then shovel 

1 Slope stakes can be located directly from the templet Cross Sections which is a 
much easier method than the railroad practice of rod and level computation. 



342 NOTES ON CONSTRUCTION 

loose material off of the edge to widen the slopes, as this loose 
side-fill is not compacted and under the action of frost will nearly 
always slough away from the harder central portion. 




Old m ^ ^ £'^ Layers 



Surface. 



To get the full benefit of the teaming in compacting the dirt, 
a deep fill should be started at a point nearest the cut from 
which the material is hauled and each load driven over the loose 
layer. In this way nearly every fill can be better compacted 
than by the use of a roller alone. For long fills where there 
is considerable teaming over each layer a roller is not usually 
needed. 

Wet clay or heavy loam should never be placed in the bottom 
of a fill, as it dries slowly when not in contact with the air and keeps 
the fill " spongy." The writer has seen cases where fills not over 
3 feet deep have remained soft for two months where wet material 
had been used and it was finally necessary to remove it. 

Transferring Grade from Stakes. A handy level for trans- 
ferring the grade from stakes to the center of the road is shown 
below. If well made it will transfer the grade elevation 50 feet 
with an error of less than 3 inches, which is close enough for this 
stage of the construction: 

Ditches. The ditches must always be dug out enough to 
protect the center grading before the fine grading (stone trench) 
is completed, and it is usually cheaper for the contractor, as 
well as better for the road, to dig them out before the fine grading 
begins. 

String * Rin 9 __ 

i " -=" — s 

String Level. 

Fig. 70 

Regulation of Material in Fills. In fills, particularly shallow 
ones, the road can be greatly improved by a judicious selection 
of available materials. Material taken from two nearby cuts, 
or at different depths in the same cut, will often vary in character 
and the most experienced man on the job should indicate which 
materials to use in the center of the fill, under the metalling, and 
which on the sides. The soils in the order of value for fills are 
gravel, coarse sand, loam, and clay. For shallow fills on a good 
foundation clay should not be used under, the stone, as men- 
tioned on page 62, and a good material must be overhauled or 
borrowed. It is better to avoid overhaul if possible, as it is an 
item liable to be disputed as to the amount. Where it is neces- 



FINE GRADING FOR STONE TRENCH 343 

sary, a good practical method of determining the amount of the 
small quantities of earth usually needed is to keep track of the 
number of wagon loads overhauled from station to station. 

Sod may be used in the sides of the fill, but should be kept at 
least eleven feet off center. It should NEVER be used as a 
shoulder close to the stone or in the center of the fill under the 
metalling. 

The author wishes to emphasize the importance of this regu- 
lation of material. At present the inspection of rough grading 
is often confined to keeping the sod from the center fill, and the 
center fill is made of the dirt just as it happens along. As a 
result, the subgrade will vary greatly in character and if a uni- 
form depth of stone is used over this " spotty " fill the results 
are often not satisfactory, while if the depth of stone is varied 
to meet the subgrade conditions an unnecessary amount of 
stone is used. In cases where there is no choice of earth materials 
the stone depth must be made thick enough to meet the require- 
ments of the grade. 

FINE GRADING FOR STONE TRENCH 

The fine grading includes the shaping and consolidation of 
the stone trench. 



, Grading ; P/'m^ Construction 







Shoulder 




Fig. 71. — Showing 3 Lines of Grading Pins 

The construction shoulder must be at least 2.5' and well consoli- 
dated in order to hold the stone solidly during rolling. This must 
be watched continually by the inspector as it is a point often 
slighted. 

Shaping the Grade. A simple guide for shaping the grade is 
shown in the accompanying sketch and consists of three strings 
(center and sides) stretched between pins driven at least every 50 
feet and preferably every 25 feet. The pins should not be placed 
at intervals of more than 50 feet as this will cause objectionable 
sag in the lines and the grade will be undulating. The grade ele- 
vation is transferred and the lines carefully set at their proper 
elevation by means of a straight-edge, level and rod, or by stretch- 
ing a line between grade stakes on opposite sides of the road as 
previously described. The string level recommended for rough 
grading cannot be used, as it is not sufficiently accurate. 

The general level of the finished consolidated grade should be 
correct to within 1 inch. This leeway of 1 inch from the figured 
grade makes it possible to get satisfactory results without wast- 



344 NOTES ON CONSTRUCTION 

ing time on finical work and does not appreciably affect the total 
amount of excavation, as the errors tend to balance. There 
should, however, be no short, small irregularities of grade notice- 
able to the eye. Continuous inspection on shaping the grade is 
not necessary. 

Consolidating the Grade. Most soils when slightly moist 
will consolidate readily if thoroughly rolled. Clay, heavy loams, 
or excessively fine sandy loams (quicksand) will not pack when 
wet. Continued rolling is injurious for these soils in this con- 
dition, as they will "work" under the roller. If they occur 
only in small pockets they can be removed and replaced with 
good material; if in stretches of any length the grade must dry 
out before placing the stone. Under drains are constructed at 
this time, where necessary, and the surface ditches are cleaned 
out and made effective. Where a hard shower has softened the 
surface only of a previously consolidated grade of this kind and 
the contractor wishes to lay stone, the surface can be hardened 
by spreading a thin layer of gravel or waste No. 2 stone and rolling 
it into the earth. This will help in preventing the stone teams 
from cutting up the grade. 

Gravels and finely pulverized clay, or clay loams (deep dust), 
will not consolidate when dry; such material must be thoroughly 
sprinkled to get a compact grade. It is not, however, customary 
to sprinkle coarse gravels, even if slightly loose, as no objectionable 
results follows from placing stone on such a grade; deep clay or 
loam dust is objectionable and must be sprinkled. 

Coarse sand makes an ideal foundation but is hard to keep 
in shape while placing the first layer of stone. In some cases 
sprinkling will harden it sufficiently; in others a layer of fine 
loam has been spread over the sand and flushed in with satisfac- 
tory results. Sometimes where loam is not available a cheap 
cheese-cloth has been spread over the top of shifting sand to 
prevent the stone from punching in too much under the roller. 
The author has never encountered any coarse sand that could 
not be successfully treated by sprinkling and covering with 1 
inch or 2 inches of No. 2 stone; the blanket of No. 2 stone pre- 
vents the sand from squeezing up into the loose' bottom stone and 
spreading the fragments. 

While coarse sand makes a good foundation, a fine sand or 
sandy loam approaching quicksand is very treacherous; it is 
difficult to judge the degree of fineness at which a sand becomes 
treacherous, particularly when it is dry. A laboratory method 
is given on page 64, but a good practical method in the field is 
to saturate the material thoroughly with water; a satisfactory 
sand becomes more compact while an exceedingly fine sand gets 
" quaky." 



DETERMINATION OF DEPTH 345 

DETERMINATION OF STONE DEPTHS AND 
CONSTRUCTION OF SUB-BASE 

Practically the only engineering problem that the constructing 
engineer has to solve is that of foundations. It is recognized 
by most designers and estimators that it is impossible from even 
a careful preliminary examination of the soil to specify exactly 
the amounts and depths of foundation stone. To meet this an 
extra quantity of sub-base or bottom stone is allowed the con- 
structor, to be used as he sees fit. During the progress of the 
rough and fine grading the exact limits of the different kinds of 
subgrade soil are determined and the stone depths varied ac- 
cording to his judgment. (See page 64.) Men that really under- 
stand this part of the work are hard to get, as it is only from ex- 
tended experience and intelligent study of their own failures 
and successes that a sound judgment is developed. A good con- 
structing engineer is much more difficult to find at present than 
a good technical designer. 

Where sub-base is used the subgrade is dug out to the required 
extra depth and rolled if it is in such shape that it will not " work." 
Peat, muck, wet fine sand, or wet clay cannot be rolled until the 
sub-base is placed and filled. Where it is possible, such soils 
should be drained and allowed to dry before placing the base, 
but is often not feasible to dry them enough to allow rolling, 
even though underdrainage is put in, which partially hardens 
them and successfully protects the road after the stone has been 
placed. This is particularly true on flats where it is hard to get 
an outlet for a drain or in the fine sands on which an under drain 
has little effect on account of the capillary action of the material. 
Where a soft subgrade of this kind is encountered, a stony gravel 
makes the best sub-base, as it contains no voids between the larger 
fragments and when rolled the soft underlying material cannot 
squeeze up through the course. In case boulder or quarry stone 
base is used on a soft grade, it is necessary to lay them in close 
contact by hand and then fill the voids completely with gravel 
or No. 2 stone before rolling; otherwise the subgrade material 
would squeeze up between the stones, separating them and par- 
tially destroying the efficiency of the base. 

In the Spring and Fall of the year it is common to find good 
material so saturated from long-continued rains that it acts 
badly under the roller and instead of waiting for the grade to 
dry out, when the normal thickness of stone would be sufficient, 
sub-base is often put in either to help the contractor so that he 
will not be delayed or because the engineer is misled as to the 
character of the material. This results in a. waste of money. 
On the other hand, clay, when thoroughly dry, is hard and firm, 
which often influences a new man to omit sub-base where it will 
surely be needed. 

The use of sub-base should not depend too much on the action 
of the grade under the roller unless the degree of saturation of 



346 NOTES ON CONSTRUCTION 

the material is considered, although it serves as a guide in 
locating doubtful spots. The final determination should depend 
on test pits, which develop the character of the underlying 
material. 

The sub-base is constructed, as explained, in the chapter on 
Foundations, either of gravel, boulder or quarry stone. The depth 
is gauged by lines. The ratio of loose to rolled depth is given 
on page 272. 

Continuous imspection is not needed on sub-base; the depth of 
grading is checked before the stone is placed and the width, depth, 
and workmanship can be readily determined after the base is 
completed, and by an occasional inspection during the progress 
of the work. 

Bottom Stone. The earth subgrade must be firm and compact 
before the stone is spread. Bottom stone must NEVER be 
laid on a soft grade. One of the most common slips of inspection 
is to allow this to be done and the result is a " punky " bottom 
course that is never up to standard. The distributing power of 
this course depends largely on the stone fragments being firmly 
interlocked; if the stone is placed on a soft grade and rolled, the 
earth will squeeze up between the fragments and separate them. 

The depth of the loose stone is gauged by the lines or cubical 
wooden blocks placed on the subgrade. Blocks are more con- 
venient than lines except over sub-base of stone fills, where lines 
must be used to get a spread true to shape and grade. The 
ratio of loose to rolled depths is given on page 272. 

The loose stone is rolled until the stones are solidly inter- 
locked and there is no movement under the roller. A thin layer 
of satisfactory filler (see materials page 129.) is spread over the 
top, rolled and broomed in; the process is repeated until the 
stone is thoroughly filled. Continuous inspection on bottom 
course is not necessary. The widths and depths can be readily 
checked by occasional inspection. The two points to be care- 
fully watched during construction are: 1. That the grade is 
firm; 2. that the loose fragments are thoroughly rolled before 
the filler is applied. 

It is desirable to complete the bottom course well in advance 
of the top, in which case the contractor can work to advantage 
after rains, and the course will be better compacted by subjecting 
it to some traffic action. 

Where local stone is crushed on the job and the stone used 
ranges in size from 1 in. to tailings, care must be used in spreading 
that the sizes are well mixed, as pockets of fine or coarse stone 
are objectionable. The simplest method of mixing is to run the 
No. 3 and No. 4 and tailings into one bin at the crusher; if 
they are separated they can be well mixed by loading one end 
of the wagons with the No. 3 and the other end with No. 4 and 
when dumped on the grade they will run together. When dif- 
ficulty is experienced with these methods in obtaining a well- 
mixed stone spread the loose stone can be harrowed. Many 
specifications call for harrowing thoroughly where a large range 



APPROXIMATE AMOUNT OF FILLER 



347 



of crushed stone size are allowed in one course. If possible, 
tailings should be used as sub-base. When used in the bottom 
course having a rolled depth of 4 or 5 inches they should be placed 
in the lower part of the course, but for a 3-inch depth they should 
be placed on top and broken with a knapping hammer into frag- 
ments of less than 3^ inches. 

The filler should not be dumped directly on the stone unless 
absolutely necessary. Drawing the loads onto the unfilled 
stone loosens the course, and, also, at each pile of filler there is 
apt to be left an excess which is hard to clean off. 

Table 52 gives the approximate amount of filler required per 
100 feet, and the spacing of ij-yard loads. The amount varies 
for the different materials used. 

Grading and foundations have been treated at some length, as 
they are the most difficult parts of the construction. 



Table 52. Giving the Approximate Amount of Filler P.e- 
quired per 100 Feet of Road for Crushed Stone Macadam 
Bottom Courses of Different Wldths and Depths, Using 
0.35 Cubic Yards of Filler per Cubic Yard of Rolled 
Bottom 









Rolled Depth of Bottom Course 






.13-0 














a & 

Tj O 














££ 


3 


" 


4" 


5* 


6" 




10' 


3.2 cu. yds. 


4.3 cu. yds. 


5.4 cu. yds. 


6.6 cu. 


yds. 


12' 


3.8 ' 


i a 


5-1 " " 


6.5 " "* 


7.6 " 


a 


i4 r 


4-5 ' 


1 a 


6.0 " " 


7-5 " " 


9.0 " 


a 


15' 


4.9 ' 


1 a 


6.4 " " 


8.0 " " 


9.9 " 


a 


16' 


5- 2 ' 


c 11 


6.9 " " 


8.6 " " 


10.4 " 


a 


18' 


5-9 ' 


( it 


7.9 " " 


9-7 " " 


11.8 " 


a 


20' 


6.4 ' 


i tt 


8.6 " " 


10.8 " " 


12.8 " 


a 


22 r 


7.0 ' 


i (t 


9-4 " " 


11.8 " " 


14.2 " 


a 



Table 5 2 A. Giving the Approximate Spacing of 1.5 Cubic 
Yard Loads of Filler for the Widths and Depths shown 
in Table 52 



Width of 


Rolled Depth 01 


Bottom Course 


Macadam 


in 


4" 


5" 


6" 


10' 


46 feet 


34 feet 


27 feet 


23 feet 


12' 


40 " 


30 " 


23 " 


20 " 


14' 


33 " 


25 " 


20 " 


17 " 


IS' 


3i " 


23 " 


19 " 


15 " 


i6 r 
18' 


29 M 

25 " 


22 " 
19 " 


i7 " 
16 " 


13 " 
12 • " 


20' 


23 " 


18 " 


13 " 


11 " 


22' 


21 " 


16 " 


12 " 


10 " 



348 NOTES ON CONSTRUCTION 

TOP COURSES 

Waterbound Top. Waterbound top is constructed in the same 
way as the bottom course except that stone dust is used for a 
filler and the course is puddled as has been described. 

If the stone used is a local stone crushed on the job the output 
of the crusher must be carefully controlled, especially where 
selected boulders are used, as it is very important that the size 
and quality of such stone shall be uniform. 
Imported stone can be inspected on the cars. Aside from this, 
comparatively little inspection is required except at the stage 
when the loose stone has been rolled and before the binder is 
spread. At this time the inspector should examine the rolled 
course very carefully to see that it is true to shape and has no 
short depressions or humps. The smooth riding quality of the 
road depends on this inspection and too much care cannot be 
taken. This point is particularly emphasized, as many of the 
stone roads in New York State have been criticized as rough for 
automobile traffic. Any depressions are filled with stone of the 
same size as the body of the course and rolled, after which the 
course is again inspected and corrected until it is made true. 
The binder is then spread, broomed in dry, and puddled. In 
puddling use plenty of water and roll rapidly. If a pipe line 
and hose are used a pressure of ioo to 125 pounds at the pump 
should be maintained. The road can be conveniently puddled 
in stretches of 100 to 200 feet. 

After the road has dried out and been opened to traffic, if 
raveling occurs it can usually be remedied by light sprinkling 
and rolling. 

Where the top course is granite, gneiss, or trap, it is often 
necessary to use a certain percentage of limestone dust with 
the normal screenings. The limestone is more effective when 
spread last, filling the top voids of the course. 

Bituminous Top. Penetration Method. The same pro- 
cedure applies to the quality, size, and laying of the stone for 
a bituminous as for waterbound top, and does not require con- 
tinuous inspection. 

Just before pouring the bitumen the course should be care- 
fully examined and any pockets of fine stone, dirt, dirty or 
dusty stone removed, as fine stone or dirt prevents the pene- 
tration of the binder and the bitumen will not adhere properly 
to the stone unless it is clean and dry. The course is not rolled 
as firmly at this stage as for waterbound tops because excessive 
rolling tightens the stone too much and prevents the penetration 
of the bitumen. There should, however, be no creep in front 
of the roller. The bitumen is poured into the voids of this 
clean, dry, partially compacted course, usually by means of hand- 
sprinkling pots or hods. Pots having vertical slots are prefer- 
able to the fan-spout pots, as they give better penetration. 

Hods are to be preferred to pots. When hods are used, however, 
the bitumen should be poured across the road instead of in a 



TOP COURSES 



349 



longitudinal direction as this prevents overlap and minimizes the 
difficulty of preventing humps or waves. 

In placing the bitumen the following precautions must be 
observed: It must be hot enough to run freely; for each grade 
the temperature of applications is usually specified and it must 
not be overheated, for if charred it is useless. In applying, by 
whatever method, care must be taken not to overlap, as waves 
or humps will develop at these points. These defects do not 
appear for some time after the road is opened to travel, and an 
inexperienced inspector fails to realize the necessity of care in 
this particular. The stone must be clean and dry, and, in the 
writer's opinion, the air temperature should not be less than 50 F., 
as bitumen applied in cold weather is so chilled when it strikes the 
cold stone that an excessive amount is retained on the surface. 
As soon as the bitumen is applied a thin layer of No. 2 stone is 
spread over the surface and rolled lightly; continued rolling at 
this point is injurious, as freshly laid bituminous tops tend to 
shove under the roller and form waves. The road can be thor- 
oughly rolled and shaped to advantage only after the bitumen 
has had some time to harden. Good results have been obtained 
by rolling thoroughly the succeeding day after the binder is 
applied, unless in the meantime rain has saturated the course, 
in which case it must be allowed to dry before rolling. 

The amount of bitumen spread per square yard is usually con- 
trolled by spreading a given number of pots or hods in a given 
length of the road. These units of length can readily be marked 
off by the inspector with a stick or tape. This method will be 
satisfactory if checked up twice a day by the number of barrels 
used. When the binder is heated in small kettles it will some- 
times catch fire, but this is usually due to scale which has col- 
lected in the tank and if cleaned out it generally remedies the 
trouble. 

Where bituminous materials are heated by steam it is often con- 
venient to know the temperature of steam at different pressures; 
the following table is inserted for this purpose : 

Table 53 



Pressure 
Gauge Lbs. 
per Sq. In. 


Temperature 

of Steam 

°F 


Pressure 

Lbs. per 

Sq. In. 


Temperature 
°F of steam 


Pressure 

Lbs. per 

Sq. In. 


Temperature 
°F of steam 


'is 

20 
40 
60 
80 
IOO 

1 


213 
228 
267 

293 
312 
328 


IOO 
I20 
140 
160 
180 
200 


328 
341 
353 

373 
382 


200 
220 
240 
260 
280 
300 


382 
390 . 

397 
404 
411 
417 



1 Fifteen pounds normal air pressure; to get ordinary steam gauge reading sub< 
tract 15 lbs. from the values given in this table. 



350 NOTES ON CONSTRUCTION 

HASSAM CONCRETE PAVEMENT 

By E. E. Kidder 

The principal mechanical difficulty in laying a Hassam pavement 
is in getting a proper penetration of the grout. 

This requires stone free from small particles and a grout of the 
proper consistency. 

Stone. The stone should be sized ij" to 3^" uniformly mixed. 
Any pockets of fine stone should be shoveled out or if they occur 
in small areas raked over till the fine goes to the bottom of the course. 

The spreading is followed by rolling with a 10- ton road roller. 
Close attention should be given to obtaining as nearly a perfect 
surface as possible as it is practically impossible to add or deduct 
material once the stone is grouted. 

Grout. The grout should penetrate to the bottom but should 
not be so thin that separation occurs. The size of sand is important. 
Coarse sand will not penetrate well. Sand passing a 10" mesh and 
containing much that is finer works well. 

Manipulation. Each morning the end of the previous day's 
work should be cut down vertically and square across the road, 
shoveled out and replaced with new stone. This insures a vertical joint. 
Continuous Inspection is Necessary on both Stone and Grout. 
The grout will float a few of the top stone out of place but the 5 -ton 
tandem roller will smooth them down. The final finish is obtained 
by hand tamping and brooming the surface. The tamping is abso- 
lutely necessary to get the best results and it will be neglected unless 
insisted upon. 

Shoulders. It is desirable that the earth shoulders be left 1" 
higher than the finished pavement until the grouting is completed 
to prevent waste. During the rolling of the grout some water will 
flush to the surface and run to the edge; it should be let off by digging 
small trenches through the shoulder. The grading of the shoulders 
should be practically complete before laying stone in order that the 
Sand and Cement may be placed on one side of the road and the 
other shoulder may be used as a walk for the workmen and traffic. 
The gang organization is shown by a sketch (page 288 Cost Data). 

FIRST CLASS CONCRETE PAVEMENTS 
By F. W. Bristow 

The sub-grade should be formed true to alignment, elevation and 
shape and consolidated well in advance of the mixing machine to 
permit the delivery of materials both on the sub-grade and shoulders. 

The materials, stone or screened gravel, sand and cement should 
be distributed uniformly in the proper quantities to construct the 
pavement as planned. (For quality of materials see specifications. 
For amounts required see Cost Data.) The cement should be de- 
livered on the road only as required and covers provided for its 
protection in case of storm. 

Inspection of Manipulation. A diagram showing a typical mixing 
gang organization is given in the chapter on Cost Data. Two inspec- 
tors are necessary to properly supervise the work. The inspection must 



CONCRETE PAVEMENT 



351 



be continuous. The inspector ahead of the mixer sees that the sub- 
grade is correct; that the edging forms are properly set; that the fine 
and coarse aggregate conforms to the requirements, and that the proper 
amount of materials are placed in each batch of concrete. 

He also should keep a daily record of the amount of cement used, 
the amount of concrete laid and should figure the amount of cement 
per cu. yd. of concrete as a check on his batch inspection. He 
should be careful to observe that no empty cement sacks from the 
previous days run are counted the second time. 

The inspector back of the mixer first sees that the sub-grade is 
smoothed as the mixing machine moves ahead; that any muddy 
conditions is remedied by removal and that a dry dusty sub-grade is 
sprinkled to prevent rapid absorption of water from the concrete; 
that the concrete as delivered from the mixer has the proper consist- 
ency and is thoroughly mixed; that the transverse expansion joints 
are properly placed; that the striking of the concrete with the screed l 
or template is so done as to leave no projecting stone, or humps or 
hollows in the surface. Any surface irregularities must be imme- 
diately remedied and the mass restruck. The screeding is kept up 
closely to the mixer and is followed by the wood float finishers work- 
ing from a bridge that spans the concrete. 

"" /6 '- —>/Body of Screed 

5 Pieces /"Planks 
Spiked Together* 



Wrought 
Iron 




Shoe^ 



F/atSubgrade 



■Side Forms 



Sketch of Screed 
Fig. 71 a 

In case surface brooming is required the inspector determines 
when it shall be done; the best time is just after the initial set starts. 
Long-handled steel brooms are used and the brooming is done lightly 
transversely to the road. 

In hot weather the fresh concrete should be sprinkled to prevent 
sun checking. It is covered within 24 hours with a coat of earth 
1" to 2" thick which is sprinkled and kept damp for 10 days when it 
is removed. Traffic must be barricaded from the road for this time. 

Before turning traffic on to the completed concrete the earth 
shoulders should be finished along the edge to prevent spauling. 

Sheet Asphalt, Topeka Mix, etc. The important points in any 
form of a mixed Bituminous surface are a proper grading of the aggre- 
gate and care not to char the binder in mixing. 

Two inspectors are required; one at the plant and one where the 
asphalt is being laid. Plant inspection should be continuous. The 
plant inspector is responsible for the proper proportions of the dif- 
ferent sizes of the aggregate and for the proper temperature of the 
mix. To insure the proper proportions he should test the measuring 
scales at short intervals and sift a sample of the dry mineral aggre- 

1 The screed should be two feet wider than the finished pavement as it progresses 
with a see saw movement rather than a direct full. 



352 



NOTES ON CONSTRUCTION 



gate at least once a day. His most important duty is to prevent 
charring of the binder. It is not necessary to take the tempera- 
ture of each batmen as with a little experience any objectionable con- 
dition can be detected by the character of the smoke; a dense white 
smoke given off when mixing indicates a dangerously high tempera- 
ture. When this is observed the batch should be tested with a 
thermometer and immediately rejected if over the specified tempera- 
ture limit. (See specifications.) The temperature of the mineral 
aggregate will fluctuate very rapidly in the small plants generally 
used for road work and care should be observed in picking the plant 
inspector that he is a very conscientious man. He should also furnish 
the driver of each load of asphalt with a ticket giving the weight 
of the mix on that load. 

The Inspector on the road records the temperature of the mix 
as received, the weight of each load and indicates to the spreaders 
the number of sq. yds it should cover. 

(The surface mix weights approx. ioo lbs. per sq. yd. per inch of 
consolidated depth.) 

He also should take a sample of the mix as delivered once a day 
and ship to the laboratory for check analysis. 

The following sketches show a sample of a plant inspector's and 
road inspector's record book. 

Sept. 29, 191 5. Plant Record 



Load Record 


Bitumen Record 


Load 


Time 


Temperature 
of Mix. 


Weight of 
Load 


Time 


Temperature 


I 
2 

3 

4 

5 

6 etc. 


7.30 
7-45 
7.55 
8.15 
8.25 

8.45 


320° F. 

310 

300 

300 

290 

310 


50000 lbs. 
5000 " 
6000 " 
6000 " 
5000 " 
5000 " 


7.00 

8.00 

9.00 

10.00 

11.00 

12.00 


310 F. 

345 
34o 
3io 

305 
320 



Test & 


\mple No. 7. Sept 


29, ic 


115. Road Record 


Load 
No. 


Time 


Tempera- 
ture of 
Mix. 


Weight as 
per Ticket 


No.Yds. 
Covered 


Location on Road 


1 

2 

3 

4 

5 etc. 


8.00 
8.20 
8.30 

8.45 
9.00 


3io°F. 

300 

295 

295 

280 


5000 lbs. 

5000 " 
6000 " 
6000 " 
5000 " 


25 
25 
30 
30 
25 


Sta. 10 + 30 to 10 + 42 
" IO+ 42 " IO+ 54 
" 10 + 54 " 10 + 69 
" 10 + 69 " 10 + 84 
" 10 + 84 " 10 + 96 



Proportions of Mix. The proportions of mix should be deter- 
mined by the engineer by screen analysis of the different materials 
that the contractor proposes to use. 

As an example assume that a mixture of cement, fine sand, coarse 
sand and buckwheat stone is proposed and it is desired to determine 
the relative amounts of the different materials to use in order to 
get the correct proportion of sizes specified. 



ASPHALT PAVEMENTS 



353 



For all ordinary purposes a size analysis can be safely made using 
the following screens: #200, #80, #40, #10, \" and V . 

The materials are thoroughly dried and the percentages expressed 
by weight. 

Fine Sand (Feeder Pit) 

Passing # 200 5 % 

1 ' #80 retained on # 200 70 % 



" #40 " " # 80 

Good Quality 

Coarse Sand (Bauerman Pit) 

Passing #200 

" # 80 retained on #200 

" #40 " " # 80 

" #10 " "#40 

Buckwheat Stone. (Commercial plant.) 

Passing #200 1 % 

" # 40 retained #200 

" #10 " #40 



25% 



1% 

2% 

29% 

68% 



A 

1" 

2 



IO 

1" 
4 • 



2% 

7% 

60% 
30% 



The proportions can now be varied to produce practically any 
required mix. 



Tabulation Showing Method of Determining the Number of Pounds of Each 
Material to be Used in a 100 lb. Batch to Produce a Required Mix. 


Material 


No. 

lbs. 


Bitu- 
men 


#200 


#40 


#10 


1 


\ 


Bitumen 

Cement 

Fine Sand 

Coarse Sand . . 
Buckwheat 

Stone 

Totals 


IO 

7 
47 
20 

16 
100 


IO 
IO 




7 
2-5 

9-5 . 


44-5 
6.0 

5o.5 


14.0 

1.0 
15.0 


9.6 
9.6 


5-4 
5-4 



In this way the effect of varying any of the component parts of 
the mix can be readily seen and determined. 

The total size of the batch is of course varied to suit the capacity 
of the plant. 

The laboratory analysis of the daily sample taken on the road 
furnishes a check on the plant inspector. 

Rollers. The best results can be obtained by the use of two tandem 
rollers; a light roller not over 5 tons for first compression to anneal 
the surface while hot and a heavier 8 to 10 ton roller for final compres- 
sion and cross-rolling. This is more important where the asphalt 
is laid on a macadam base than when laid on concrete. 



354 NOTES ON CONSTRUCTION 

BRICK ROADS 

To cover the points of construction of brick roads we cannot 
do better than to give " Instructions for Inspectors," by William 
C. Perkins, Resident Engineer, New York State Department 
of Highways. Mr. Perkins is well qualified to judge of this 
class of work. 

Grading. " Read your specifications carefully and follow 
them in every particular. 

" Do not let the contractor dig beyond the back slopes of your 
ditches. Your ditches should be straight, no sudden jogs; 
back slopes all true; no rubbish deposited back of the ditches, 
and be sure that your ditches drain. 

" Follow your cross-sections as closely as possible. Try to 
aid the contractor to take care of his dirt so that when the road 
is cleaned up there will not be a great amount of material to be 
moved. 

" Never make a shovel nil over 6 inches without rolling it. 

" In making a heavy fill with dump wagons begin to dump 
at the end toward your dirt supply. Have each pile of dump 
dirt spread thin and draw the next load over this, which will 
help to pack it. All should then be thoroughly rolled. 

" Examine your subgrade carefully, particularly when the 
roller is going over same, and if it waves or shakes under the 
roller, sub-base or drain should be put in, or the material dug 
out and the proper material put in. Do not make a fill with 
any old material found along the road. Use judgment in this 
particular. 

" Clearing and grubbing does not mean the grubbing of sod. 
It means the cutting down of bushes, trees, etc. Remember 
that the life of your pavement is the condition of your subgrade. 
The same should be inspected by the engineer in charge before 
any stone or concrete is placed. 

" Grade the full width of your macadam or concrete. Never 
deposit stone in the rut. Keep your sub-base free of ruts. 

" If your roller is not working on other work roll your subgrade. 
You cannot roll it too much. 

" Do not shift center line or grades until you have reported 
the necessity for it to headquarters, and if absolutely necessary 
give an estimate of the increase or decrease in quantities that 
such change would make. 

" Shoulders should not contain sod within 18 inches of the 
macadam. 

" Back slope all ditches i on i|. Be careful that your 
gutters are not too deep. Deep gutters where not necessary for 
drainage purposes make a road dangerous and must be avoided. 

" In trimming shoulders and ditches a good inspector should 
be put on the work, and instructed to see that the contractor 
sets proper stakes. A stake should be set out from the edge of 
the macadam, and also one in the ditch, and should be set at 
least every ioo feet. The bottom of the ditch must be a true 



BRICK ROADS 



355 



grade, no depression, and the ditch alignment must be good. 
These stakes can be easily set with a 1 6-foot level board. When 
approaching a culvert it is not necessary to deepen the gutters 
until you reach within 50 feet of same, when a straight grade 
can then be run to the invert. 

" In all cases be sure your ditches will carry water, and, I re- 
peat, be sure they are not ragged and the back slopes are well 
graded. In trimming shoulders be sure there is no ridge next 
to the macadam. 

" In setting your stakes for the shoulder work use the or- 
dinates and distances shown on the standard section. 

" Subgrade. Be sure that your subgrade has been properly 
graded so as to obtain 5 inches of concrete. If the contractor 
builds the curb first, a templet should be run over the curbing 
and test made to be sure that you have the correct depth. 

" Concrete Edging. Stakes for concrete edging can be placed 
every 50 feet for line and grading, with the exception at change 
of grades and curves, where they should be placed every 25 feet. 

" Be sure that your forms are properly set as to line and grade. 

" With stakes 50 feet apart be careful that there is no sag 
in the line when the forms are set. 

" If edging is set first it is better that the concrete be hand- 
mixed, as a machine turns out too large a quantity and cannot be 
placed in the proper time. 

" See that your forms are wet before the concrete is placed, 
and if steel forms are used they should be oiled. 

" Have a careful inspector on the mixing of the concrete for 
the edging and watch the mix. 

" Keep track of the number of bags of cement used and see 
that the proper proportion of cement to the lineal foot of edging 
is obtained. 

" Edging 6" X 10 \" will use 1 bag in 12.95 feet 
" Edging 8" X io|" will use 1 bag in 9.73 feet 
" Mixture, 1-2^-5. 

" Make the mixture rather wet and spade the same thoroughly, 
using a hoe straightened and punched full of holes, or some similar 
instrument, so as to get a good face next to the forms. 

" If you find you cannot get a good top surface keep the edging 
a couple of inches low, and about every third batch mix a batch 
of fine material and bring the edging up to the proper height, 
throughly working the same in. 

" Do not get a plaster effect, but get a good top surface. 

" Round both edges with a rounding tool, making the inner 
edge of a smaller radius than the outer edge. 

" When the forms are taken down all spots which are honey- 
combed, or rough, should be floated at once with cement. A 
rough edging should not be left on any road. 

" Have the contractor back up the edging as soon as possible. 

" In warm weather the edging should be kept wet for, at least, 



356 NOTES ON CONSTRUCTION 

twenty-four hours. Have the contractor use care in delivering 
materials after the edging is built so that the edges of same are 
not broken by wagons, etc. 

" A good edging is often ruined by carelessness on the part of 
the contractor. 

" Concrete Base. Before laying base be sure that the founda- 
tion is in proper shape and of a proper depth. 

" Lay the concrete rather wet and drag same with a heavy 
templet. Have men back of the templet with tamping irons or 
blocks, tamping the concrete. This is important if you wish to 
get a smooth surface, and you must insist that the concrete be 
well tamped, 

" Be sure that you keep track of your bags, and, also, that 
the machine is working properly. 

" For a 16-ft. road nf bags will lay 10 ft. concrete base, mix- 
ture 1-2^-5. 

" After the day's run examine your base, and if there are any 
spots which are porous, grout same and check up your bags at 
the end of each day. 

" If the weather is very hot the base should be kept wet for 
twenty-four hours. 

" Sand Cushion. Sand for this cushion should be absolutely 
free of stones, and you must insist that the contractor screen 
same, if stones are in the sand delivered. No excuses will be 
taken for stones or pebbles in the cushion. Spread sand for a 
sufficient depth, then roll same with a small roller; then drag, 
roll again, and then drag with templet. 

" This should be sufficient to give a firm cushion. 

" The smoothness of the pavement depends on the proper 
form of the cushion. 

" Brick. Great care must be used in obtaining proper brick 
surface. 

" Be sure that your strips on the side expansion joints are in 
when the contractor starts to lay brick. 

" Allow no pinning in at the ends under 2§ inches. 

" Be sure that the expansion joint is not ragged. It must be 
uniform in width, otherwise you will have transverse cracks. 

" All bricks should be laid with lugs in the same direction. 
This is a point that the bricklayers very often do not do. The 
bricks should be laid by experienced bricklayers, not by 
amateurs. 

" After the brick are laid the contractor will start culling. 
Then you and your inspectors should carefully go over them, 
marking all soft 1 bricks to be taken out and rejected; all kiln- 
marked bricks to be turned over, and if not satisfactory to be 
taken out and used for pinning in; all overburned bricks, 2 

J Soft brick are found by sprinkling the pavement lightly; the soft or under-burned 
brick will absorb the moisture, rapidly becoming dull , while the good brick still glisten 
with the water. 

2 Over-burned brick are known by their color, which is much darker than the 
average. 



BRICK ROADS 



357 



which are burned to a cinder to be rejected. All underburned 
bricks, which, in your opinion, will not make a satisfactory 
pavement, to be rejected. All bronzed bricks (which have the 
appearance of overburned brick but this on one side only) to 
be turned over, and if satisfactory allowed to remain in the pave- 
ment. 

" Be sure that you have culled all of the bricks before the 
pavement is rolled, for after the pavement is rolled if much cull- 
ing is done you are liable to have a rough pavement. After 
the pavement is rolled go over same and mark all broken and 
spalled bricks, to be taken out or turned over. 

" Be careful of all high and low bricks in the pavement, for 
same will wear badly when the road is finished. 

" Be sure that your bricks are laid at right angles to the curb 
and are not wavy as to line. 

" In no case allow any ' Dutchman' 1 in your pavement except 
on curves where absolutely necessary. 

" Grouting. The grouting of the pavement is its life, and the 
greatest care must be used. Insist that all grout be placed on the 
pavement by the use of scoops from a box with unequal legs. 

" The grout should be mixed in small quantities and of the 
exact proportions. The sand should be sharp, not too coarse 
nor too fine. Care should be taken in using lake sand, as same 
is probably not sharp and too heavy for the grout. As soon 
as the grout reaches the pavement it should, at once, be pushed 
into the joints by means of brooms or squeegees. 

" It is best to use brooms on the first grouting and a squeegee 
on the second and third groutings. 

" Be sure that the joints are well filled in the first grouting, 
and do not let the grout escape over the edging and be lost. 

" Follow closely with the second grouting, otherwise the two 
groutings will not unite. 

" Be careful that the second grouting does not overlap the 
first. After the second grouting examine the pavement care- 
fully and, if necessary, put on a third grout to get flush joints. 

" The pavement should be completely covered with grout and 
all joints should be well filled before you pass on same. 

" Allow enough time for the grout to obtain initial set, and 
cover pavement with a layer of sand to protect same from the 
weather; and pavement should be kept wet for, at least, twenty- 
four hours. 

" In no case permit traffic on the pavement under ten days; 
longer, if possible. 

"Expansion Joints. Be careful in removing the expansion 
Joint boards that you do not disturb the pinning-in bricks and 
break the bond. We found it advisable to use two wedge-shaped 
boards to make the expansion joints and loosen up the back one 
as soon as grouting was started. 

1 "Dutchman." Brick chipped to wedge shape to fill in between radial courses 
on curves. 



358 . NOTES ON CONSTRUCTION 

" In pouring the asphalt filler be sure that the joints are abso- 
lutely clean the full depth. This is very important, or, other- 
wise, you will have cracks in the pavement. The joints are to 
be flushed with asphalt." 

CULVERTS 

Culverts are usually constructed before the road is graded. 
They should be completed well in advance of the macadam, 
because even though the back-fill is carefully tamped there is 
bound to be some additional settlement under traffic action, and 
if the macadam is laid over a fresh back-fill depressions are sure 
to develop which, if not repaired, make " thank-you-marms " 
in the road. 

Cast-iron Pipe. Trenches for pipe are dug the required depth, 
making the bottom wide enough to allow the joints to be properly 
calked. This requires a trench 18" to 24" wider than the pipe 
diameter, i.e., for a 12" pipe the trench is 30" to 36". Bell 
holes are dug as shown in Fig. 72, so that the pipe will have a 
uniform bearing its entire length. At no point should it rest 
directly on boulders or ledge rocks. If the foundation is soft 
the pipe should be laid on a concrete base. For ordinary soils 
the only precaution the inspector need take is to prevent back- 
fill under the pipe. 



Fig. 72 

Unless the foreman is alert the trench is often excavated too 
much in some places, which are then back-filled. This is bad 
practice except where boulders are encountered which must be 
removed and the cavities back-filled with good material. 

Pipe. The pipe is inspected for flaws; it is then placed in 
the trench with the bell end upstream. At each joint the spigot 
end is placed in the bell and forced against the shoulder, making a 
tight joint. The pipe is then lined correctly and a gasket of 
jute or oakum driven into the joint with an iron calking tool 
having a 2" to 3" offset, as shown in Fig. 73- The balance of the 
joint is then filled with a 1 to 1 cement mortar. 



Fig. 73. — Steel Caulking Tool 

The trench is then back-filled, care being taken not to throw 
the pipe out of line; the back-fill must be well tamped in layers 
not exceeding 6", using heavy paver's rammers. A good work- 
ing rule is to use two of the best men on the job tamping and the 
laziest man on the force throwing dirt to them. 



CONCRETE CULVERTS 



359 



Head-walls for Culverts. The face of the head-wall should 
extend beyond the end of the pipe, as it is difficult to get a good- 
looking connection if it is flush with the end. 




-*_ 



Fig. 74 



Figure 74 shows a convenient plug form for this extension. 
This plug is set into the end of the pipe and can be readily re- 
moved; the resulting head-wall being pleasing in appearance. 
The head-wall form can, also, be readily skewed (set at an angle 
with the pipe) if required. 

CONCRETE CULVERTS 

Excavation. The trench is dug to the required depth; if the 
material will stand vertically no back forms are necessary, and 
the width of the trench is made the width of the out to out di- 
mensions of the culverts. If back forms are needed the trench 
is usually made 2 feet wider. If running water is encountered 
which cannot be temporarily dammed, or diverted, the trench is 
made wide enough to flume the stream through on one side of the 
back forms for small culverts, or between the abutments for 
larger span structures. 

Back-fill. The back-fill is made as for cast-iron pipe except 
that it should not be deposited on the fresh top of a culvert 
within twenty-four hours of laying the concrete. 

Forms. Forms should be true to shape and constructed of 
planed tongue and groove lumber, for the exposed surfaces. 
They should be water-tight, as otherwise the fine material will 
run out of the face of the concrete and leave a rough " pop-corn " 
surface. They must be well braced to prevent bulging. Tri- 
angular or feather-edged grooved moldings are placed in the 
angles of the forms to shape them satisfactorily. 

Removal of Forms. The length of time that the forms should 
remain in place is a matter of judgment; it depends upon the 
cement and weather conditions. 

The author's practice is as follows: 

Head-walls or parapet forms are removed within thirty-six 
hours in dry weather or within forty-eight hours in damp, cold 
weather, in order to rub down the surfaces. 

Low side-wall forms for spans of 2' to 3', where the deck is 
constructed later, may be removed in 36 to 48 hours. 

Trunk forms for small culverts 2' to 3' span may be removed 
in from 3 to 7 days. 



360 NOTES ON. CONSTRUCTION 

Trunk forms for medium culverts up to io' span 7 to 14 days. 

Deck forms for spans above io' may be removed in from 14 
to 28 days. 

Any unusual load, such as a roller, should not be allowed over 
a new culvert of even a small span in less than seven days, unless 
precautions are taken to distribute the pressure by planking the 
back-fill, or otherwise, and on the larger structures a time limit 
of three to four weeks is advisable. 

Amount of Cement, Sand, and Stone required. 

Table 49, page 304 gives these amounts for one yard of concrete. 

The following table gives the amount of stone, sand, and cement 
required for culverts similar to Plate 6, assuming that no embedded 
boulders are used in the sides and bottom. If boulders are used see 
footnote, Table 49. 

MIXING AND PLACING CONCRETE 

The strength of the concrete depends largely upon the 
thoroughness of the mixing. 

The author's practice has been as follows: 
Hand-mixing. Cement and Sand. 

3 turns dry. . . .3d class concrete (foundations and side walls) 

4 " " .... 2d " " (decks and parapets) 

Add water and mix mortar. 

Drench stone and turn stone and mortar 

3 times for 3d class concrete 

4 " " 2d " 

Deposit in forms by dropping. Do not cast, as this separates 
the coarse and fine material. Use enough water to give a mixture 
that quakes like liver under the rammer. 

Deposit in layers not over 6" deep and ram each layer thor- 
oughly; spade the concrete thoroughly, and work an excess of 
the fine stuff to the face of the forms by prying the larger frag- 
ments back from the form with a narrow spade or broad-tined 
fork. 

Machine -mixing. Culverts generally contain such a small 
quantity of concrete that machine-mixing is rarely used. In case 
a batch-mixer is employed, the inspection is simplified to checking 
the quantities of cement, sand, and stone in each charge. If a 
continuous mixer is used it is well to keep watch of the cement 
hopper, as the cement is liable to run low, feeding only a portion 
of the worm, or a large lump of cement may ride on top of the 
worm and hinder the feed; or the worm may become coated with 
damp cement which reduces the capacity. If the inspector 
watches the cement hopper the contractor will tend to the sand 
and stone hoppers. 

Finishing Concrete. If a smooth, marble-like surface is de- 
sired it can be obtained by rubbing down the surface before it 
has fully set with a cement sand brick moistened with water. If 



CONCRETE CULVERTS 

Concrete Culverts 



361 







1. 


5' high X 2.0' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Paving 
Square 
Yards 


Ex. Met. 

Square 

Feet 


Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 








Second 


Third 










Yards 


20 


2.2 


5.6 


6.4 


80 


8.4 


3-6 


7.2 


21 


2.2 


5-8 


6.4 


84 


8.6 


3-7 


74 


22 


2-3 


6.1 


6.4 


88 


9.0 


3-9 


7.8 


23 


2.4 


6-3 


6.4 


92 


9-3 


4.1 


8.1 


24 


2.5 


6.5 


6.4 


96 


9-7 


4.2 


8-3 


25 


2.5 


6. 7 


6.4 


IOO 


9.9 


4-3 


8-5 


26 


2.6 


6.9 


6.4 


I04 


10.2 


4.4 


8.8 


27 


2.7 


7.2 


6.4 


IO8 


10.6 


4.6 


9.2 


28 


2.8 


7-4 


6.4 


112 


10.9 


4.8 


9-5 


29 


2.8 


7.6 


6.4 


Il6 


11. 1 


4-9 


9.6 


30 


2.9 


7.8 


6.4 


I20 


n-5 


5.o 


9.9 


31 


3-o 


8.1 


6.4 


124 


11.9 


5-2 


10.3 


32 


3-i 


8-3 


6.4 


128 


12.2 


5-3 


10.6 


33 


3-1 


8-5 


6.4 


132 


12.4 


5-4 


10.8 


34 


3-2 


8.7 


6.4 


I36 


12.7 


5.6 


11. 


35 


3-3 


8.9 


6.4 


I40 


13-1 


5-7 


"-3 


36 


3-4 


9.2 


6.4 


144 


!3-5 


5-9 


11. 7 


37 


3-4 


9.4 


6.4 


I48 


*3-7 


6.0 


11.9 


38 


3-5 


9.6 


6.4 


152 


14.0 


6.1 


12. 1 


39 


3.6 


9.8 


6.4 


156 


14-5 


6.3 


12.4 


40 


3.6 


10. 1 


6.4 


l6o 


14.8 


6.4 


12.7 


4i 


3-7 


10.3 


6.4 


164 


i5-i 


6-5 


13.0 


42 


3-8 


io-5 


6.4 


168 


15.4 


6.7 


T-3-3 


43 


3-9 


10.7 


6.4 


172 


15-7 


6.8 


13-5 


44 


3-9 


10.9 


6.4 


176 


15-9 


6.9 


*3-7 


45 


4.0 


11. 2 


6.4 


l8o 


16.4 


7-i 


14.1 


46 


4.1 


11.4 


6.4 


184 


16.7 


7.2 


14.4 


47 


4.2 


11. 6 


6.4 


188 


17.0 


■ 7-4 


14-7 


48 


4.2 


11.8 


6.4 


I92 


17.2 


7-5 


14.8 


49 


4-3 


12. 1 


6.4 


I96 


17.6 


7-7 


15.2 


5o 


4.4 


12.3 


6.4 


200 


18.0 


7.8 


15.5 



362 



NOTES ON CONSTRUCTION 

Concrete Culverts. — Continued 









2' high 


X 2' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 
Square 


Paving 
Square 
Yards 


Portland 
Cement 
Barrels 


Sand 

Cubic 

Yards 


Crushed 
Stone 
Cubic 








Second 


Third 


Feet 








Yards 


20 


2.4 


7-1 


80 


9.8 


IO. I 


4-4 


S.S 


21 


2.4 


7-3 


84 


9.8 


10.4 


4-5 


9.0 


22 


2-5 


7.6 


88 


9.8 


10.8 


4-7 


9.4 


23 


2.6 


7-9 


92 


9.8 


II. 2 


4.9 


9-7 


24 


2.7 


8.1 


96 


9.8 


us 


5.o 


10.0 


25 


2.7 


8.4 


100 


9.8 


11. 8 


5-2 


10.3 


26 


2.8 


8.6 


104 


9.8 


12.2 


5-3 


10.6 


27 


2.9 


8.9 


108 


9.8 


12.6 


5.5 


10.9 


28 


3.0 


9.2 


112 


9.8 


13.0 


5-7 


ii.3 


29 


3.o 


9-4 


116 


9.8 


13.2 


5.8 


11. 5 


30 


3-1 


9-7 


120 


9.8 


13.6 


6.0 


11.9 


31 


3-2 


9.9 


124 


9.8 


14.0 


6.1 


12. 1 


32 


3-3 


10.2 


128 


9.8 


14.4 


6.3 


12.5 


33 


3-3 


10.5 


132 


9.8 


14.7 


6.4 


12.8 


34 


3-4 


10.7 


136 


9.8 


i5-o 


6.6 


13.0 


35 


3-5 


11.0 


140 


9.8 


15-4 


6.8 


13-4 


36 


3-6 


11. 2 


144 


9.8 


15.8 


6.9 


13-7 


37 


3-6 


"•5 


148 


9.8 


16.1 


7-1 


14.0 


38 


3-7 


11.8 


152 


9.8 


16.5 


7.2 


14.4 


39 


3-8 


12.0 


156 


9.8 


16.8 


7-4 


14.7 


40 


3-9 


12.3 


160 


9.8 


17-3 


7.6 


15.0 


4i 


3-9 


12.5 


164 


9.8 


17.5 


7.7 


15-2 


42 


4.0 


12.8 


168 


9.8 


17.9 


7-9 


15.6 


43 


4.1 


131 


172 


9.8 


18.3 


8.0 


16.0 


44 


4.2 


13-3 


176 


9.8 


18.6 


8.2 


16.2 


45 


4.2 


13.6 


180 


9.8 


18.9 


8-3 


I6.S 


46 


4-3 


13-9 


184 


9.8 


19.4 


8-5 


16.9 


47 


4-4 ■ 


14.1 


188 


9.8 


19.7 


8.6 


17.2 


48 


4.4 


14.4 


192 


9.8 


20.0 


8.8 


17-4 


49 


4.5 


14.6 


196 


9.8 


20.4 


8.9 


17.7 


5o 


4.6 


14.9 


200 


9.8 


20.8 


9.1 


18.1 



CONCRETE CULVERTS 

Concrete Culverts. — Continued 



3£>3 







2' high 


X 3' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expended 
Metal 
Square 


Steel 
Pounds 


Portland 

Cement 

Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 








Second 


Third 


Feet 








Yards 


20 


2-3 


7.6 


IOO 


78 


I0.5 


4.6 


9.2 


21 


2-4 


7.9 


105 


81 


II. O 


4-8 


9.6 


22 


2-S 


8.2 


no 


85 


11.4 


5-o 


9.9 


23 


2.6 


8-5 


ii5 


88 


11.8 


5-2 


IO.3 


24 


2.6 


8.8 


120 


9i 


12. 1 


5-3 


IO.6 


25 


2.7 


9.1 


125 


95 


12.5 


5-5 


IO.9 


26 


2.8 


9.4 


130 


98 


13.0 


5-7 


II-3 


27 


2.9 


9-7 


135 


101 


13-4 


5-9 


11. 7 


28 


3.0 


9.9 


140 


!05 


13-7 


6.0 


12.0 


29 


3-i 


10.2 


145 


108 


14.1 


6.2 


12.3 


30 


3-2 


10.5 


150 


112 


14.6 


6.4 


12.7 


31 


3-3 


10.8 


155 


115 


i5-o 


6.6 


i3-i 


32 


3-4 


11. 1 


160 


Il8 


15-4 


6.8 


13-4 


33 


3-5 


11.4 


165 


122 


15-9 


7.0 


13.8 


34 


3-6 


11. 7 


170 


125 


16.3 


7.2 


14.2 


35 


3-7 


12.0 


175 


128 


16.7 


7-3 


14.6 


36 


3.8 


12.2 


180 


132 


17.0 


7-5 


14.8 


37 


3-9 


12.5 


185 


135 


17.5 


7-7 


15-2 


38 


3-9 


12.8 


190 


139 


17.8 


7.8 


15-5 


39 


4.0 


13. 1 


195 


142 


18.2 


8.0 


15-9 


40 


4-i 


13-4 


200 


145 


18.6 


8.2 


16.2 


41 


4.2 


13-7 


205 


149 


19.0 


8.4 


16.6 


42 


4-3 ' 


14.0 


210 


152 


19-5 


8.6 


17.0 


43 


4.4 


14-3 


215 


156 


19.9 


8.7 


17-3 


44 


4.5 


14.5 


220 


159 


20.2 


8.9 


17.6 


45 


4.6 


14.8 


225 


l62 


' 20.7 


9.1 


18.0 


46 


4-7 


i5-i 


230 


166 


21. 1 


9.2 


18.4 


47 


4.8 


15-4 


235 


169 


21.5 


9-4 


18.7 


48 


4-9 


15-7 


240 


172 


21.9 


9.6 


19.1 


49 


5-o 


16.0 


245 


176 


22.4 


9.8 


19-5 


5o 


5-1 


16.3 


250 


179 


22.8 


10. 


19.8 



364 



NOTES ON CONSTRUCTION 

Concrete Culverts. — Continued 









2' high 


X 4' wide 






Length 
Feet 


• Con 
Cubic 


crete 
Yards 


Expanded 
Metal 
Square 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 

Cubic 

Yards 


Crushed 
Stone 
Cubic 




Second 


Third 


Feet 








Yards 


20 


2.7 


8.4 


120 


78 


11.8 


5-2 


10.3 


21 


2.8 


8.7 


126 


81 


12.3 


5-3 


10.7 


22 


2.9 


9.0 


132 


85 


12.7 


5-6 


II. O 


23 


3-i 


9-3 


138 


88 


13.2 


5-8 


II.5 


24 


3-2 


9-7 


144 


9i 


13.8 


6.0 


I2.0 


25 


3-3 


10. 


I50 


95 


14.2 


6.2 


12.3 


26 


3-4 


10.3 


156 


98 


14.6 


6.4 


12.7 


27 


3-5 


10.6 


162 


101 


15.0 


6.6 


13. 1 


28 


3-6 


10.9 


168 


105 


i5-5 


6.8 


13-4 


29 


3-7 


11. 2 


174 


108 


15-9 


6.9 


13.8 


30 


3-8 


"•5 


180 


112 


16.3 


7-1 


14.2 


31 


3-9 


11.9 


186 


115 


16.8 


7-4 


14.6 


32 


4.0 


12.2 


192 


118 


*7-3 


7.6 


15-0 


33 


4.2 


12.5 


198 


122 


17.8 


7.8 


15-5 


34 


4-3 


12.8 


204 


125 


18.3 


8.0 


15-9 


35 


4-4 


13. 1 


2IO 


128 


18.7 


8.2 


16.2 


36 


4-5 


134 


216 


132 


19.1 


8.4 


16.6 


37 


4.6 - 


13.8 


222 


135 


19.6 


8.6 


17. 1 


38 


4-7 


14.1 


228 


139 


20.1 


8.7 


17.4 


39 


4.8 


14.4 


234 


142 


20.5 


9.0 


17.8 


40 


4-9 


14.7 


240 


145 


20.9 


9.1 


18.2 


4i 


5.o 


15.0 


246 


149 


21.4 


9.4 


18.6 


42 


5-2 


15-3 


252 


152 


21.9 


9.6 


19.1 


43 


5-3 


15.6 


258 


156 


22.3 


9.8 


19.4 


44 


5-4 


16.0 


264 


159 


22.9 


10. 


19.9 


45 


5-5 


16.3 


270 


162 


23-3 


10.2 


20.2 


46 


5-6 


16.6 


276 


166 


23-7 


10.4 


20.6 


47 


5-7 


16.9 


282 


169 


24.1 


10.6 


21.0 


48 


5-8 


17.2 


288 


172 


24.6 


10.8 


21.3 


49 


5-9 


i7-5 


294 


176 


25.0 


10.9 


21.7 


5o 


6.0 


17.8 


3OO 


179 


25-4 


11. 1 


22.1 



CONCRETE CULVERTS 

Concrete Culverts. — Continued 



3°5 







3' high 


X 3' wick 


■ 






Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 
Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 


Feet 






Square 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


2-3 


10.4 


IOO 


82 


134 


5-9 


II.8 


21 


2.4 


10.8 


105 


85 


13-9 


6.2 


12.3 


22 


2-5 


11. 2 


no 


88 


14.4 


6.4 


12.7 


23 


2.6 


n-5 


115 


92 


14.9 


6.6 


i3-i 


24 


2.6 


11.9 


120 


95 


15-3 


6.8 


13.5 


25 


2.7 


12.2 


125 


99 


15-7 


7.0 


13.8 


26 


2.8 


12.6 


130 


102 


16.2 


7.2 


14.3 


27 


2.9 


13.0 


135 


105 


16.8 


7-4 


14.8 


28 


3-0 


t-3-3 


140 


109 


17.2 


7.6 


i5-i 


29 


3-i 


13-7 


145 


112 


17.7 


7-9 


15.6 


30 


3-2 


14.0 


150 


116 


18.2 


8.1 


16.0 


3i 


3-3 


14.4 


155 


119 


18.7 


8-3 


16.4 


32 


3-4 


14.8 


160 


122 


19.2 


8-5 


16.9 


33 


3-5 


i5-i 


165 


126 


19.6 


8.7 


17.3 


34 


3.6 


15-5 


170 


129 


20.2 


8.9 


17.6 


35 


3-7 


15.8 


175 


133 


20.6 


9.1 


18.1 


36 


3-8 


16.2 


180 


136 


21. 1 


9-4 


18.6 


37 


3-9 


16.6 


185 


139 


21.6 


9.6 


19.0 


38 


3-9 


16.9 


190 


143 


22.0 


9-7 


19-3 


39 


4.0 


17-3 


195 


146 


22.5 


10. 


19.8 


40 


4.1 


17.6 


200 


150 


22.9 


10.2 


20.1 


4i 


4.2 


18.0 


205 


153 


23-4 


10.4 


20.6 


42 


4.3 


18.4 


210 


156 


24.0 


10.6 


21. 1 


43 


4.4 


18.7 


215 


160 


24.4 


10.8 


21.4 


44 


4-5 


19.1 


220 


163 


24.9 


n. 


21.9 


45 


4.6 


19.4 


225 


167 


25-4 


11. 2 


22.3 


46 


4-7 


19.8 


23O 


170 


25.9 


11.4 


22.7 


47 


4.8 


20.2 


235 


*73 


26.4 


n. 7 


23.2 


48 


4-9 


20.5 


24O 


177 


26.8 


11.9 


23.6 


49 


5.o 


20.9 


245 


180 


27.4 


12. 1 


24.0 


50 


5-1 


21.2 


25O 


184 


27.8 


12.3 


24.4 



3 66 



NOTES ON CONSTRUCTION 
Concrete Culverts. — Continued 







3' high 


X 4' wide 






Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 


Feet 






Square 


Pounds 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


2.7 


n-3 


I20 


82 


14.8 


6.5 


13.0 


21 


2.8 


11. 7 


126 


85 


15-3 


6.8 


13-5 


22 


2.9 


12. 1 


132 


88 


is-8 


7.0 


13-9 


23 


3-i 


12.5 


138 


92 


16.5 


7-3 


14-5 


24 


3-2 


12.9 


144 


95 


17.O 


7-5 


14.9 


25 


3-3 


13.2 


I50 


99 


17.4 


7.7 


15-3 


26 


3-4 


13.6 


156 


102 


18.0 


7-9 


15.8 


27 


3-5 


14.0 


162 


105 


18.5 


8.2 


16.3 


28 


3.6 


14.4 


168 


109 


19.0 


8.4 


16.7 


29 


3-7 


14.8 


174 


112 


19.6 


8-7 


17.2 


30 


3-8 


15.2 


180 


116 


20.I 


8.9 


17.6 


31 


3-9 


15.6 


186 


119 


20.6 


9.1 


18.1 


32 


4.0 


16.0 


192 


122 


21. 1 


9-4 


18.6 


33 


4.2 


16.4 


198 


126 


21.8 


9.6 


19.1 


34 


4-3 


16.8 


204 


129 


22.3 


9.8 


19.6 


35 


44 


17. 1 


210 


133 


22.8 


IO.I 


20.0 


36 


4-5 


17-5 


216 


136 


23-3 


10.3 


20.4 


37 


4.6 


17.9 


222 


139 


23.8 


10.5 


20.9 


38 


4-7 


18.3 


228 


143 


24-3 


10.8 


21.3 


39 


4.8 


18.7 


234 


146 


24.9 


II.O 


21.8 


40 


4.9 


19. 1 


240 


150 


25.4 


II. 2 


22.3 


4i 


5.o 


19-5 


246 


153 


25-9 


II.4 


22.7 


42 


5-i 


19.9 


252 


156' 


26.5 


11. 7 


23.2 


43 


5-3 


.20.3 


258 


160 


27.1 


12.0 


23-7 


44 


5-4 


20.7 


264 


163 


27.7 


12.2 


24.2 


45 


5-5 


21.0 


27O 


167 


28.1 


12.4 


24.6 


46 


5-6 


21.4 


276 


170 


28.6 


12.6 


25.0 


47 


5-7 


21.8 


282 


173 


29.1 


12.9 


25.5 


48 


5-8 


22.2 


288 


177 


29.7 


i3-i 


26.0 


49 


5-9 


22.6 


294 


180 


30.2 


13-3 


26.4 


5o 


6.0 


23.0 


3OO 


184 


30.7 


13.6 


26.9 



CONCRETE CULVERTS 

Concrete Culverts. — Continued 



367 









4' high 


X 4' wide 






Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 


Feet 






Square 


Pounds 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


2.7 


14-5 


120 


^ 


18.1 


8.1 


15-9 


21 


2.8 


15.0 


126 


90 


18.7 


S-3 


16.5 


22 


2.9 


15-4 


132 


94 


19.2 


8.6 


17.0 


23 


3-i 


15-9 


138 


97 


20.O 


8.9 


17.6 


24 


3-2 


16.4 


144 


100 


20.6 


9.2 


18.2 


25 


3-3 


16.8 


I50 


104 


21. 1 


9.4 


18.7 


26 


3-4 


17-3 


156 


107 


21.8 


9-7 


19.2 


27 


3-5 


17.7 


162 


in 


22.3 


9.9 


19.7 


28 


3-6 


18.2 


168 


114 


22.9 


10.2 


20.2 


29 


3-7 


18.7 


174 


117 


23-5 


io-5 


20.8 


30 


3-8 


19.1 


180 


121 


24.I 


10.7 


21.2 


31 


3-9 


19.6 


186 


124 


24.7 


11.0 


21.8 


32 


4.0 


20.1 


192 


128 


25-3 


n-3 


22.4 


33 


4.2 


20.5 


198 


131 


26.0 


11.6 


22.9 


34 


4-3 


21.0 


204 


134 


26.6 


11.9 


23-5 


35 


4.4 


21.4 


2IO 


138 


27.1 


12. 1 


24.0 


36 


4.5 


21.9 


216 


141 


27.8 


12.4 


24.5 


37 


4.6 


. 22.4 


222 


145 


28.4 


12.6 


25.1 


38 


4-7 


22.8 


228 


148 


28.9 


12.9 


25.5 


39 


4.8 


23-3 


234 


151 


29.6 


13. 1 


26.1 


40 


4-9 


23.8 


24O 


155 


30.2 


13-4 


26.6 


4i 


5.o 


24.2 


246 


158 


30.7 


13-7 


27.1 


42 


5-i 


24.7 


252 


162 


31-4 


14.0 


27.7 


43 


5-3 


25.2 


258 


165 


32.1 


14.3 


28.3 


44 


5-4 


25.6 


264 


168 


32.6 


14.5 


28.8 


45 


5-5 


26.1 


270 


172 


33-3 


14.8 


29-3 


46 


5-6 


26.5 


276 


175 


33-8 


i5-o 


29.8 


47 


5-7 


27.0 


282 


179 


34-4 


15-3 


30.3 


48 


5-8 


27-5 


288 


182 


35-i 


i5-6 


30-9 


49 


5-9 


27.9 


294 


185 


35-6 


15.8 


31-4 


5o 


6.0 


28.4 


300 


189 


36.2 


16.1 


3i-9 



368 NOTES ON CONSTRUCTION 

Concrete Culverts. — Continued 









3 ; high 


X 5' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 
Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 






Square 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


4.0 


12.4 


140 


^3 


17.5 


7-7 


15-2 


21 


4.2 


12.8 


147 


86 


18.1 


7-9 


15-7 


22 


4-4 


^3-3 


154 


90 


18.9 


^3 


16.4 


23 


4.6 


13-7 


161 


93 


19-5 


8.6 


17.0 


24 


4-7 


14.1 


168 


96 


20.1 


8.8 


17-4 


25 


4-9 


14-5 


175 


100 


20.7 


9.1 


18.0 


26 


5-i 


14.9 


182 


103 


21.4 


9-3 


18.5 


27 


5-3 


15-4 


189 


106 


22.1 


9.6 


19.2 


28 


5-4 


15-8 


196 


no 


22.6 


9.9 


19.7 


29 


5.6 


16.2 


203 


113 


23-3 


10.2 


20.2 


30 


5-8 


16.6 


2IO 


117 


23-9 


10.5 


20.8 


31 


5-9 


17.0 


217 


120 


24.5 


10.7 


21.2 


32 


6.1 


17.4 


224 


123 


25-1 


n. 


21.8 


33 


6-3 


17.9 


231 


127 


25-9 


n-3 


22.4 


34 


6-5 


18.3 


238 


130 


26.5 


11.6 


23.0 


35 


6.6 


18.7 


245 


134 


27.1 


11.8 


23-5 


36 


6.8 


19. 1 


252 


137 


27.7 


12. 1 


24.0 


31 


7.0 


19-5 


259 


140 


28.4 


12.4 


24.6 


38 


7.2 


19.9 


266 


144 


29.0 


12.7 


25.1 


39 


7-3 


20.4 


2 73 


147 


29.6 


12.9 


25-7 


40 


7-5 


20.8 


280 


150 


30-3 


13.2 


26.2 


4i 


7-7 


21.2 


287 


154 


30-9 


13-5 


26.8 


42 


7-8 


21.6 


294 


157 


3i-5 


13-7 


27-3 


43 


8.0 


22.0 


301 


161 


32.1 


14.0 


27.8 


44 


8.2 


22.4 


308 


164 


32.8 


14-3 


28.4 


45 


8.4 


22.9 


315 


167 


33-4 


14.6 


29.0 


46 


8-5 


23-3 


322 


171 


34-i 


14.8 


29-5 


47 


8-7 


23-7 


329 


174 


34-7 


15.1 


30.0 


48 


8.9 


24.1 


336 


177' 


35-3 


15-3 


30.6 


49 


9.1 


24-5 


343 


181 


36.0 


15.6 


31.2 


50 


9.2 


24.9 


35o 


184 


36.5 


15.9 


31.6 



CONCRETE CULVERTS 

Concrete Culverts. — Continued 



369 









4' high 


X 5' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 
Square 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 








Second 


Third 


Feet 








Yards 


20 


4.0 


15.8 


140 


88 


2I.O 


9.2 


18.4 


21 


4.2 


16.3 


147 


92 


21.7 


9.6 


19.0 


22 


4.4 


16.8 


154 


95 


22.5 


9.9 


19.7 


23 


4.6 


17.2 


161 


99 


23.I 


I0.2 


20.2 


24 


4-7 


17.7 


168 


102 


23-7 


io-5 


20.8 


25 


4.9 


18.2 


175 


105 


24.5 


10.8 


21.4 


26 


5-i 


18.7 


182 


109 


25.2 


11. 1 


22.1 


27 


5-3 


19.2 


189 


112 


26.O 


n-5 


22.7 


28 


5-4 


19.7 


196 


116 


26.6 


11. 7 


23-3 


29 


5.6 


20.2 


203 


119 


27.4 


12. 1 


23-9 


30 


5-8 


20.7 


2IO 


122 


28.I 


12.4 


24.6 


31 


5-9 


21.2 


217 


126 


28.8 


12.7 


25.1 


32 


6.1 


21.7 


224 


129 


29-5 


13.0 


25.8 


33 


6.3 


22.1 


231 


133 


30.2 


13-3 


26.3 


34 


6-5 


22.6 


238 


136 


30.9 


13.6 


27.O 


35 


6.6 


23.I 


245 


139 


3i-5 


13-9 


27.6 


36 


6.8 


23.6 


252 


143 


32-3 


14.2 


28.2 


37 


7.0 


24.I 


259 


146 


33-o 


14.5 


28.8 


38 


7.2 


24.6 


266 


150 


33-8 


14.9 


29-5 


39 


7-3 


25.I 


273 


153 


34-4 


i5-i 


30.I 


40 


7-5 


25.6 


280 


156 


35-2 


15-5 


30.7 


4i 


7-7 


26.I 


287 


160 


35-9 


15-8 


31-3 


42 


7.8 


26.6 


294 


163 


36.6 


16.1 


3i-9 


43 


8.0 


27.O 


301 


167 


37-2 


16.4 


32.5 


44 


8.2 


27.5 


308 


170 


38.0 


16.7 


33-?- 


45 


8-4 


28.O 


315 


173 


38.7 


17.0 


33-8 


46 


8-5 


28.5 


322 


177 


39-3 


17.3 


34-3 


47 


8.7 


29.O 


329 


180 


40.1 


17.6 


35-0 


48 


8.9 


29.5 


336 


184 


40.9 


18.0 


35-6 


49 


9.1 


30.0 


343 


187 


41.6 


18.3 


36-3 


5o 


9.2 


30-5 


35o 


190 


42.2 


18.6 


36.8 



37° 



NOTES ON CONSTRUCTION 

Concrete Culverts. — Continued 









5' high 


X 5' wide 




• 


Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 


Feet 






Square 


Pounds 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


4.0 


19-5 


140 


93 


24.7 


11. 


21.8 


21 


4.2 


20.0 


147 


•96 


25-5 


11.3 


22.5 


22 


4.4 


20.6 


154 


100 


26.3 


II. 7 


23.2 


23 


4.6 


21.2 


161 


103 


27.2 


12. 1 


24.2 


24 


4-7 


21.7 


168 


106 


27.8 


12.4 


24.8 


25 


4.9 


22.3 


175 


no 


28.7 


12.7 


25-4 


26 


5-i 


22.9 


182 


113 


29.5. 


i3-i 


26.2 


27 


5-3 


23.4 


189 


117 


30-3 


13-4 


26.8 


28 


5-4 


24.0 


196 


120 


31.0 


13.8 


27.6 


29 


5-6 


24.6 


203 


123 


3**9 


14.1 


28.2 


30 


5-8 


25.1 


210 


127 


32.6 


14-5 


29.0 


31 


5-9 


25-7 


217 


130 


33-4 


14.8 


29.6 


32 


6.1 


26.2 


224 


134 


34-i 


i5-i 


30.2 


33 


6.3 


26.8 


231 


*37 


35-o 


15-5 


31.0 


34 


6-5 


27.4 


238 


140 


35-8 


15-9 


31.8 


35 


6.6 


27.9 


245 


144 


36.4 


16.2 


32.4 


36 


6.8 


28.5 


252 


147 


37-3 


16.5 


33-o 


37 


7.0 


29.1 


259 


150 


38.2 


16.9 


33-8 


38 


7.2 


29.6 


266 


154 


38.9 


17.2 


34-4 


39 


7-3 


30.2 


2 73 


157 


39-6 


17.6 


35-i 


40 


7-5 


30.8 


280 


161 


40.5 


17.9 


35-8 


4i 


7-7 


3^-3 


287 


164 


41.2 


18.3 


36.5 


42 


7.8 


3i-9 


294 


167 


42.0 


18.6 


37-2 


43 


8.0 


32.5 


301 


171 


42.8 


19.0 


37-9 


44 


8.2 


33-o 


308 


174 


43-6 


19-3 


38.6 


45 


8.4 


33-6 


315 


178 


44.4 


19.7 


39-3 


46 


8-5 


34-2 


322 


181 


45-2 


20.0 


40.0 


47 


8.7 


34-7 


329 


184 


45-9 


20.3 


40.6 


48 


8.9 


35-2 


336 


188 


46.7 


20.6 


41.2 


49 


9.1 


35-9 


343 


191 


47.6 


21.0 


42.0 


5o 


9.2 


36.4 


35o 


195 


48.3 


21.4 


42.8 



CONCLUSION 



371 



a rough sandpaper-like finish is wanted it can be secured by 
rubbing with a wooden float moistened with water. This finish 
is not as apt to hair-check as the smooth finish. 

Freshly laid concrete should be protected from a hot sun by 
covering it with canvas, or blankets, and wetting it down fre- 
quently for four or five days. No plastering of surfaces should 
be allowed after the cement has set. If, however, it has been 
badly hair-checked from heat the defect can usually be remedied 
by rubbing with a carborundum brick. Freshly laid concrete 
must be protected from frost. A satisfactory method is to 
cover with canvas and a thick layer of manure or straw. If the 
concrete has been frost-pitted, on the surface only, bush hammer- 
ing will give a rough stone finish, pleasing in appearance. No 
culvert work should be allowed in continued cold weather, as it 
is difficult to get a good finish and in roadwork there is no neces- 
sity of doing this work in the winter. Concrete inspection must 
be continuous. 

CONCLUSION 

For obvious reasons the inspection of construction is generally 
the weak point in Municipal and State Engineering undertak- 
ings. It is often due to the employment of inferior inspectors, 
and frequently to the impossibility of even good inspectors con- 
trolling certain contractors. The work is rarely bad, but it 
will not be as strong nor as lasting as a first-class job, and if 
such conditions are foreseen, and cannot be avoided, it is, per- 
haps, best to design the work stronger than would otherwise be 
required, as this seems to be the only practical method of meeting 
a recognized evil. 



CHAPTER XII 

SPECIFICATIONS 

Under this heading are included extracts from the State speci- 
fications of New York and Washington covering "Materials" and 
the more common construction methods. It is difficult to write a 
specification that is definite and fair, and it is impossible to avoid 
criticism. The following clauses are examples of current practice. 
They are not ideal, but show the points to be considered. No 
attempt is made in this book to discuss methods of bidding or of 
forms of proposals. 

MATERIALS 

(New York State Specifications, 19 14) 

Materials of Construction 

All materials proposed to be used in construction shall have due 
examination and pass all required tests before acceptance. Those 
which are to be tested by the Bureau of Tests at Albany shall have 
samples taken and submitted in accordance with the commission's 
instructions to its employees. Samples are to be taken of all sand, 
gravel, cement, concrete, bituminous material, stone, and all other 
pavement ingredients, of which the engineer in charge has not been 
notified that satisfactory samples have already been taken. None 
of this material is to be used until the written notification of accept- 
ance is received by the engineer in charge of the contract, and then 
only so long as its quality remains equal to that of the accepted 
sample. 

Portland Cement 

0.1. All the cement used in the work shall be true Portland cement 
of well-known brands which have been in successful use on large 
engineering works in America for not less than two years and which 
are manufactured at works which have been in successful operation 
for at least one year. 

0.2. Tests will be made as follows: — first, for fineness; second, 
for constancy of volume; third, for time of setting; fourth, for tensile 
strength; fifth, for composition by chemical tests; sixth, for specific 
gravity. 

The average result of the separate samples shall be the test for 
tensile strength of any lot. The samples of each lot shall be required 
to show uniform results in tests. Marked deviations' from such 
results may be considered cause for rejection, even though test re- 
quirements may be otherwise fulfilled. 

The results of the tests may be expected in 12 days after shipment 
of samples. 

372 



CEMENT TESTS 373 

Cement not satisfactory in the 7-day tests will be held awaiting 
the result of the 28-day tests before acceptance or rejection. 

0.3. The cement shall meet the following requirements: 

It shall be ground to such fineness that not less than 92 per cent 
by weight shall pass through a No. 100 standard sieve of 10,000 
meshes per square inch, and not less than 75 per cent by weight 
shall pass through a No. 200 standard sieve of 40,000 meshes per 
square inch. 

0.4. Pats of neat cement about 3 inches by 4 inches in size, i inch 
thick at the center, and tapering to a thin edge, shall be kept in 
moist air for a period of 24 hours. 

Normal Tests 

Air Test. One of these pats is then kept in air at normal tempera- 
ture for 28 days. 

Water Test : Another pat is kept in water maintained as near 70 
degrees Fahrenheit as practical for 28 days. 

Accelerated Test : A pat is exposed in any convenient way in an 
atmosphere of steam, above boiling water, in a loosely closed vessel 
for 5 hours. 

These pats are observed at intervals and, to satisfactorily pass 
the requirements, shall remain firm and hard and show no signs of 
distortion, checking, cracking or disintegration. 

0.5. Cement shall not develop its initial set in less than 30 minutes, 
and shall develop a hard set in not less than 60 minutes nor more 
than 600 minutes, the determination being made with the Vicat 
needle apparatus from pastes of normal consistency, as follows: 

The paste is molded upon a glass in a conical hard rubber mold 
4 centimeters high; this cake is to set in moist air and a Vicat needle 
with a wire 1 millimeter in diameter and loaded to 300 grammes 
shall be placed upon it. When the needle ceases to pass a point 5 
millimeters above the upper surface of the glass plate the initial set 
has taken place. 

0.6. Briquettes of neat cement mixed 1 minute, in an air tem- 
perature between 65 and 70 degrees Fahrenheit and using water of 
about the same temperature, and put into the molds with fingers 
and trowel and kept in moist air at this temperature for 1 day of 
24 hours, shall show an average tensile strength of one hundred and 
seventy-five (175) pounds per square inch. 

Briquettes of neat cement mixed and molded as above and kept 
under above temperature for 1 day in moist air and 6 days in 
water shall show an average tensile strength of at least five hundred 
(500) pounds per square inch. 

Briquettes of neat cement mixed and molded as above and kept 
under above temperature for 1 day in moist air and 27 days in 
water shall show an average tensile strength of six hundred (600) 
pounds per square inch. 

Briquettes of 3 parts by weight of standard Ottawa sand 
and 1 part by weight of cement, mixed in the same manner 
as above and kept 7 days under the same conditions, shall show 



374 SPECIFICATIONS 

an average tensile strength of at least two hundred pounds (200) 
per square inch. 

Briquettes of sand and cement mixed and molded as above and 
kept under above conditions for 28 days shall show an average tensile 
strength of at least two hundred and seventy-five (275) pounds per 
square inch. 

In the above tests for tensile strength the briquettes must not show 
any retrogression in strength within the periods specified. 

0.7. The Commission of Highways may cause chemical tests, or 
analyses, of cement to be made, and may reject any cement which 
shows any adulteration, or excess of ingredients, which in its judgment 
would be detrimental to the work. 

The cement shall not contain more than 1.75 per cent of anhy- 
drous sulphuric acid (SO3) nor more than 4 per cent of magnesia 
(MgO). 

0.8. The specific gravity of the cement after ignition to a low red 
heat shall not be less than 3.10; and the cement shall not show a 
loss in weight on ignition of more than 4 per cent. 

0.9. The standard sand used in the tests shall be natural sand 
from Ottawa, 111., screened to pass a No. 20 standard sieve of 400 
meshes per square inch and be retained on a No. 30 standard sieve 
of 900 meshes per square inch. 

Fine Aggregate for Concrete 

0.10. Fine aggregate shall consist of sand free from organic matter; 
that which shows a coating on the grains shall not be used until 
satisfactorily washed. Sand shall be classified as No. 1, No. 2 and 
No. 3, and Grout Sand. 

No. 1 Sand 

0.1 1. No. 1 sand shall be of the following gradation: 100 per 
cent shall pass a J-inch screen; not more than 20 per cent shall pass 
a No. 50 sieve; and not more than 6 per cent shall pass a No. 100 
sieve. In special cases where more than 20 per cent of a sand passes 
a No. 50 sieve and the sand is well graded to give a low percentage of 
voids, written permission for use of the sand may be given by the 
first deputy commissioner. Sand may be rejected for this class if 
it contains more than 5 per cent of loam and silt. 

0.12. Mortar in the proportion of 1 part of cement to 3 parts 
of the sand to be tested shall develop a compressive strength at 
least equal to the strength of a similar mortar of the same age 
composed of the same cement and standard Ottawa sand. 

No. 2 Sand 

0.13. No. 2 sand shall fulfill all of the requirements for No. 1 sand 
except that restrictions on the percentage that will pass a No. 50 and 
No. 100 sieve shall be governed by the compressive strength of the 
mortar. The compressive strength of the mortar shall be at least 
equal to that obtained with the standard Ottawa sand. 



COARSE AGGREGATE FOR CONCRETE 375 

No. 3 Sand 

0.14. Sand may be rejected for this class if it contains more than 
8 per cent of loam and silt. Mortar in the proportion of 1 part of 
cement to 3 parts of the sand when tested shall develop a compressive 
strength of at least 80 per cent of the strength of a similar mortar of 
the same age composed of the same cement and standard Ottawa sand. 

Screenings 

0.15. Screenings shall not be used as fine aggregate except to 
the extent and under the restrictions given below. The division 
engineer shall submit samples to the Bureau of Tests; they must 
pass the required tests; their use must be approved in writing by 
the First Deputy Commissioner. 

0.16. Screenings may be substituted for a portion of the No. 1, 
2 and 3 sand under the following conditions : 

The screenings shall be free from dust coating and other dirt. 
100 per cent shall pass a | inch screen and not more than 6 per cent 
shall pass a No. 100 sieve. The compressive strength of a mortar 
in which the screenings and sand are in the proportions intended for 
use, shall be at least equal to the standard strength obtained with 
sand of the given class. 

. Grout Sand 

0.17. Grout sand shall be a sand of which 100 per cent passes a 
No. 20 sieve, and not over 30 per cent a No. 160 sieve. Sand may 
be rejected for this class if it contains more than 5 per cent of loam 
and silt. The grains shall be free from coating. 

Mortar in the proportion of 1 part of cement to 3 parts of the sand 
shall develop a compressive strength of at least 40 per cent of the 
strength of a similar mortar of the same age composed of the same 
cement and standard Ottawa sand. 

Cushion Sand 

0.18. Cushion sand shall be a sand of which 100% passes a No. 
6 sieve and 90% passes a No'. 20 sieve; an excessively fine sand will 
not be accepted in this class. Sand may be rejected for this class 
if it contains more than 10% of loam and silt. 

Coarse Aggregate for Concrete 

Stone 

0.19. Crushed stone for concrete shall be of hard, durable stone, 
tested by the Bureau of Tests and satisfactory to the engineer. 
Stone for concrete shall be of an approved kind and quality of rock 
and shall be free, before being crushed, from soil, mud and dust. 
Crushed stone for first-class concrete shall be in fragments that will 
pass through a ij-inoh circular hole and that will not pass through 
a J-inch square hole. Crushed stone for second-class or third-class 
concrete shall be in fragments that will pass through a 2|-inch cir- 
cular hole and that will not pass through a J-inch square hole. 



376 SPECIFICATIONS 

Gravel 

0.20. Gravel shall not be used in concrete except when it has been 
submitted by the Division Engineer to the Bureau of Tests, has been 
approved by the Bureau of Tests, and its use has been approved by 
the First Deputy Commissioner in writing, — and then only under 
the restrictions given below. 

0.21. Gravel for use in concrete pavement and first-class concrete 
shall be composed of hard, durable stone absolutely clean and free 
from coating. No gravel will be accepted that contains any disin- 
tegrated or soft stone or shale. Gravel containing any flat stone 
shall not be permitted. Gravel for use in second and third class 
concrete shall be composed of a sound, durable stone. It shall be 
clean and free from coating. It shall not contain more than 10 per 
cent of soft stone or shale. Gravel containing a larger percentage 
of flat stone shall not be permitted. 

0.22. Gravel for first-class concrete shall be in particles that will 
pass through a ij-inch circular hole and that will not pass through a 
J inch square hole. Gravel for second and third-class concrete 
shall be in particles that will pass through a 2j-inch circular hole 
and that will not pass through a f-inch square hole. 

0.23. Gravel mixed with mud, clay, dirt or quicksand shall be 
washed to the satisfaction of the engineer. Run of bank gravel 
shall not be permitted. All gravel shall be properly screened and 
the coarse and fine aggregate regularly proportioned thereafter. 

0.24. All coarse aggregate used for concrete shall be uniformly 
graded from the minimum to the maximum sizes of stone or gravel 
specified above for the several types of concrete, thus producing an 
aggregate in which the voids will be a minimum. 

Stone, Gravel, etc., for Pavements 

0.25. The sizes of all stone, gravel, etc., used under these specifi- 
cations shall be determined by the size of screen aperture through 
which the stone will pass when revolved in a rotary screen. They 
shall be designated as follows: 

Diameter of Aperture 
Min. Max. 

J-inch square Screenings 

J-inch square f-inch circular No. 1 

f-inch circular ii-inch circular No. 2 

1 1-inch circular 2f-inch circular No. 3 

2 f-inch circular 3f-inch circular No. 4 

0.26. Gravel shall consist of clean, sound, tough hard stone. 
Gravel shall be separated into five grades or sizes by means of a 
rotary screen having openings as specified above for broken stone. 
All the general specifications given below relating to broken stone 
shall apply to gravel, excepting that gravel may contain not 
more than 5 per cent, of loam, but must otherwise be free from 



BITUMINOUS MATERIALS 377 

dirt or foreign matter and shall be washed if so directed by the 
engineer. 

0.27. Broken slag shall be approved acid slag, clean, sound, tough, 
hard, sharp-angled and weigh not less than 1,800 pounds per cubic 
yard. If specified for use, it shall conform to all the general require- 
ments for broken stone as specified below. 

0.28. Broken stone shall be clean and sharp angled, shall pass 
the standard tests for abrasion and toughness as adopted by the 
American Society for Testing Materials, and shall be approved by 
the Bureau of Tests and acceptable to the engineer before being used. 

0.29. Field stones, boulders, or fence stones which are crushed 
for macadam purposes shall be 6 or more inches in diameter, if con- 
sisting of rounded cobbles. If of the flat variety, the minimum 
thickness shall be 2 inches, which latter requirement will also apply 
to laminated quarry stone. 

0.30. If after trial it is found that partially developed quarries, 
ledges or other sources of supply do not furnish a uniform product, 
or if, for any reason, the product from any source, at any time, proves 
to be unsatisfactory to the engineer, said engineer may require the 
contractor to furnish stone from other sources of supply, and the 
contractor shall have no claim for increased payment on account 
of such requirement. 

0.31. The contractor shall furnish one or more stone crushing 
plants of type, composition, and capacity satisfactory to the engineer. 
The rotary screens shall be provided with openings of size and shape 
given under "Stone Sizes," unless otherwise ordered by the engineer. 

All crushing plants installed on the work shall be fitted up with 
a tailing chute so that no stone will reach the bins other than that 
which passes through the proper screen. 

0.32. All stone must be of the required size when placed in the 
roadway, and no breaking up of stone by hammers or otherwise 
will be permitted after the stone has been placed in the work. 

0.33. In no case shall any constituent of macadam pavement be 
dumped into place in mass; the final placing shall be by shovel or 
by thin spreading such that no appreciable fall occurs. 

Filler or Binder. The filler for the bottom course shall be 
clean, coarse sand or stone screenings supplemented by product of 
the crusher not otherwise used in top or bottom courses. The filler 
and wearing surface for the top course shall be of top course stone 
screenings and when bituminous binder is used screenings must 
be dry, free from dust, and not larger than will pass a f-inch screen. 



BITUMINOUS MATERIALS 

Methods of Testing Bituminous Materials in the 

Laboratory of the Commission 

Preparing Laboratory Samples. Each laboratory sample is 
usually composed of several samples that have been taken to repre- 
sent one lot of material. The material in the separate samples is 
examined, and, if uniform in appearance, equal amounts are taken 



378 SPECIFICATIONS 

from each and thoroughly blended to form a sample of about one- 
half pint on which the complete analysis is run. 

In case of mineral bitumen, the sample received is thrown on a 
large piece of paper, pieces which are evidently foreign to the material 
are rejected, and the whole " quartered down" to a sample of about 
300 grams. This is ground in a mortar and the analysis run on this 
part of the original sample. 

Water Present. The presence of water in an oil, asphalt, or tar 
is determined by putting about 40 grams of the material into a deep, 
seamless 3-ounce tin box, a thermometer being suspended in the 
material. This is then heated to about 230 F. without stiring. If 
water is present, even in very small quantities, the material will 
froth when heated to about 212 F. The per cent of water present 
is determined by heating 20 grams of the material in a 2-ounce seam- 
less tin box in an oven maintained at a temperature of 212 F. for 
an hour. The per cent of water in mineral bitumen is determined 
in a similar manner. The loss in weight, while not absolutely cor- 
rect, is considered as moisture. 

Homogeneity. The homogeneity of the mixture is shown by its 
general appearance at a temperature of 77 F. when in a melted 
condition and when examined under the microscope. 

Gravity. The gravity is determined by taking a small test tube 

about f of an inch by 3^ inches, which is accurately weighed (weight 

A). The tube is then filled with distilled water at 77 F. and weighed 

(weight B). To get the gravity of the oil, asphalt, or tar the tube 

is filled with the material, cooled to a temperature of 77 F., cut off 

level with the top, and weighed (weight C) . The gravity is determined 

C — A 

as follows: ~ = gravity. 

Jj — A 

Penetration. The penetration test is made by putting the ma- 
terial to be tested in a 3-ounce deep, seamless tin box. Melting the 
material at the lowest possible temperature, cooling in air and then 
placing the material in a bath, for one hour, maintained at the tem- 
perature at which the test is to be made. The penetration is the 
distance expressed in hundredths of a centimeter which a standard 
needle under a stated load, and at a stated temperature, will pene- 
trate into the material. The factors usually employed are a No. 2 
sewing needle, loaded with 100 grams, applied for five seconds at a 
temperature of 77 Fahrenheit. 

Residue having a Penetration of 10 Millimeters. This test is 
made as follows: 50 grams of the oil are placed in a 3-ounce deep, 
seamless tin box, the box placed in a sand bath and heated over a 
Bunsen Burner. A thermometer is suspended in the oil, the bulb 
not touching the bottom of the box. The temperature of the oil is 
kept at from 480 F. to 500 F. and the oil is stirred from time to 
time with the thermometer to prevent overheating in any part. 
Depending upon the nature of the oil, as usually indicated by its 
flash, consistency at 77 F. and gravity, the operator can tell about 
what per cent it will be necessary to evaporate before coolmg and 
taking a penetration as described under the test for penetration. _ It 
is sometimes necessary to make several trials before the desired 



BITUMINOUS MATERIALS 379 

result is obtained. When the required penetration is reached, the 
residue left from evaporation is weighed and its per cent of the orig- 
inal sample taken is computed. 

Ductility. The ductility of an asphalt cement or bitumen is 
determined by the distance in centimeters that a briquette of the 
material will draw out before breaking. The briquette of the asphalt 
cement is molded in a Dow briquette mold having a central cross- 
section 1 centimeter square, a 2-square centimeter cross-section at 
mouth of clips, and a distance of 3 centimeters between clips. The 
molding of the briquette is done as follows: The mold is placed on 
a brass plate. To prevent the asphalt cement from adhering to this 
plate and the inner sides of the two pieces of the mold, they shall be 
well amalgamated. The asphalt cement to be tested is poured into 
the mold While in a molten state, a slight excess being added to allow 
for shrinkage on cooling. After the asphalt cement is nearly cooled, 
the briquette is smoothed off level by means of a hot spatula. When 
it is thoroughly cooled to the temperature at which it is desired to 
make the test, the clamp and the two side-pieces are removed, leaving 
the briquette of asphalt cement held at each end by the ends of the 
mold which serve as clips. The test is made by pulling the two clips 
apart at a uniform rate of 5 centimeters per minute by means of 
hooks inserted in the eyes, until rupture occurs. The briquette is 
kept in water at 77 F. for at least 30 minutes before testing, and the 
test is performed while the briquette is so immersed in the water 
at the above temperature, and at no time is the temperature of the 
water allowed to vary more than half a degree from the standard 
temperature. 

Toughness. The bitumen is heated until liquid; it is then poured 
into an amalgamated brass mold of such shape as to give a cylinder 
of the bitumen if inches in height by if inches in diameter. After 
cooling, the mold is removed and the cylinder of bitumen is placed 
in a mixture of finely crushed ice and water, giving a temperature 
of zero degrees centigrade. After remaining in the freezing mixture 
for about three hours the cylinders are broken in a Page impact 
machine (the standard machine of the American Society for Testing 
Materials for determining the toughness of macadam stone). When 
the cylinder to be broken is placed in the impact machine a piece 
of linen cloth about one inch square is placed on the end on which 
the plunger rests. This prevents the plunger from sticking to the 
bitumen and makes it easier to clean the machine. In making the 
test, the first drop of the hammer is from a height of five centimeters, 
and for each succeeding blow the height of the drop is increased five 
centimeters. The height from which the hammer falls when rupture 
occurs is given as the toughness of the material. 

Melting Point of Bitumen. The melting or softening point of 
bitumen is determined by filling a ring f inch in diameter by \ inch 
in depth, with the bitumen to be tested. After cooling, the bitumen 
is cut off level with the top of the ring. The ring containing the bitu- 
men is placed in water at 41 F. for 20 minutes before making the 
test. In performing the test the ring is put in a support so placed 
that the bottom of the ring is 1 inch above the bottom of an 800 cc. 



380 SPECIFICATIONS 

beaker. On the center of the bitumen in the ring, is placed a f-inch 
steel ball, a thermometer being placed with its bulb on a level with 
the ring containing the bitumen. The beaker is nearly filled with 
water at a temperature of 41 F. and the temperature raised at the 
rate of 8° F. to io° F. per minute. The temperature recorded by the 
thermometer at the time the ball touches the bottom of the beaker 
is taken as the melting point of the bitumen. 

Evaporation. Fifty grams of the material are weighed into a 
flat-bottomed dish 2y-g in. in diameter by if in. in depth. This is 
placed in an oven maintained at a uniform temperature of 325 
Fahrenheit for a period of five hours. At the end of this period the 
loss in weight or per cent of loss is found by reweighing. 

Flash. About 40 grams of the material to be tested are placed 
in a 3-ounce deep, seamless tin box. The box containing the ma- 
terial is placed on a sand bath over a Bunsen Burner, the bulb of a 
thermometer being placed in the material, but so adjusted as not to 
touch the bottom of the box. The flame of the Bunsen Burner is so 
adjusted that the temperature of the material being tested is raised 
at the rate of io° F. to 15 F. per minute. As soon as vapors are 
seen coming off, the small flame from a capillary tube is passed over 
the center of the liquid and about \ inch above it, and repeated for 
about every 5 F. rise in temperature until the slight explosion indi- 
cates the flash-point is reached. The temperature at this point is 
recorded as the open flash-point of the material being tested. 

Total Bitumen. The solubility in C S 2 is found by weighing 
approximately 1 gram of the material into an Erlenmeyer flask, 
adding 50 cc. of C 5 2 and allowing the solvent to act 12 hours at lab- 
oratory temperature, care being taken to break up all lumps before 
filtering. The filtration is made through a C. S. & S. 9-centimeter 
filter paper No. 589. The papers are first dried, and weighed imme- 
diately before using. The filtration is made in a valve funnel, a 
watch glass beieg placed on the funnel to prevent evaporation of 
the solvent. After washing until washings come clean, the filter 
and residue are placed in an oven at 212 F. for 30 minutes, 
cooled in a desiccator and weighed. The difference in weight gives 
the amount of material insoluble in C So from which the per cent of 
soluble bitumen is computed. 

The total bitumen in mineral bitumen is determined by weighing 
about 25 grams of the dried material into a dried and weighed C. S. 
& S. extraction cartridge and extracting in a continuous extraction 
apparatus, using C S 2 for a solvent; drying and weighing after 
extraction is completed. The loss gives the amount of bitumen 
soluble in C S 2 . 

Carbon Tetrachloride Solubility. This test is made in the 
same manner as determining the bitumen soluble C S 2 , except that 
C C I4 is used as solvent^ 

Naphtha Solubility. The amount of material soluble in 76 
naphtha (boiling point 140 F. to 190 F.) is found by the same 
method that is used in getting the amount soluble in C S 2 , except 
that naphtha is used for a solvent in place of C 5 2 . The character of 
the filtrate is determined by placing about 10 cc. of the nitrate in the 



BITUMINOUS MATERIALS 381 

tin covers of the 2-ounce boxes used in making the heating tests and 
allowing the nitrate to evaporate. The residue is noted to be sticky 
or oily by rubbing between the fingers. 

Water Soluble Materials. Water soluble materials in tar are 
determined by weighing about 2 grams into a casserole, adding 
50 cc. of distilled water, and boiling for 1 hour. The solution is 
then filtered into a weighted porcelain evaporating dish, using hot 
distilled water for a wash and evaporated to dryness on a steam bath. 
The weight at the evaporating dish and contents after drying to a 
constant weight at 212 F., less the weight of the dish itself, gives 
the amount of water soluble materials in the tar, from which the per 
cent may be calculated. 

Free Carbon. The free carbon in tar is determined by extrac- 
tion at room temperature with C 5 2 . In extraction C S 2 is used in 
the same manner as making the determination for the amount of 
bitumen soluble in C S2 in asphalts. Determination as to whether 
extraction is complete is made by placing some of the carbon on 
white porcelain, moistening it with C S2, and if the porcelain is stained 
the extraction is not complete, and the carbon requires more washing. 

Paraffine. Fifty grams of the material are placed in a half -pint 
retort, E. & A. No. 4521, fitted with a tee condenser. To the 20- 
inch iron delivery tube of the retort is attached a 10-inch glass tube, 
and between the cover and the retort is placed a paper gasket cut 
from heavy wrapping-paper. The material is rapidly distilled to a 
dry coke from wTiich no further distillate can be obtained, not over 
25 minutes being allowed from the time of placing flame under retort 
until distillation ceases. About 5 grams of the distillate are taken 
if the materials contain 2 per cent or less of paraffine and about 3 
grams if the material contains over 2 per cent of paraffine. This 
amount of distillate is dissolved in 25 cc. of Squibbs Absolute Ether 
in a 2-ounce glass flask, after which 25 cc. of Squibbs Absolute Alco- 
hol are added. A one-to-one wash of 25 cc. each of similar ether and 
alcohol is made up, and the solution of oil and the wash are then 
frozen separately for 40 minutes in a salt and ice mixture, giving a 
temperature of o° F. The precipitate is filtered quickly by means 
of a suction pump by using a No. 575 C. S. & S. 9-centimeter hardened 
filter-paper; the paper being placed in a funnel packed in a freezing 
mixture of salt and ice. The paraffine caught on the filter-paper is 
washed with the cool one-to-one wash until the paraffine is white. 
The paraffine is then scraped into a weighted crystallizing dish and 
maintained at a temperature of 212 F. until a constant weight is 
obtained, after which it is weighed and the percentage of paraffine 
in the original material is computed by dividing the weight of the 
paraffine obtained by the number of grams of distillate taken for 
freezing, and multiply this result by the percentage distilled from the 
original sample (i.e., by 100 per cent less weight of coke expressed 
in percentage). The paraffine so determined to have a melting 
point of at least 120 F. 

The melting-point of paraffine is determined by covering the bulb 
of a thermometer with the paraffine; suspending the thermometer 
in a beaker of water at 65 F., and heating the water at the rate of 



382 SPECIFICATIONS 

8° to io° F. per minute. The temperature recorded by the ther- 
mometer at the time the paraffine melts from the bulb is taken as 
the melting-point of the paraffine. 

Distillation of Tar. The distillation test of tar is made by 
measuring 100 cubic centimeters of the tar into a 250 cc. Engler 
distilling flask with delivery tube at the middle of the neck. The 
thermometer is so placed that the mercury bulb is opposite the outlet 
of the flask. The thermometer used to have a nitrogen chamber 
to insure accurate reading at high temperatures. The flame is so 
regulated that approximately 1 cc. of distillate is caught per minute. 
The distillation is made continuous. 

The following fractions should be reported: 

Start of distillation to no° C. 
no° C. " 170 C. 
170 C. " 235 C. 
235 C. " 270 C. 
270 C. " 300 C. 
Residue (pitch) 

Fixed Carbon and Mineral Matter. The fixed carbon is deter- 
mined by weighing approximately 1 gram of the material into a 
weighed platinum crucible with a tightly fitting cover. The crucible, 
with its cover in place, is then placed about 4 inches over a freely 
burning Bunsen Burner so as to be completely enveloped in the 
flame and exposed to the full heatof the burner for about 3 minutes 
or until the top of the crucible cover is burned free from the carbon; 
the under side of the cover being covered with the carbon. The 
flame is then withdrawn, the crucible cooled and weighed. The 
weight after burning, less the weight of the crucible, gives the amount 
of fixed carbon plus the mineral matter. The fixed carbon is then 
burned off in the open crucible until a constant weight is obtained; 
the crucible cooled and weighed. This weight is the crucible plus 
the mineral matter. The mineral matter subtracted from the com- 
bined weight of fixed carbon and mineral matter gives the fixed 
carbon. 

Items 64 to 74 Inclusive — Bituminous Materials 

64.1. Under items 64 to 74 inclusive the Contractor shall furnish 
and deliver on the work at such points as the Engineer may direct, 
bituminous material of the kind shown on the proposal sheet as to 
be furnished under its respective item. 

64.2. Bituminous material furnished shall be of approved quality 
and shall meet the requirements specified below for the kind of ma- 
terial furnished, and for any contract, the material furnished shall 
be of one brand and shall show a uniform test unless special permis- 
sion is given to furnish other brands of material. 

64.3. The quantity to be paid for under this item shall be the 
number of gallons delivered on the work, unless the material is to 
be incorporated in the work by the same Contractor, and under the 
same contract. 



BITUMINOUS MATERIAL A 383 

If the material is to be incorporated in the work by the same Con- 
tractor, and under the same contract, the quantity to be paid for 
under this item shall be the number of gallons incorporated in the 
work under directions of the Engineer. 

Bituminous material that has been rendered unfit for use by over- 
heating or by long-continued heating, shall not be paid for. For 
purposes of measurement, a gallon shall be a volume of 231 cubic 
inches and measurement shall be based on the volume of the bitu- 
minous material of a temperature of 60 degrees Fahrenheit. 

The price bid when the material is not to be incorporated in the 
work under this contract, shall include the furnishing of the material 
along the road as directed by the Engineer. Any material wasted 
through careless handling will not be paid for. 

The price bid shall include the furnishing of the bituminous 
material alongside the road at places designated by the Engineer. 
Where the material delivered is to be incorporated into the work 
under this contract, the cost of manipulating and incorporating this 
material shall be included in the price bid for the top course of the 
pavement being constructed. 

Item 64 — Specification for Bituminous Material A 

Mixing Method (Type i) 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a 
homogeneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of 
not less than 0.97. 

(4) The penetration shall be between 8 and 12 millimeters when 
tested for 5 seconds at 77 degrees Fahrenheit with a No. 2 needle, 
weighted with 100 grams. 

(5) Fifty grams of it upon being maintained at a uniform tempera- 
ture of 325 degrees Fahrenheit for 5 hours in a cylindrical vessel 5! 
centimeters in diameter by 3 J centimeters high shall not lose more 
than 4 per centum in weight. The penetration (5 seconds, 77 de- 
grees Fahrenheit, No. 2 needle, 100 grams weight) of this residue 
shall be at least 50 per centum of the original penetration. 

(6) Its solubility at air temperature in chemically pure carbon 
disulphide for the following named materials, or materials similar 
thereto, shall be at least 99.5 per centum for pure bitumen products, 
96 per centum for Bermudez products, 81 per centum for Cuban 
products and 66 per centum for Trinidad products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees 
Beaume paraffine petroleum naphtha distilling between 140 degrees 
and 190 degrees Fahrenheit, shall be between 68 and 88 per centum. 

(8) The bitumen shall show between 8 and 17 per centum fixed 
carbon. 

(9) It shall show an open flash point not less than 375 degrees 
Fahrenheit. 



384 SPECIFICATIONS 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less 
than 10 centimeters. Toughness is determined by breaking a cylinder 
of the material if inches in diameter by if inches in height in a Page 
impact machine. (American Society of Testing Materials, August 
15, 1908.) The first drop of the hammer is from a height of 5 centi- 
meters and each succeeding blow is increased by 5 centimeters. 

(12) It shall have a ductility at 77 degrees Fahrenheit of not less 
than 25 centimeters (Dow mould). 

(13) All bituminous material A. will be sampled by an Engineer 
of the Department of Highways and samples sent to the Bureau of 
Tests, Albany, N. Y. 

Item 65 — Specification for Bituminous Material A 

Mixing Method (Type No. 2) 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in 
a homogeneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of 
not less than 0.97. 

(4) The penetration shall be between 6 and 8 millimeters when 
tested for 5 seconds at 77 degrees Fahrenheit with a No. 2 needle, 
weighted with 100 grams. 

(5) Fifty grams of it being upon maintained at a uniform tempera- 
ture of 325 degrees Fahrenheit for 5 hours in a cylindrical vessel, 
5 1 centimeters in diameter by 3 J centimeters high shall not lose more 
than 4 per centum in weight. The penetration (5 seconds, 77 de- 
grees Fahrenheit, No. 2 needle, 100 grams weight) of this residue 
shall be at least 50 per centum of the original penetration. 

(6) Its solubility at air temperature in chemically pure carbon 
disulphide for the following named materials, or materials similar 
thereto, shall be at least 99.5 per centum for pure bitumen products, 
96 per centum for Bermudez products, 81 per centum for Cuban 
products and 66 per centum for Trinidad products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees 
Beaume paraffine petroleum naphtha distilling between 140 degrees 
and 190 degrees Fahrenheit shall be between 68 and 88 per centum. 

(8) The bitumen shall show between 8 and 17 per centum fixed 
carbon. 

(9) It shall show an open flash point not less than 375 degrees 
Fahrenheit. 

(10) It shall not contain more than 4.7 per centum paraffine scale, 
(n) It shall show a toughness at 32 degrees Fahrenheit not less 

than 5 centimeters. Toughness is determined by breaking a cylinder 
of the material if inches in diameter by if inches in height in a Page 
impact machine. (American Society of Testing Materials, August 
15, 1908.) The first drop of the hammer is from a height of 5 centi- 
meters and each succeeding blow is increased by 5 centimeters. 



BITUMINOUS MATERIAL A 385 

(12) It shall have a ductility at 77 degrees Fahrenheit of not less 
than 25 centimeters (Dow mould). 

(13) All bituminous material A. will be sampled by an Engineer 
of the Department of Highways and samples sent to the Bureau of 
Tests, Albany, N. Y. 



Item 66 — Specification for Bituminous Material A 

Penetration Method 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a 
homogeneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of 
not less than 0.97. 

(4) The penetration shall be between 14 and 19 millimeters when 
tested for 5 seconds at 77 degrees Fahrenheit with a No. 2 needle, 
weighted with 100 grams. 

(5) Fifty grams of it upon being maintained at a uniform tempera- 
ture of 325 degrees Fahrenheit for 5 hours in a cylindrical vessel 5 J 
centimeters in diameter by 3! centimeters high shall not lose more 
than 5 per centum in weight. The penetration (5 seconds, 77 degrees 
Fahrenheit, No. 2 needle, 100 grams weight) of this residue shall be 
at least 50 per centum of the original penetration. 

• (6) Its solubility at air temperature in chemically pure carbon 
disulphide for the following named materials, or materials similar 
thereto, shall be at least 99.5 per centum for pure bitumen products, 
96 per centum for Bermudez products, 81 per centum for Cuban 
products and 66 per centum for Trinidad products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees 
Beaume parafnne petroleum naphtha distilling between 140 degrees 
and 190 degrees Fahrenheit shall be between 70 and 88 per centum. 

(8) The bitumen shall show between 8 and 16 per centum fixed 
carbon. 

(9) It shall show an open flash point not less than 375 degrees 
Fahrenheit. 

(10) It shall not contain more than 4.7 per centum parafnne 
scale. 

(n) It shall show a toughness at 32 degrees Fahrenheit not less 
than 15 centimeters. Toughness is determined by breaking a 
cylinder of the material if inches in diameter by if inches in 
height, in a Page impact machine. (American Society of Testing 
Materials August 15, 1908.) The first drop of the hammer is from 
a height of 5 centimeters and each succeeding blow is increased by 5 
centimeters. 

(12) It shall have a ductility at 77 degrees Fahrenheit of not less 
than 40 centimeters (Dow mould). 

(13) All bituminous material A. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau 
of Tests, Albany, N.Y. 



386 SPECIFICATIONS 

Item 67 — Specification for Bituminous Material H. O. 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a 
homogeneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of 
not less than 0.96. 

(4) When evaporated in the open air at a temperature not exceed- 
ing 500 degrees Fahrenheit until the residue remaining has a pene- 
tration (5 seconds, 77 degrees Fahrenheit, No. 2 needle, 100 grams 
weight) of 10 millimeters the amount of such residue shall not be 
less than 85 per centum nor more than 95 per centum of the original 
oil. At a temperature of 77 degrees Fahrenheit such residue shall 
have a ductility of at least 25 centimeters (Dow mould). 

(5) Fifty grams of it upon being maintained at a uniform tempera- 
ture of 325 degrees Fahrenheit for five hours, in a cylindrical vessel 
5I centimeters in diameter by 3! centimeters high, shall not lose more 
than 10 per centum in weight. 

(6) It shall be soluble in chemically pure carbon disulphide at 
air temperature to the extent of at least 99.5 per centum. 

(7) It shall be soluble at air temperature in j6 degrees Beaume 
paraffine petroleum naphtha distilling between 140 degrees and 190 
degrees Fahrenheit to the extent of not less than 75 per centum and 
not more than 90 per centum. 

(8) It shall show between 6 and 14 per centum of fixed carbon. 

(9) It shall show an open flash point of not less than 325 degrees 
Fahrenheit. 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less 
than 20 centimeters. Toughness is determined by breaking a 
cylinder of the material 1 J inches in diameter by if inches in height in 
a Page impact machine. (American Society of Testing Materials, 
August 15, 1908.) The first drop of the hammer is from a height of 
5 centimeters and each succeeding blow is increased by 5 centimeters. 

(12) All bituminous material H. O. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau 
of Tests, Albany, N. Y. 

Item 68 — Specification for Bituminous Material C. O. 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in 
a homogeneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of 
not less than 0.93. 

(4) When evaporated in the open air at a temperature not exceed- 
ing 500 degrees Fahrenheit until the residue remaining has a pene- 
tration (5 seconds, 77 degrees Fahrenheit, No. 2 needle, 100 grams 
weight) of 10 millimeters the amount of residue shall not be less than 
50 per centum nor more than 65 per centum of the original oil. At 



BITUMINOUS MATERIAL T 387 

a temperature of 77 degrees Fahrenheit such residue shall have a 
ductility of at least 25 centimeters (Dow mould). 

(5) Fifty grams of it upon being maintained at a uniform tempera- 
ture of 325 degrees Fahrenheit for five hours, in a cylindrical vessel 
Si centimeters in diameter by 3 J centimeters high, shall not lose 
more than 30 per centum in weight. 

(6) It shall be soluble in chemically pure carbon disulphide at 
air temperature to the extent of at least 99.5 per centum. 

(7) It shall be soluble at air temperature in 76 degrees Beaume 
paraifine petroleum naphtha distilling between 140 and 190 degrees 
Fahrenheit to the extent of not less than 80 per centum and not more 
than 95 per centum. 

(8) It shall not show more than 10 per centum fixed carbon. 

(9) It shall show an open flash point of not less than 125 degrees 
Fahrenheit. 

(10) It shall not contain more than 4.0 per centum paraffine scale. 
(n) All bituminous material C. O. will be sampled by an Engineer 

of the Department of Highways, and samples sent to the Bureau 
of Tests, Albany, N. Y. 

Item 69 — Specification for Bituminous Material T 

High Carbon — Binder 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity of not less than 1.20 at 25 
degrees centigrade. 

(4) It shall contain not more than 25 per centum nor less than 12 
per centum of free carbon. 

(5) When distilled by the method of the American Society for 
Testing Materials, it shall contain no body that distills at a lower 
temperature than 170 degrees centigrade; not over 3 per centum 
shall distill below 235 degrees centigrade; not over 12 per centum 
shall distill below 270 degrees centigrade, and not over 16 per cen- 
tum shall distill below 300 degrees centigrade. The specific gravity 
of the entire distillate shall not be less than 1.03 at 25 degrees centi- 
grade. The residue from the foregoing distillation shall have a melting 
point not greater than 75 degrees centigrade ball and ring method. 

(6) It shall have a melting point of not less than 27 degrees C, 
and not more than 34 degrees C., by ball and ring method. 

(7) .All bituminous material T. will be sampled by an Engineer 
of the Department of Highways and samples sent to the Bureau of 
Tests, Albany, N. Y. 

Item 70 — Specification for Bituminous Material T 

High Carbon — Hot Application 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 



$88 SPECIFICATIONS 

(3) It shaU have a specific gravity not less than 1.19 at 25 degrees 
centigrade. 

(4) It shall contain not more than 22 per centum nor less than 10 
per centum of free carbon. 

(5) When distilled by the method of the American Society for 
Testing Materials, it shall contain no body that distills at a lower 
temperature than 170 degrees centigrade, not over 10 per centum 
shall distill below 235 degrees centigrade; not over 16 per centum 
shall distill below 270 degrees centigrade and not over 20 per cen- 
tum shall distill below 300 degrees centigrade. The specific gravity 
of the entire distillate shall not be less than 1.03 at 25 degrees centi- 
grade. The residue from the foregoing distillation shall have a melting 
point not greater than 75 degrees centigrade ball and ring method. 

(6) It shall have a float test (New York Testing Laboratory method) 
at 100 degrees centigrade between eighteen and twenty-eight seconds. 

(7) All bituminous material T. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau of 
Tests, Albany, N. Y. 

Item 71 — Specification for Bituminous Material T 

High Carbon — Cold Application 

This bituminous material shall have the following characteristics: 

(1) It shall have a specific gravity of 1.14 to 1.18 at 25 degrees 
centigrade. 

(2) It shall contain not more than 12 per centum nor less than 4 
per centum of free carbon. 

(3) When distilled by the method of the American Society for 
Testing Materials, not over 5 per centum shall distill below 170 de- 
grees centigrade; not over 18 per centum shall distill below 235 
degrees centigrade; not over 25 per centum shall distill below 270 
degrees centigrade, and not over 32 per centum shall distill below 
300 degrees centigrade. The specific gravity of the entire distillate 
shall not be less than 1.01 at 25 degrees centigrade. The residue 
from the foregoing distillation shall have a melting point not greater 
than 70 degrees centigrade ball and ring method. 

(4) The viscosity when tested by the standard Engler viscosim- 
eter shall not be more than 125 seconds at 60 degrees centigrade 
for the first 100 cubic centimeters. 

(5) All bituminous material T. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau 
of Tests, Albany, N. Y. 

Item 72 — Specification for Bituminous Material T 
Low Carbon — Binder 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity not less than 1.16 at 25 degrees 
centigrade. 



BITUMINOUS MATERIAL T 389 

(4) It shall contain not more than 5 per centum free carbon. 

(5) When distilled by the method of the American Society for 
Testing Materials, it shall contain no body that distills at a lower 
temperature than 170 degrees centigrade; not over 5 per centum 
shall distill below 235 degrees centigrade; not over 15 per cen- 
tum shall distill below 270 degrees centigrade; not over 20 per 
centum shall distill below 300 degrees centigrade. The residue from 
the foregoing distillation shall have a melting point not greater than 
75 degrees centigrade ball and ring method. 

(6) It shall have a melting point of not less than 27 degrees C, 
and not more than 34 degrees C, by ball and ring method. 

(7) All bituminous material T. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau 
of Tests, Albany, N. Y. 

Item 73 — Specification for Bituminous Material T 

Low Carbon — Hot Application 

This bituminous material shall have the following characteristics: 

(1) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity of not less than 1.14 at 25 
degrees centigrade. 

(4) It shall contain not more than 4 per centum of free carbon. 

(5) When distilled by the method of the American Society for 
Testing Materials, not over 1 per centum shall distill below 170 de- 
grees centigrade; not over 12 per centum shall distill below 235 
degrees centigrade; not over 20 per centum shall distill below 270 
degrees centigrade, and not over 25 per centum shall distill below 
300 degrees centigrade. The residue from the foregoing distillation 
shall have a melting point not greater than 75 degrees centigrade 
ball and ring method. 

(6) It shall have a float test (New York Testing Laboratory method) 
at 100 degrees centigrade between fifteen and twenty-five seconds. 

(7) All bituminous material T. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau of 
Test, Albany, N. Y. 

Item 74 — Specification for Bituminous Material T 

Low Carbon — Cold Application 

This bituminous material shall have the following characteristics: 

(1) It shall have a specific gravity of 1.10 to 1.13 at 25 degrees 
centigrade. 

(2) It shall contain not more than 2 per centum of free carbon. 

(3) When distilled by the method of the American Society for 
Testing Materials, not over 5 per centum shall distill below 1 70 de- 
grees centigrade; not over 20 per centum shall distill below 235 
degrees centigrade; not over 28 per centum shall distill below 270 
degrees centigrade, and not over 35 per centum shall distill below 
300 degrees centigrade. The residue from the foregoing distilla- 



390 SPECIFICATIONS 

tion shall have a melting point not greater than 70 degrees centigrade 
ball and ring method. 

(4) The viscosity when tested by the standard Engler viscosim- 
eter shall not be more than 125 seconds at 60 degrees centigrade 
for the first 100 cubic centimeters. 

(5) All bituminous material T. will be sampled by an Engineer 
of the Department of Highways, and samples sent to the Bureau of 
Tests, Albany, N. Y. 

BRICK 

Paving brick shall be reasonably perfect in shape — shall be free 
from marked warping or distortion, and shall be uniform in size, 
so as to fit closely together and to make a smooth pavement. All 
brick shall be homogeneous in texture and free from laminations and 
seams. All brick shall be evenly burned and thoroughly vitrified. 

Soft, brittle, cracked, or spalled brick, or brick kiln-marked to 
a height or depth of over q\ parts of an inch will be rejected. 

If brick have rounded corners, the radius shall not be greater than 
X6 part of an inch. 

Brick must have not less than two nor more than four vertical 
lugs or projections not more than i inch wide, on one side of each 
brick, the total area of all lugs being not more than 3 square inches, 
so that when laid there shall be a separation between the bricks of 
at least | inch and not more than J inch. The imprint, or name of 
the brick, or maker, if used, shall be by means of recessed and not by 
raised letters. The two ends of the brick shall have a semi-circular 
groove, with a radius of not less than J of an inch and not more than 
\ of an inch. Grooves shall be so located that when the brick are 
laid together the grooves shall match perfectly; grooves shall be 
horizontal when brick is laid in pavement. 

All brick shall not be less than 3 J* X 3!" X 8§" nor more than 
3i" X 4" X9" in size. 

All brick shall be subject to tests for abrasion and impact, for 
absorption, according to the standard methods prescribed by the 
National Brick Manufacturers' Association, as follows : 



THE RATTLER 

The machine shall be of good mechanical construction, self-con- 
tained, and shall conform to the following details of material and 
dimensions, and shall consist of barrel, frame and driving mechanism 
as herein described. 

THE BARREL 

The barrel of the machine shall be made up of the heads, head- 
liners and staves. 

The heads shall be cast with trunnions in one piece. The trunnion 
bearings shall not be less than two and one-half (2 \) inches in diam- 
eter or less than six (6) inches in length. 



BRICK RATTLER 



391 




V4/L- -j6 ••■U?h- ' i 



|J fES^§ ilBl 






S> >* 




Fig. 74 a 



392 . SPECIFICATIONS 

The heads shall not be less than three-fourths (J) inch thick nor 
more than seven-eighths (f ) inch. In outline they shall be a regular 
fourteen-sided (14) polygon inscribed in a circle twenty-eight and 
three-eighths (28I) inches in diameter. The heads shall be provided 
with flanges not less than three-fourths (}) inch thick and extending 
outward two and one-half (2 J) inches from the inside face of head 
to afford a means of fastening the staves. The flanges shall be 
slotted on the outer edge, so as to provide for two (2) three-fourths 
(f) inch bolts at each end of each stave, said slots to be thirteen- 
sixteenths (i-f) inch wide and two and three-fourths (2!) inches 
center to center. Under each section of the flanges there shall be 
a brace three-eighths (f) inch thick and extending down the outside 
of the head not less than two (2) inches. Each slot shall be provided 
with recess for bolt head, which shall act to prevent the turning of 
the same. There shall be for each head a cast-iron headliner one 
(1) inch in thickness and conforming to the outline of the head, but 
inscribed in a circle twenty-eight and one-eighth (28!) inches in 
diameter. This liner or wear plate shall be fastened to the head by 
seven (7) five-eighths (f) inch cap screws, through the head from the 
outside. These wear plates, whenever they become worn down one- 
half (J) inch below their initial surface level, at any point of their 
surface, must be replaced with new. The metal of which these wear 
plates are to be composed shall be what is known as hard machinery 
iron, and must contain not less than one (1) per cent of combined 
carbon. The faces of the polygon must be smooth and give uniform 
bearing for the staves. To secure the desired uniform bearing the 
faces of the head may be ground or machined. 

THE STAVES 

The staves shall be made of six (6) inch medium steel structural 
channels twenty- seven and one-fourth (2 7 J) inches long and weighing 
fifteen and five-tenths (15.5) pounds per lineal foot. 

The channels shall be drilled with holes thirteen-sixteenths (y|) 
inch in diameter, two (2) in each end, for bolts to fasten same to head, 
the center line of the holes being one (1) inch from either end and 
one and three-eighths (if) inches either way from the longitudinal 
center line. 

The space between the staves will be determined by the accuracy 
of the heads, but must not exceed five-sixteenths ( T \) inch. The 
interior or flat side of each channel must be protected by a lining 
or wear plate three-eighths (f ) inch thick by five and one-half (si) 
inches wide by nineteen and three-fourths (19D inches long. The 
wear plate shall consist of medium steel plate, and shall be riveted 
to the channel by three (3) one-half (J) inch rivets, one of which shall 
be on the center line both ways and the other two on the longitudinal 
center line and spaced seven (7) inches from the center each way. 
The rivet holes shall be countersunk on the face of the wear plate 
and the rivets shall be driven hot and chipped off flush with the sur- 
face of the wear plate. These wear plates shall be inspected from 
time to time, and if found loose shall be at once reriveted, but no 



THE ABRASIVE CHARGE 



393 



wear plate shall be replaced by a new one except as the whole set 
is changed. No set of wear plates shall be used for more than one 
hundred and fifty (150) tests under any circumstances. The record 
must show the date when each set of wear plates goes into service 
and the number of tests made upon each set. 

The staves when bolted to the heads shall form a barrel twenty 
(20) inches long, inside measurement, between wear plates. The 
wear plates of the staves must be so placed as to drop between the 
wear plates of the heads. These staves shall be bolted tightly to 
the heads by four (4) three-fourths (f) inch bolts, and each bolt 
shall be provided with lock nuts, and shall be inspected at not less 
frequent intervals than every fifth (5th) test and all nuts kept tight. 
A record shall be made after each such inspection, showing in what 
condition the bolts were found. 



THE FRAME AND DRIVING MECHANISM 

The barrel should be mounted on a cast-iron frame of sufficient 
strength and rigidity to support same without undue vibration. 
It should rest on a rigid foundation and be fastened to same by bolts 
at not less than four (4) points. 

It should be driven by gearing whose ratio of driver to driven 
should not be less than one (1) to four (4). The counter shaft upon 
which the driving pinion is mounted should not be less than one and 
fifteen- sixteenths (if\) inches in diameter, with bearings not less 
than six (6) inches in length and belt driven, and the pulley should 
not be less than eighteen (18) inches in diameter and six and one-half 
(6|) inches in face. A belt of six (6) inch double-strength leather, 
properly adjusted, so as to avoid unnecessary slipping, should be 
used. 

(As a part of this publication will be found a complete working 
drawing of a machine which will meet the above specifications and 
requirements.) 

THE ABRASIVE CHARGE 

(a) The abrasive charge shall consist of two sizes of cast-iron 
spheres. The larger size shall be three and seventy-five-hundredths 
(3.75) inches in diameter when new and shall weigh when new approx- 
imately seven and five- tenths (7.5) pounds (3.40 kilos) each. Ten 
shall be used. 

These shall be weighed separately after each ten (10) tests, and if 
the weight of any large shot falls to seven (7) pounds (3.175 kilos) 
it shall be discarded and a new one substituted; provided, however, 
that all of the large shot shall not be discarded and substituted by 
new ones at any single time, and that so far as possible the large 
shots shall compose a graduated series in various stages of wear. 

The smaller size spheres shall be when new one and eight hundred 
seventy-five-thousandths (1.875) inches in diameter and shall weigh 
not to exceed ninety-five-hundredths (.95) pounds (0.430 kilos) each. 
Of these spheres so many shall be used as will bring the collective 



394 SPECIFICATIONS 

weight of the large and small spheres most nearly to three hundred 
(300) pounds, provided that no small sphere shall be retained in use 
after it has been worn down so that it will pass a circular hole one 
and seventy-five-hundredths (1.75) inches in diameter, drilled in a 
cast-iron plate one-fourth (J) inch in thickness or weigh less than 
seventy-five-hundredths (.75) pounds (or .34 kilos). Further, the 
small spheres shall be tested by passing them over such an iron plate 
drilled with such holes, or shall be weighed after every ten (10) tests, 
and any which pass through or fall below specified weight, shall be 
replaced by new spheres, and provided, further, that all of the small 
spheres shall not be rejected and replaced by new ones at any one 
time, and that so far as possible the small spheres shall compose a 
graduated series in various stages of wear. At any time that any 
sphere is found to be broken or defective it shall at once be replaced. 
(b) The iron composing these spheres shall have a chemical com- 
position within the following limits: 

Combined carbon — Not less than 2.50%. 
Graphitic carbon — Not more than 0.10%. 
Silicon — Not more than 1 %. 
Manganese — Not more than 0.50%. 
Phosphorus — Not more than 0.25 %. 
Sulphur — Not more than 0.08 %. 

For each new batch of spheres used the chemical analysis must 
be furnished by the maker, or be obtained by the user, before intro- 
duction into the charge, and unless the analysis meets the above 
specifications, the batch of spheres shall be rejected. 

THE BRICK CHARGE 

The number of brick per charge shall be ten (10) for all bricks of 
the so-called " block size" whose dimensions fall between from eight 
(8) to nine (9) inches in length, three (3) and three and three-fourths 
(3D inches in breadth and three and three-fourths ($j) and four and 
one-fourth (4I) inches in thickness. No block should be selected 
for test that would be rejected by any other requirements for the 
specifications. 

The brick shall be clean and dried for at least three (3) hours in 
a temperature of one hundred (100) degrees Fahr. before testing. 

SPEED AND DURATION OF REVOLUTION 

The rattler shall be rotated at a uniform rate of not less than 
twenty-nine and one-half (29 J) nor more than thirty and one-half 
(30 J) revolutions per minute, and eighteen hundred (1,800) revolu- 
tions shall constitute the standard test. 

A counting machine shall be attached to the rattler for counting 
the revolutions. A margin of not to exceed ten (10) revolutions 
will be allowed for stopping. Only one (1) start and stop per test 
is regular and acceptable. 






RECORDS 



395 



THE RESULTS 

The loss shall be calculated in percentage of the original weight 
of the dried brick composing the charge. In weighing the rattled 
brick any piece weighing less than one (i) pound shall be rejected. 

RECORDS 

(a) The operator shall keep an official book, in which the alternate 
pages are perforated for removal. The record shall be kept in dupli- 
cate, by use of a carbon paper between the first and second sheets, 

REPORT OP 

Standard Rattler Test of Paving Bricks 

Identification Data Serial No. ( ) 

Name of the firm furnishing sample 
Name of the firm manufacturing sample 
Street or job which sample represents 
Brands or marks on the brick 
Quantity furnished 
Date received 
Length Breadth 

Standardization Data 
Number of charges tested since last inspection 



Drying treatment 
Date tested 

Thickness 



Weight of Charge 
(After Standardization', 



i of Locknuti on Staves 



Condition of Scale* 



10 Large spheres 
Small spheres 



Total 



Number of charges tested since stave linings were renewed 
Repairs (Note any repairs affecting the condition of the barrel) 

Running Data 



Time Readings 


Revolution Counter Readings 


Running Notes, Stops, Etc. 




Hours 


Minutes 


Seconds 






Beginning of test . . • 
Final Reading .... 











Weights and Calculations 



Initial Weight of 10 Bricks . 
Final Weight of Same . . 
Loss of Weight 



Percentage Loss 

(Note.— The Calculation Must Appear) 



Number of broken bricks and remarks on same 

I certify that the foregoing test was made under the specifications 
of and is a true record. 



Date 



Location of Laboratory 

Fig. 74 B 



396 SPECIFICATIONS 

and when all entries are made and calculations are completed the 
original record shall be removed and the carbon duplicate preserved 
in the book. All calculations must be made in the space left for that 
purpose in the record blank, and the actual figures must appear. 
The record must bear its serial number and be filled out completely 
for each test, and all data as to dates of inspection and weighing of 
shot and replacement of worn-out parts must be carefully entered, 
so that the records remaining in the book constitute a continuous 
one. In event of further copies of a record being needed, they may 
be furnished on separate sheets, but in no case shall the original 
carbon copy be removed from the record book. 

(b) The blank form upon which the record of all official brick tests 
is to be kept and reported is shown in Fig. 74B. 

Any brick which loses twenty-four (24) per cent or more in the 
rattler, or increases more than 3^ per cent in weight or less than § 
of 1 per cent in the absorption test, will be rejected. 

HILLSIDE BRICK 

On grades of five (5%) per cent or over the engineer may, if he 
deems advisable for the traffic, order the contractor to use special 
form of brick suitable for steep grades. 

Expansion Joint Paving Pitch. This cushion shall be composed 
of heavy pitch or asphaltum composition, having a melting point of 
not less than 120 F. nor more than 140 F., filling the allotted space. 

PREMOLDED EXPANSION JOINT 

The expansion joints shall be composed of a high grade asphalt, 
that shall pass the following tests: 

Specific gravity at 77 F., .98 to 1.05. 
Melting point, ball and ring method, 220 to 250 F. 
Loss on heating for 5 hours at 325 F., not over 1 %. 
Bitumen soluble in carbon disulphide, at least 98.5 %. 
Bitumen soluble in carbon tetrachloride, at least 99.8%. 
Bitumen soluble in 76 Beaume naphtha, 50 to 75 %. 
Penetration at 32 F. 200 grams, 1 min., at least 12. 
Penetration at 77 F. 100 grams. 5 sec. between 15 and 35. 
Penetration at 115 F. 50 grams, 5 sec. not more than 45. 

BLOCK STONE PAVEMENT 

(City of Rochester, N. Y., Specifications, 191 i) 

Paving blocks shall consist of the best quality of Medina sand- 
stone free from quarry checks or cracks, and shall be quarried from 
fine-grain live rock, showing a straight and even fracture. The 
material shall be of uniform quality and texture, free from seams or 
lines of clay or other substances which, in the opinion of the City 
Engineer, will be injurious to its use as paving material. 






SECOND QUALITY BLOCKS 397 

Blocks shall measure not less than three (3) nor more than six 
(6) inches thick, and not less than six (6) nor more than six and one- 
half (6i) inches deep, and from seven (7) to twelve (12) inches in 
length. Stones to have parallel sides and ends, and right-angle 
joints. All roughness in joints of stone to be broken off, so that 
when set in place they shall have tight joints for a distance of at 
least two and one-half .(2 J) inches from the top down. The top to 
have a smooth even surface, with no projection or depression exceed- 
ing one-quarter (J) inch. 

When approved by the City Engineer, paving blocks of the fol- 
lowing dimensions may be used. 

Three to five inches in width; five inches in depth, with an allowable 
variation of one-quarter inch, more or less, in said depth, and seven 
to twelve inches in length. 

Paving blocks as here referred to shall be understood to mean 
blocks of Medina sandstone, prepared in the usual manner for 
dressed block paving by nicking and breaking the stone from larger 
blocks, as is done at the quarries where such blocks are usually 
prepared, and not made by re-dressing or selecting from common 
stone paving material. 

The stones will be carefully inspected after they are brought on the 
line of the work, and the blocks which, in quality and dimensions, 
do not conform strictly to these specifications, will be rejected and 
must be immediately removed from the line of the work. The con- 
tractor will be required to furnish such laborers as may be necessary 
to aid the inspector in the examination and the culling of the blocks. 

The stones brought upon the ground having been carefully and 
thoroughly inspected, as provided for herein, and all rejected stones 
removed from the line of the work, the contractor will then be re- 
quired to pile such stone as may have been approved, neatly, on the 
front of the sidewalk, and not within three (3) feet of any fire hydrant, 
and in such manner as will preserve sufficient passageway, on the 
line of the sidewalks, and also permit of free access from the roadway 
to each entrance on the line of the street. 

SECOND QUALITY BLOCKS 

(the following not in any specifications) 

Second quality block, known as pavers, are practically the same 
material as the first quality block, the only difference being a greater 
range of size and a less careful top and joint finish. They cost So . 50 
per square yard less. These pavers can be furnished under a speci- 
fication allowing the following range of size and joint width : 

(City of Cleveland Specifications) 

"Common paving stones shall consist of the best quality of Medina 
sandstone, and shall be not less than three (3) nor more than five 
(5) inches thick, and not less than seven (7) nor more than eight 
(8) inches deep, and from eight (8) to thirteen (13) inches long. The 
stones to have parallel sides and ends, with right-angle joints, all 



398 SPECIFICATIONS 

roughness and points of stone to be broken off so that when set in 
place they shall have tight joints for a distance of at least three inches 
from the top; the area of the bottom of any stone to be not less than 
three-quarters (f ) of the area of the top, the top of all stones to have 
a smooth even surface." 

CAST-IRON PIPE 

Cast-iron pipe shall be light weight and may be second quality, 
but it shall be free from all defects impairing its strength. The 
iron must be of good quality, uniform in thickness and of full strength, 
and the pipe shall be coated with coal pitch varnish mixed with lin- 
seed oil to form a firm, tough coating. The joint shall be formed by 
calking into the hub a gasket of jute or oakum and then filling with 
mortar formed of equal parts of Portland Cement and clean sharp 
sand. 

MESH REINFORCEMENT 

Mesh reinforcement shall be placed where called for on the plans 
or ordered by the engineer. It shall be of medium steel. 

If expanded metal is used it shall conform to the above require- 
ments, and the weight per square foot shall be as shown on the stand- 
ard structure sheet, and any reinforcement shall be of a character 
that it will distribute the loads evenly. 

DEFORMED BARS 

Deformed bars shall be placed where called for on the plans or 
ordered by the engineer. They shall be of medium steel and shall 
have a deformed cross-section, that is, the various cross-sections 
must be of different shape or their centers must not lie in the same 
axis. 

CAST IRON 

Cast iron shall be of full standard pattern for shapes or forms 
used, according to drawings or detailed specifications. All cast 
iron shall be of good gray iron, free from blows, sand holes, or other 
defects, and shall have a tensile strength of not less than 17,000 
pounds per square inch of section. 

WROUGHT IRON 

Wrought iron shall be tough, fibrous, and uniform in quality and 
shall be manufactured by approved methods. Steel scrap shall not 
be used in its manufacture. Finished material shall be clean, 
smooth, straight, true to shape, of workmanlike finish and free from 
defects. 

Test pieces cut from finished material shall show an ultimate 
tensile strength of not less than 48,000 pounds per square inch, an 
elastic limit of not less than 25,000 pounds per square inch, and an 
elongation of not less than 20 per cent in 8 inches. 



STEEL 399 

Wrought-iron test pieces cut from finished material when cold, 
or when heated to a bright, cherry-red, shall endure bending 180 
degrees around a circle whose diameter is equal to twice the thickness 
of the test piece, without signs of cracking. Test pieces when nicked 
and broken shall show a fracture not less than 90 per cent fibrous, 
free from coarse, crystalline spots. 

Wrought iron when welded shall not show signs of red shortness. 

STEEL 

(1) Steel, except as otherwise provided by these specifications, 
shall be made by the acid or basic open-hearth process and shall be 
uniform in character; finished material shall be clean, smooth, 
straight, true to shape, of workmanlike finish, and free from defects. 

(2) Fractures must show a uniform fine grain of a blue, steel-gray 
color entirely free from a fiery luster or a blackish cast. 

(3) No work shall be put upon any steel at or near the blue tem- 
perature or between the temperature of boiling water and of the 
ignition of hardwood sawdust. 

(4) No sharp or unfilleted corners will be allowed in any piece of 
metal. 

(5) Annealing. Crimped stiffeners and buckled plates need not 
be annealed. All other steel that has been bent cold or partially 
heated and all forgings must be wholly annealed; exception may be 
made in unimportant cases and then only upon written permission 
from the Commission. 

(6) Tests of steel that is to be annealed shall be made after anneal- 
ing, or strips cut from such steel shall be annealed at the same time, 
before testing. 

(7) Tests of Medium Steel. Test pieces cut from finished 
material shall show an ultimate strength of not less than sixty thou- 
sand (60,000) pounds per square inch and not more than sixty-eight 
thousand' (68,000) pounds per square inch, an elastic limit of not 
less than thirty-five thousand (35,000) pounds per square inch, an 
elongation of not less than twenty-two (22) per cent in eight (8) 
inches, and a reduction of area at the fracture of not less than forty 
(40) per cent. 

(8) Medium steel shall not contain more than five one-hundredths 
(5-100) of one per cent of sulphur. 

(9) Acid steel shall not contain more than eight one-hundredths 
(8-100) of one per cent, and basic steel shall not contain more than 
four one-hundredths (4-100) of one per cent of phosphorus. 

(10) Medium steel shall endure bending cold or after quenching 
from a red heat in water at 8o° F., 180 around a circle whose di- 
ameter is equal to the thickness of the test piece, without signs of 
cracking. 

(11) Tests for Soft Steel. Test pieces cut from finished 
material shall show an ultimate strength of not less than fifty thou- 
sand (50,000) pounds per square inch and not more than fifty-eight 
thousand (58,000) pounds per square inch, an elastic limit of not less 
than thirty thousand (30,000) pounds per square inch, an elongation 



400 SPECIFICATIONS 

of not less than twenty-eight per cent in eight inches, and a reduction 
in area at the fracture of not less than fifty (50) per cent. 

(12) Soft steel shall not contain more than four one-hundredths 
(4-100) of one per cent of sulphur. 

(13) Acid steel shall not contain more than six one-hundredths 
(6-100) of one per cent, and basic steel shall not contain more than 
four one-hundredths (4-100) of one per cent of phosphorus. 

(14) Soft steel shall endure bending flat upon itself without signs 
of cracking, when cold, or after quenching, from a red heat, in water 
at eighty (80) degrees F. 

VITRIFIED PIPE 

Vitrified pipe shall be double strength salt-glazed vitrified stone- 
ware sewer pipe of the first quality. The item will include the fur- 
nishing, delivering, handling, laying, and cementing of joints; also 
the operations of excavating the trench, bracing, sheeting, or other- 
wise supporting the sides, grading and preparing the bottom, back- 
filling and compacting to the original surface, and the removal of 
all surplus material. 

POROUS TILE 

Where called for on the plans, or ordered by the engineer, porous 
tile shall be laid true to line and grade, and firmly bedded in clean 
cinders, gravel, or crushed stone. The tile must be whole and free 
from cracks and other defects, and must be satisfactory to the 
engineer. 

TIMBER 

(Washington State Specifications) 

Quality of Timber and Plank. All timber and plank in cul- 
verts, trestlework, bridge abutments, and pile bridges shall be of 
good quality, of such kinds as the highway commissioner may direct, 
free from shakes, wanes, black and unsound knots, and all descrip- 
tions of decay, and shall be measured by the thousand feet, board 
measure; the price shall be understood to cover the expense of all 
labor (including all necessary digging and filling at the ends of bridges 
where grading is done before bridges are put in) and materials, pins, 
or treenails required in the performance of the work. 

All timber structures shall be built in conformity with plans to 
be furnished by the engineer. 

Piles and Pile-driving. Piles, whether used in foundations, 
trestlework, or pile bridges, shall be of good, sound quality of such 
timber as the Highway Commissioner may accept, not less than 
ten inches in diameter at the smaller end and of such lengths as the 
engineer may require. They shall be measured by the lineal foot 
after they are driven and cut off to receive the superstructure, and 
the price per lineal foot shall be understood to cover the expense of 
driving, cutting off, removing the bark from the part above the 
ground, and all other labor and material required in the performance 






EXCAVATION 401 

of the work; but that portion of each pile cut off shall be estimated 
and paid for by the lineal foot as " piling cut off." Piles shall be 
driven of such lengths and to such depths as the engineer may re- 
quire. All piles shall be capped during the driving to prevent 
brooming. 

CLEARING AND GRUBBING 

Clearing. The right-of-way must be cleared to the width of 
feet on each side of the center line, or as shall be designated 



by the engineer; all trees, brush, and other vegetable matter within 
the space designated to be cut down, and the same, together with 
all other logs, brushwood, and fences already down, shall be burned 
or removed from the grounds, as the engineer may direct, so as not 
to injure the adjoining lands or to obstruct the line of the fences 
along the boundaries of the said right-of-way. When the embank- 
ments exceed two feet in height it will be required to cut the trees, 
brush, and stumps close to the ground. 

Light clearing shall include the removal of all standing trees of 
a size up to one foot in diameter, together with all other logs, brush, 
and other vegetable matter already down or lying loose on the ground. 

Heavy clearing shall include the removal of all standing trees 
over one foot in diameter, together with all other logs, brush, and 
other vegetable matter already down or lying loose on the ground. 

Grubbing. From the space required for the roadbed and neces- 
sary slopes and side drains, and whatever additional space may be 
required by the engineer, except where the excavations are three 
feet or more in depth, or embankments two feet or more in height, 
all stumps and other wood or vegetable matter embedded in the 
ground shall be grubbed up, and removed or disposed of as the 
engineer may direct, and only the area so grubbed shall be estimated. 



EXCAVATION 

Under the head of excavation shall be included all excavations 
required for the formation of the road-bed, the digging of all ditches, 
cutting new channels for streams, preparing foundations, the altering 
of all highway or private roads and all excavations in any way con- 
nected with or incidental to the construction of the road, and the 
expense of hauling and depositing same in embankments wherever 
required. 

Embankments. Under the head of embankments shall be included 
all embankments for any of the purposes mentioned not formed from 
excavations taken from the prism of the road or other necessary 
excavations. 

All grading shall be done and estimated by the cubic yard, meas- 
ured in the excavation, except material borrowed for embankment, 
which shall be measured in embankment, and shall be comprised 
under heads, viz.: 

Earth, Hard-pan, Loose Rock, Solid Rock, Shell Rock, and Solid 
Rock Borrow. 



402 SPECIFICATIONS 

Earth. Earth will include clay, sand, loam, gravel, and all hard 
material that can, in the opinion of the chief engineer, be reasonably 
plowed, and all earthy matter or earth containing loose stones or 
boulders intermixed, and all other material that does not come under 
the classification of hard-pan, loose rock, solid rock, shell rock, and 
solid rock borrow. 

Hard-pan. Hard-pan will include material, not loose or solid rock, 
that cannot, in the opinion of the chief engineer, be reasonably 
plowed on account of its own inherent hardness. 

Loose Rock. Loose rock will include all stone and detached rock, 
found in separate masses, containing not less than one cubic foot, nor 
more than one-half cubic yard, and all slate or other rock, soft or 
loose enough to be removed without blasting, although blasting 
may occasionally be resorted to. 

Solid Rock. Solid rock will include all rock in place, and boulders 
measuring one-half cubic yard and upwards, in removing which it 
is necessary to resort to drilling and blasting. 

Shell-Rock Excavation. Shell-rock excavation will include all 
deposits composed entirely of rock in masses of less than one cubic 
foot which have broken off from the cliffs above the roadbed, but 
will only be estimated when in large deposits. 

Solid Rock Borrow. Solid rock borrow shall consist of solid 
rock, according to above classification, excavated outside of the 
regular cross-sections of the cuts for the roadbed, and placed and 
measured in embankment. 

EXCAVATION 

Item 2 — Earth Excavation 
Item 3 — Rock Excavation 

2.1. Under these items the Contractor shall grade the entire 
length of roadway, ditches and side slopes to the required lines and 
grades; shall make all excavations for culverts, under-drains, catch 
basins, leaching basins, and other structures except posts; shall 
grade connecting public highways as directed and remove spongy 
material from the sub-grade to the depths required — all as shown 
on the plans or as directed by the Engineer. 

This item includes the excavation, filling and rolling necessary 
to complete the road and all structures connected therewith except 
as noted above, and includes the removal of all objectionable material 
for the full width of the improvement except as noted under section 
1.1, and the filling to the required grade with acceptable material 
of all areas originally below the required grade, or excavated below 
grade under orders of the Engineer. 

Backfill for structures, old macadam excavated, and sod ordered 
removed from the site of a new embankment, shall be paid for as 
Earth Excavation. 

2.2. All suitable materials from the excavation shall be used so 
far as practicable in making embankments, building up low places 
on the sub-grade or shoulders, and such other places as directed. 



EXCAVATION 403 

2.3. Surplus material shall be placed in embankments, shall be 
used for extending the shoulders or shall be deposited in spoil banks, 
as directed by the engineer. All surplus materials shall be removed 
and disposed of as directed by the Engineer before the sub-grade 
or shoulder rolling is completed and beofre any stone is placed on 
the roadway. 

2.4. If there is not sufficient suitable material to complete the 
grading and to bring the sub-grade to the required height, the con- 
tractor shall borrow additional material from the sides of the roadway 
or from other borrow pits as directed by the engineer so that the estab- 
lished grade for the road, embankments, etc. will be secured. All 
borrow pits outside the highway shall be acquired by the Contractor 
at his own expense, and any borrow pits in or adjacent to the high- 
way shall be left in a neat and satisfactory condition and shall be 
thoroughly drained. 

2.5. The contractor shall remove boulders and all muck, quick- 
sand, soft clay and spongy material which will not consolidate under 
the roller, from the sub-grade to a depth to be determined by the 
engineer, and refill the space with acceptable materials from the 
excavations, or with stone or gravel, as directed. If stone or gravel 
is used, the same will be paid for at the contract price bid for item 
" Foundation Course." After all drains have been laid and the 
surface of the sub-grade has been properly shaped, it shall be thor- 
oughly rolled and compacted with an approved self-propelled roller 
weighing not less than 10 tons. Water puddling shall be resorted 
to in case the soil requires it. Care shall be taken not to roll clay 
foundations too much, thus developing a plastic condition. All 
hollows and depressions which develop shall be rilled with acceptable 
material, and the sub-grade shall again be rolled. This process of 
filling and rolling shall be repeated until no depressions develop. In 
places where the character of the material makes the use of such a 
roller impracticable, a lighter one may be permitted. The sub- 
grade shall not be muddy, or otherwise unsatisfactory when the 
foundation course is placed upon it. All culverts, ditches, and drains 
shall be satisfactorily completed to effectively drain the highway 
before the placing of any pavement will be permitted. The shoulders 
shall be rolled and left in a compact and satisfactory condition at 
the completion of the pavement. 

2.6. Embankment shall be formed of suitable materials. If 
formed of stone, all reasonable precautions must be taken to ensure 
a solid embankment. The upper surface of the embankment shall 
be rolled and left in a satisfactory condition and approximately true 
to lines and grades. Large stone shall not project within 6 inches 
of the finished sub-grade, and all hollows and depressions shall be 
filled with the smaller stone from the excavation, with gravel or with 
other acceptable material. Stone in embankments shall not be used 
nearer than 6 inches to the surface of shoulders. 

Where the filling is less than 2 feet in depth all vegetable matter 
shall be removed from the original surface. Where necessitated 
by the existing slope, the original surface shall be trenched or other- 
wise broken up before placing new embankment thereon. 



404 SPECIFICATIONS 

Embankment shall be constructed in successive horizontal layers 
not exceeding 12 inches in thickness; when concrete is to be placed 
thereon, these layers shall not exceed 6 inches in thickness. Each 
layer shall extend across the entire fill and shall be thoroughly rolled 
and compacted by approved methods. If impracticable to use a 
heavy roller for this work a grooved roller shall be used. 

2.7. At all intersecting public highways the contractor shall grade 
back to a sufficient distance with acceptable materials, as directed 
by the engineer so that a smooth riding and satisfactory junction 
will be produced. 

2.8. The quantity of excavation to be paid for under items 2 and 
3 shall be the number of cubic yards of material, measured in its 
original position, excavated and disposed of as directed by the En- 
gineer, and the limits shall not exceed those shown upon the plans or 
fixed by the Engineer. 

The price bid for Earth Excavation shall include the removal 
of all materials, as specified under section 2.1 — except as provided 
below for "Rock Excavation," — the placing of same in embank- 
ment or spoil, the rolling, compacting, grading and all other work 
incidental thereto. 

No direct payment shall be made under Items 2 or 3 for work in 
connection with contractor's plant, nor for his other requirements 
in carrying out the provisions of this contract, but compensation 
therefor shall be considered as having been included in the prices 
stipulated for the various items of the contract. 

The price bid for Item 3 shall include the removal of all boulders 
of more than 13 cubic feet and all hard ledge rock and the placing of 
same in embankment or spoil if not used under other items of the 
contract, and rolling, compacting, grading and all other work inci- 
dental thereto. Boulders of less than 13 cubic feet, and all soft or 
disintegrated rock which can be removed with pick and shovel, shall 
not be paid for under Rock Excavation, but under "Earth Excava- 
tion." The price bid for the Items shall include all labor, materials, 
supplies, and plant and incidentals necessary to complete the work. 

Item 4 — Overhaul 

4.1. If the haul on any material either from cuts or borrow pits 
made in accordance with directions from the Engineer exceeds 2,000 
feet it shall be classified as overhaul. 

For each 100 feet of haul greater than 2,000 feet the Contractor 
shall receive the price bid for Overhaul per cubic yard of all material 
so moved, measured in its original position. 

The price bid shall include all labor, appliances, and incidentals 
necessary to complete the work. 

Item 5 — Vitrified Clay Pipe 

5.1. Under this item the Contractor shall furnish and place vitri- 
fied pipe where directed by the Engineer. 

5.2. Pipe shall be first quality, double strength, salt glazed, sound, 
vitrified, stoneware sewer pipe with bell joints. 



CONCRETE LEACHING BASINS 405 

5.3. All pipe shall be laid true to line and grade with bells up- 
stream, and shall have a full, firm and even bearing. The joints 
shall be filled with jute and mortar consisting of one part Portland 
cement and two parts sand. 

5.4. The quantity to be paid for under this item shall be the number 
of linear feet of pipe incorporated in the work under the directions 
and to the satisfaction of the Engineer. 

The price bid shall include the furnishing and laying and all mate- 
rials and incidentals necessary thereto, except that all excavation in 
connection therewith will be paid for under item " Excavation. " 

Item 6 — Vitrified Clay Underdrains 

6.1. Under this item the Contractor shall furnish and lay 6-inch 
salt glazed vitrified pipe wherever required for drainage. 

6.2. The pipe shall be laid true to line and grade with the bells 
up grade. A strap of burlap at least 6 inches wide and long enough 
to reach around the pipe and lap at least 1 foot shall be wrapped 
around each joint of pipe to give double thickness on the top and to 
act as a strainer. The pipe shall be covered as laid with clean gravel 
or broken stone of No. 2 or No. 3 size placed around and above it to 
the surface of the sub-grade. 

6.3. The amount to be paid for under this item shall be the number 
of linear feet of pipe furnished and incorporated in the work. 

The price bid shall include all labor, materials, and incidentals 
necessary to complete the work, except that the necessary excava- 
tion will be paid for under item " Excavation," and the necessary 
broken stone will be paid for under item "Broken Stone, Loose 
Measurement." 

Item 7 — Porous Tile Underdrain 

7.1. Under this item the Contractor shall furnish and lay 6-inch 
porous tile wherever required for drainage. 

7.2. The tile must be whole and free from cracks and other defects, 
and must be satisfactory to the Engineer. 

7.3. The tile shall be laid true to line and grade and shall be covered 
as laid with clean gravel or broken stone placed around and above 
it to the surface of the sub-grade. 

7.4. The amount to be paid for under this item shall be the number 
of linear feet of pipe furnished and incorporated in the work. 

The price bid shall include all labor, materials, and incidentals 
necessary to complete the work, except that the necessary excava- 
tion will be paid for under item "Excavation," and the necessary 
broken stone will be paid for under item "Broken Stone, Loose 
Measurement." 

Item 8 — Concrete Leaching Basins 

8.1. Under this item the Contractor shall build at places indicated 
on the plan or ordered by the Engineer, concrete leaching basins of a 
type shown on the detail plans. 



406 SPECIFICATIONS 

8.2. The concrete used in these basins shall be second-class con- 
crete. 

8.3. The grating shall be of cast iron of the quality specified in 
item "Miscellaneous Iron and Steel." 

8.4. For each basin completed, the Contractor shall receive the 
price bid. 

The price bid shall include all concrete, stone, grating, and all 
material, labor and incidentals necessary to complete the work, 
except that the excavation will be paid for under item "Excavation." 

Item 9 — Vitrified Leaching Basins 

9.1. Under this item the Contractor shall build at places indicated 
on the plans or ordered by the Engineer, leaching basins of a type 
shown on the detail plans. 

9.2. Vitrified pipe shall be of double thickness, sound, and thor- 
oughly tamped in place. 

9.3. The broken stone used for filling shall be No. 4 broken stone 
or gravel. 

9.4. The grating shall be of cast iron of the quality specified in 
item "Miscellaneous Iron and Steel." 

9.5. For each basin completed in accordance with plans and 
under orders of the Engineer, the Contractor shall receive the price 
bid. 

The price bid shall include all materials, labor and appliances, and 
all expenses incidental to completing the work, except the excava- 
tion — which last will be paid for under item "Excavation." 

Item 10 — Catch Basins 

10. 1. Under this item the Contractor shall build catch basins 
as shown on the plans, as directed by the Engineer. 

10.2. The catch basins may be built of second-class concrete or 
of acceptable brick at the option of the Contractor. If bricks are 
used they shall be sound, hard burned brick of acceptable quality, 
and shall be laid by a competent mason and in a workmanlike manner. 
Mortar of one part Portland cement and two parts sand shall be 
used. 

10.3. For each catch basin complete with cast iron top, as shown 
on plans and ordered by the Engineer, the Contractor shall receive 
the price bid. 

The price bid shall include all labor, materials and incidentals 
required to complete each basin, except that the excavation will be 
paid for under item " Excavation." 

drop inlets 

Drop inlets shall be constructed where shown upon the plans, or 
directed by the Engineer. The details of construction shall be such 
as he may direct. 

Payment for drop inlets will be made under appropriate items at 
the contract price for the materials entering into their construction; 
that is, payment will be made , for the various amounts of excava- 



RELAYING OLD PIPE 407 

tion, concrete, cast iron, cast-iron pipe, etc. Payment under these 
items shall include all labor and materials necessary to complete the 
work. 

Item 11 — Changing Elevation of Manholes and Catch Basins 

1 1. 1. Under this item the Contractor shall raise or lower to the 
grades given all existing covers of catch basins or manholes. 

1 1.2. All changes shall be made with acceptable brick laid in 
Portland cement mortar of one part cement and two parts sand. 

All work shall be done in a workmanlike manner by competent 
masons. 

1 1.3. For each manhole or catch basin raised or lowered as directed 
by the Engineer, the Contractor shall receive the unit price bid. 

The price bid shall include all labor, materials and incidentals 
necessary to complete the work. If any manhole or catch basin 
heads or covers are broken through carelessness on the part of the 
Contractor, they shall be replaced at his expense. 

Item 12 — Cast-iron Pipe 

1 2. 1. Under this item the Contractor shall furnish and place 
cast-iron pipe as directed for culverts, drains and other necessary 
uses, and of the sizes and weights ordered. 

12.2. Pipe shall be of class A unless otherwise called for by the 
plans or ordered in writing by the Division Engineer, and may be 
second^ quality; but it shall be free from all defects impairing its 
strength or utility. The iron must be of good quality, uniform in 
thickness and of full strength. The pipe shall be coated with coal- 
pitch varnish mixed with linseed oil to form a firm, tough coating. 
Joints shall be formed by caulking into the hubs a gasket of jute or 
oakum and then rilling with mortar composed of equal parts of Port- 
land cement and clean, sharp sand. It shall be laid true to line and 
grade and shall have a full, firm, even bearing. 

12.3. The number of tons of cast-iron pipe to be paid for under 
this item shall be the actual weight in place in the work as directed 
by the Engineer when of class A, or an equal weight when of heavier 
class; except that when a heavier weight is used under written order 
of the Division Engineer, such weight shall be paid for. 

The price bid shall include the furnishing, delivering, handling, 
laying, cutting and all work and materials necessary to complete 
the work. 

Item 13 — Relaying Old Pipe 

1 3. 1. Under this item the Contractor shall as directed carefully 
remove, preserve and relay old pipe found in existing culverts. 

13.2. The old pipe when relaid shall be true to line and grade 
and have a full, firm, even bearing, and the work shall be in every way 
the same as if new pipe were being laid. 

13.3. Any old pipe in good condition which is damaged in removing, 
due to the carelessness of the Contractor, shall be replaced with new 
pipe at the Contractor's expense. 



408 SPECIFICATIONS 

Any old pipe which is, in the Engineer's judgment, unfit for relay- 
ing may be destroyed before removing. 

13.4. The amount to be paid for under this item shall be the number 
of linear feet incorporated in the work. New pipe furnished to re- 
place old pipe which is destroyed through the carelessness of the 
Contractor shall be paid for as if the old pipe had been preserved and 
relaid. 

The price bid shall include all labor, materials and incidentals 
necessary to complete the work, except that the excavation neces- 
sary will be paid for under the item " Excavation." 

Item 14 — Stone Filling 

14. 1. Under this item the Contractor shall furnish and place 
acceptable stone of either quarry, field or cobble stone for filling 
crib work, and similar work as required. 

14.2. Stone filling shall be of acceptable quarry, field or cobble 
stone. The larger stones shall be properly embedded at the bottom 
of the fill; all stones shall be so placed as to make a fill of maximum 
stability. 

14.3. The quantity to be paid for under this item shall be the 
number of cubic yards measured in its final position and incorporated 
in the work as directed by the Engineer. The price stipulated shall 
include the cost of obtaining the stone, placing, and all materials 
and expenses incidental thereto. 

Item 15 — Piles 

1 5. 1. Under this item the Contractor shall furnish and drive 
piles of acceptable material and lengths for foundations, revetment 
and elsewhere as required. 

15.2. Piles shall be furnished to fit the localities. The Contractor 
shall, when required, drive preliminary test piles, each of which will 
be paid for at the contract price therefor. After the test piles are 
driven a statement will be furnished the Contractor by the Engineer, 
showing for the information of the Contractor the probable number 
of piles of the different kinds required, grouped between certain 
lengths in feet. 

15.3. Piles, shall be driven by hammer or combination of hammer 
and water jet methods, and the driving shall be satisfactory to the 
Engineer in every case. In driving piles the heads shall be protected 
from injury by a cap or shall be banded if required. The fall of the 
hammer shall not exceed 20 feet, and shall be regulated so as not to 
injure or shatter the pile. Driving shall continue until £he penetra- 
tion and bearing values are satisfactory to the Engineer. 

15.4. The tops of all piles shall be sawed level and true to the ele- 
vation fixed by the Engineer. 

15.5. Broken, split or misplaced piles shall be drawn and properly 
replaced. Piles driven below the grade fixed by the Engineer shall 
be drawn and replaced by new, and if necessary, longer, piles. No 
payment will be made for driving or withdrawing piles so injured or 
misplaced. 



RIP-RAP 409 

15.6. The number of linear feet paid for under this item shall be 
the total length of piles driven in accordance with plans or orders of 
the Engineer. 

The price bid shall include the furnishing and delivering upon the 
work, the peeling, banding, tenoning, framing, driving, painting 
and all other labor and incidentals necessary to complete the work. 

Item 16 — Timber and Lumber 

16. 1. Under this item the Contractor shall furnish timber and 
lumber of various sizes as may be ordered for sills or platforms 
beneath the road, for culverts, bridges, reinforcing existing struc- 
tures and for other similar purposes as ordered by the Engineer. 

16.2. Timber and lumber shall be of short leaf yellow pine or 
spruce or other acceptable kind, sound, square-edged, free from shakes, 
loose knots or decay, and shall be planed, and tongued-and- 
grooved if required. 

16.3. No payments will be made under this item for timber or 
lumber for forms, moulds, or centers, for sheeting or bracing, scaffolds, 
fences, guard rails or any part of the contractor's temporary bridges, 
roads, or plant; but payment for timber and lumber used in the 
above cases shall be included under the appropriate items covering 
the same. 

16.4. The quantity of timber and lumber to be paid for shall be 
the number of thousand feet, board measure, actually placed in 
accordance with orders of the Engineer. If any round timber is 
used it shall be estimated as square timber of the largest size, omit- 
ting fractions of an inch, which can be inscribed in the small end of 
the log. 

Xo second hand timber shall be used except with the approval 
of the Engineer. The price bid shall include all bolts, spikes and 
other fastenings and all other material expenses incidental to fur- 
nishing, framing and placing the timber and lumber satisfactorily. 

Item 17 — Rip-Rap 

1 7. 1. Under this item the Contractor shall furnish and place rip- 
rap for slope protection where shown upon the plans or ordered by 
the Engineer. 

17.2. Rip-rap shall consist of field stone or rough, unhewn quarry 
stones as nearly cubical in form as is practicable, placed upon a slope 
not steeper than the angle of repose, and so laid that the weight of 
the large stones is carried by the soil and not by the stones adjacent. 
Fifty per centum of the mass shall be large stones of two cubic feet 
or more. The largest stones shall be placed first, roughly arranged 
and in close contact; the stones shall rest upon a 6-inch bed of 
stone chips or gravel or other acceptable porous material, where 
ordered by the Engineer. The spaces between the larger stones 
shall be filled with spalls of suitable size. 

17.3. The quantity of rip-rap to be paid for under this item shall 
be the number of cubic yards placed in accordance with the plans 
or as directed by the Engineer. When a porous bed is placed in 



410 SPECIFICATIONS 

accordance with the directions of the Engineer, the quantity of the 
same shall be included in the quantity of rip-rap and paid for as such. 
The price bid shall include all labor, materials and incidental 
expenses necessary to satisfactorily complete the work. 



CONCRETE MASONRY 

Item 18 — First-Class Concrete 

Item 19 — Second-Class Concrete 

Item 20 — Third-Class Concrete 

18. 1. Under Items 18, 19 and 20 the Contractor shall place con- 
crete of the class indicated on the plans or ordered by the Engineer, 
for culverts, abutments, wing walls and in other structures as directed 
by the Engineer. 

This item shall not include concrete used in curbs, catch-basins, 
edging, sign posts, guard railing, resetting old curb, concrete pave- 
ment foundations or " Concrete Pavements" or in other structures 
for which there is a contract item, unless it is specifically stated under 
that item that such shall be. the case. All concrete placed in the 
work, whether included under Items 18, 19, or 20 or under other items, 
shall conform to the requirements for concrete of the class specified. 

18.2. Concrete shall consist of approved Portland cement, a fine 
aggregate of sand, and a coarse aggregate of broken stone or gravel, 
mixed in the proportions specified for the various classes given below. 
Samples of all these ingredients shall be submitted to and approved 
by the Bureau of Tests, and shall be acceptable to the Engineer before 
being used in the work. 

18.3. Concrete will be classified as follows: 

First-class concrete shall be made of one part Portland cement, 
two parts of No. 1 or No. 2 sand (see page 374) and four parts of 
coarse aggregate. 

Second-class concrete shall be made of one part Portland cement, 
two and one-half parts of No. 2 or No. 3 sand, and five parts of coarse 
aggregate. 

Third-class concrete shall be made of one part of Portland cement, 
three parts of No. 3 sand, and six parts of coarse aggregate. 

Cement, fine and coarse aggregate shall be proportioned by loose 
volumes. For this purpose one bag of cement shall be considered 
as T 9 o 5 o of a cubic foot. The fine and coarse aggregate shall be meas- 
ured separately. 

PORTLAND CEMENT 

18.4. All the cement used in the work shall conform to the require- 
ments given under "Materials of Construction," pages 372-374; 
it shall be subject to rigid inspection, shall be sampled by the Engineer 
at once on delivery, and shall conform to the prescribed tests made 
at the testing laboratories of the Bureau of Tests. All cement which 
is rejected because of failure to stand the required tests shall be imme- 
diately removed at the expense of the contractor. 



CONCRETE 411 

18.5. Cement barrels shall contain 376 pounds of Portland cement. 
Each bag of Portland cement shall contain 94 pounds net. 

18.6. Provision shall be made by the Contractor for storing cement 
in a dry place. 

FINE AGGREGATE 

18.7. Fine aggregate shall conform in all respects to the require- 
ments given under " Materials of Construction," page 374. Sand 
which contains foreign matter shall be satisfactorily washed before 
using. Screenings shall not be used except when they have been 
submitted by the Division Engineer to the Bureau of Tests, have 
been accepted by the Bureau of Tests, and their use has been approved 
by the First Deputy Commissioner in writing, and then only under 
the restrictions laid down under "Materials of Construction," 
page 375. 

COARSE AGGREGATE 

18.8. Coarse aggregate shall conform in all respects to the require- 
ments given under "Materials of Construction," page 375. 
Materials which contain foreign matter shall be satisfactorily washed 
before using. 

MIXING, DEPOSITING AND FINISHING CONCRETE 

18.9. Approved batch mixers shall be used in all cases where 
required by the Engineer. No continuous mixer shall «be used. 
Mixing shall continue through at least twelve revolutions of the 
mixer, and until every face of every, particle of stone of gravel is 
completely coated with mortar. In all machine mixing the batches 
of concrete shall be proportioned to the size of the mixer to produce 
the best results, 

18.10. If hand mixing is permitted the following method shall be 
used: 

The sand and cement shall be thoroughly mixed dry and made 
into a thin mortar. After the mortar has been brought to the proper 
consistency, the broken stone or gravel, having been just previously 
drenched with water, shall be added, and the whole thoroughly mixed 
to the satisfaction of the Engineer. The mixing shall be done upon 
water-tight platforms, in a satisfactory manner; after the materials 
are wet, the work shall proceed rapidly until the concrete is in place, 
and is so thoroughly manipulated that water flushes to the surface 
and all the interstices between the stones are entirely filled with 
mortar. 

1 8.1 1. All mortar and concrete shall be used while fresh and before 
the initial set has begun. Any mortar or concrete in which the initial 
set has begun shall be removed from the mixing boards or receptacle 
and not used in the work. No retempering of mortar or concrete 
shall be allowed. 

18.12. The quantity of water to be used in making concrete shall 
be determined by the Engineer, but in general a wet mixture shall 
be used as tending to produce a uniform, dense and impervious 
concrete. 



412 SPECIFICATIONS 

18.13. When required by the Engineer, concrete shall be deposited 
in. layers averaging not more than six inches in thickness before 
compacting. In joining new concrete to old, or to concrete that has 
already set, the work already in place shall have its surface cut over 
thoroughly with picks to remove all laitance, loose and foreign ma- 
terial; this surface shall then be washed and be scrubbed with wire 
brooms before the new concrete is placed. In order to bond the 
successive courses, horizontal keys shall be formed at the top of the 
upper layer of each day's work and at such other levels as work is 
interrupted until the concrete has taken its initial set. Rough stone 
may, at the discretion of the Engineer, be embedded instead of using 
the keys. 

Whenever concreting is suspended on any section for more than 
one hour, all edges which will be exposed in the finished work shall 
be brought to a level. 

In any given layer the separate batches shall follow each other so 
closely that each one shall be placed and compacted before the pre- 
ceding one has set, so that there will be no line of separation between 
the batches. 

After the concrete has begun to set, it shall not be walked upon in 
less than twelve hours. 

The operation of compacting the concrete shall be conducted so 
as to form a compact, dense, impervious artificial stone which shall 
show a smooth face on exposed surfaces. The weight of rammers, 
if used, shall be satisfactory to the Engineer. If any monolith, the 
concrete of which is found porous, has been plastered or is otherwise 
defective, it shall be removed and replaced in whole or in part, as 
directed by the Engineer, entirely at the Contractor's expense. 

18.14. The Contractor shall construct suitable forms, the cost of 
which shall be included in the contract price per cubic yard for the 
concrete, the interior shape and dimensions of which shall be such 
that the finished concrete shall be of the form and dimensions shown 
on the plans. Lagging for faces shall not be less than two (2) inches 
in thickness before being dressed, except where used for curved or 
special surfaces. Especial attention must be paid to bracing, and 
where the forms appear to be insufficiently braced, or unsatisfactorily 
built, either before or during concreting, the Engineer shall order 
work to be stopped until the defects have been corrected to his sat- 
isfaction. If desired, small rods to hold the forms may be embedded 
in the concrete, but in all such cases provision must be made by sleeve 
nuts or other satisfactory methods for the removal of the two inches 
nearest the surface. All holes thus left shall be immediately and 
completely filled with cement mortar and the surface left smooth and 
even. All forms shall be set and maintained true to the lines desig- 
nated until the concrete is sufficiently hardened. All forms shall 
be satisfactory to the Engineer and shall remain in place as long as 
he deems necessary. The interior surfaces of the forms which come 
in contact with the surfaces of the concrete which will be exposed in 
the finished work shall be of lumber dressed on both faces and both 
edges and having water-tight joints, and shall be so constructed as 
to leave all such exposed surfaces of the concrete with a smooth even 



CONCRETE 413 

finish. Forms reused shall be maintained at all times in good con- 
dition as to accuracy of shape, strength, rigidity, watertightness 
and smoothness of surface. Forms unsatisfactory in any respect 
shall not be used, and if condemned shall be removed immediately 
from the work. 

18.15. Boulders and fragments of rock may be bedded in a large 
mass of third-class concrete. Each stone before being bedded or 
placed shall be thoroughly washed and scrubbed, if necessary, to 
free it from all dirt. Stones bedded in concrete shall be at least 
three inches apart at all points, and no stones shall be placed within 
three inches of any face of the concrete. Stones shall be laid on their 
largest bed and worked down into the concrete by bars so as to exclude 
the air from any pockets in the lower surface of the stone. 

18.16. The Contractor shall construct weep holes in all retaining 
walls at such points as are indicated on the plans or designated by 
the Engineer. Selected stones shall be placed by hand at the inner end 
of the holes to assist drainage in escaping and to prevent the overflow 
of earth. Payment for all labor and materials required to construct 
and protect these weep holes will be included in the contract price 
for concrete. 

18.17. Whenever directed by the Engineer, newly laid masonry 
shall be protected to prevent freezing, and the protection shall be in 
all respects satisfactory to him. 

The Contractor shall be responsible for all damage to concrete 
by freezing, and any concrete so damaged shall be cut out and re- 
placed at the Contractor's expense as directed by and to the satis- 
faction of the Engineer. 

When the temperature falls below 35 degrees Fahrenheit the fine 
aggregate, water and stone shall be heated, and the newly laid con- 
crete shall be covered with canvas or otherwise protected from 
freezing. No concrete foundation for pavement or concrete pave- 
ment shall be laid when the temperature falls below 35 degrees 
Fahrenheit. 

18.18. All damage to or disfigurement of concrete of any kind 
occurring prior to the final acceptance of the work shall be remedied 
by the Contractor at his own expense and to the satisfaction of the 
Engineer. 

18.19. No piece of stone shall be left within one inch of any face, 
a broad-tined fork or other implement, if approved, being thrust 
between the form and the concrete to pry the fragments of stone 
back from the face. 

The top surface of concrete shall be formed immediately after 
the underlying course is completed and before this course takes its 
initial set. The top surface shall be formed by cutting off the excess 
with a template and shall then be rubbed smooth and hard with a 
wooden float by skilled men. As soon as the concrete has sufficiently 
set and the Engineer shall so direct, the forms shall be removed and 
all exposed faces immediately finished by being rubbed smooth with 
a mortar block and water. No plastering of any surface will be 
allowed, the required finish being obtained by rubbing down the 
irregularities of the face. All exposed surfaces shall be smooth, 



414 SPECIFICATIONS 

dense, without pits, irregularities, blow holes or bubbles. The surface 
of all finished and unfinished work shall be kept wet for a period of 
six days unless otherwise directed by the Engineer. 

All edges, joints of sections and angles which will be exposed in the 
finished structure shall be rounded. A radius of one inch shall be used 
unless otherwise designated on the plans or directed by the Engineer. 

18.20. Concrete shall not be laid in water nor exposed to the action 
of the water before setting, except by written permission of the 
Engineer, and then in such manner as he may specially direct. 

18.21. Where concrete is to rest on any excavated surface other 
than rock, special care shall be taken not to disturb the bottom of 
the excavation, and the final removal of material to grade shall not 
be made until just before the concrete is laid, except in concrete 
foundations for pavement. 

The excavation lines and bases of structures shown on the plans 
shall be considered as only approximate; and they may be ordered 
in writing by the Engineer, to be placed at any elevation or of any 
dimensions that will give a satisfactory foundation. Any additional 
concrete that may be required by the Engineer below or beyond the 
lines shown on the plans will be paid for at the contract price. 

No structure shall be commenced without the Engineer's approval. 

All rock or hardpan foundation surfaces shall be freed from loose 
pieces, cut to firm surfaces and cleaned to the satisfaction of the 
Engineer, before laying concrete. All seams shall be cleaned out 
and filled with concrete or mortar; and payment for such cleaning 
out and filling shall be made at the contract price for the class of 
concrete used. 

18.22. The quantity to be paid for under Items 18, 19 and 20 
shall be the number of cubic yards of the various classes measured 
in place in the finished structures placed in accordance with the 
plans or as ordered by the Engineer. No payment will be made for 
any concrete outside of these limits, nor for any concrete whose 
placing is rendered necessary owing to lack of proper care. 

The price bid for Items 18, 19 and 20, respectively, shall include 
all materials, forms, labor and other incidental expenses necessary 
to satisfactorily complete the work as specified in the foregoing 
paragraphs for first-class concrete, second-class concrete and third- 
class concrete respectively. 

Item 21 — Stone Masonry 

2 1. 1. Under this item the Contractor shall furnish and build all 
stone masonry in structures or elsewhere, as shown upon the plans 
or ordered by the Engineer. 

21.2. Stone masonry shall be built of clean stone, free from 
structural defects, laid in full cement mortar beds. Selected stone, 
roughly squared and pitched to line, shall be used at all angles and 
ends of walls. 

21.3. The stone shall be laid on its natural bed to form substan- 
tial masonry, presenting a neat and finished appearance. Spalls 
and pinners shall not be allowed to show on the face of the wall, and 



STONE CURBING AND HEADERS 415 

shall be used only where necessary. The length of stretchers shall 
not exceed three times their rise; the width of stretchers shall in 
no case be less than their rise. At least one-fourth of the stone in 
the face shall be headers, and these shall be evenly distributed; the 
length of headers shall not be less than the thickness of the wall, 
where the wall is four feet or less in thickness; where the wall is 
more than four feet in thickness, the length of the headers shall not 
be less than two feet and eight inches, and not more than two-thirds 
of the thickness of the wall; the width of the headers shall not be 
less than their rise. All stones shall be laid to break joints six inches 
or more and to thoroughly bond the work. No joint of the face 
shall be over one inch in width. Backing shall consist of good- 
sized, well-shaped stone so laid as to break joints. All spaces between 
the stone shall be filled with spalls set in mortar. The rear faces 
shall present approximately plain surfaces. 

21.4. End walls of culverts and retaining walls shall be capped with 
concrete or with stone, roughly squared, extending across the entire 
width of the wall, and on steps of wing walls the coping shall extend 
under the step next above it at least eight inches. 

21.5. On all exposed faces, the joints shall be raked out and cleaned 
to a depth of two inches and then pointed with Portland cement 
mortar mixed in a proportion of one to one. 

21.6. The quantity of stone masonry to be paid for under this 
item shall be the number of cubic yards measured in the completed 
work, and the limits shall not exceed those shown upon the plans or 
fixed by the Engineer. 

The price bid shall include all labor, materials and incidental 
expenses necessary to satisfactorily complete the work. 

Item 22 — Stone Curbing and Headers 

22.1. Under this item the Contractor shall furnish and place 
stone curbing and headers where shown on the plans or ordered by 
the Engineer. 

22.2. Stone curbing and headers shall be of approved bluestone, 
sandstone or granite, sound, uniform, free from seams or other imper- 
fections, and shall be nowhere less than 5 inches thick, 15 inches deep, 
and 3 feet long. 

The upper face shall be evenly cut and the front face shall be 
dressed for the full depth to an even surface with no projections or 
depressions exceeding one-quarter inch. The bottom shall be 
roughed off parallel to the top so that there will be no projections 
exceeding 2 inches beyond the required depth. 

The ends shall be squared and dressed to form joints 'not exceed- 
ing one-eighth inch for a depth of at least 2 inches from top and front 
face. The backs shall be rough dressed for full depth and dressed 
the same as the face for a depth of 2 inches from the top. The 
joints of circular curbing shall be cut on radial lines. 

22.3. The curb or header shall be set in third-class concrete, as 
shown on the plans. It shall be true to line and grade and settled 
so as to have a firm and uniform bearing. 



416 SPECIFICATIONS 

22.4. If required by the plans, porous drain- tile shall be placed 
under stone curbing and firmly embedded and covered with cinders, 
gravel or broken stone. 

22.5. After the curb or header has been set the trenches shall be 
filled with earth and thoroughly tamped. 

22.6. The quantity to be paid for under this item shall be the 
number of linear feet of curbing or headers set in accordance with 
plans and directions of the Engineer. 

The price bid for this item shall include the furnishing and setting 
of the curb or header, all concrete, tile, broken stone or gravel, and 
all labor, materials and incidental expenses necessary to complete 
the work. 

Item 23 — Resetting Old Curbing 

23.1. Under this item the Contractor shall remove and reset old 
curbing, as shown upon the plans or ordered by the Engineer. 

23.2. Care shall be taken in removing old curbing so that there 
shall be no unnecessary breakage, and any curbing damaged in 
removing, hauling, or storing, due to the carelessness of the Contractor, 
shall be replaced with new curbing at his own expense. 

23.3. All joints and tops shall be redressed, if directed by the 
Engineer, to obtain a smooth top surface and to obtain joints of the 
same class as specified for new curbing. 

23.4. The quantity to be paid for under this item shall be the 
number of linear feet removed, stored, hauled, and reset in accordance 
with the plans and as directed by the Engineer. 

The price bid shall include all concrete, tile, removing, redressing, 
hauling, storing, resetting, and all materials, labor and incidental 
expenses necessary to complete the work. 

Item 24 — Concrete Curbing 

24.1. Under this item the Contractor shall place concrete curbing, 
of the type shown on the plans, where shown on the plans or ordered 
by the Engineer. 

24.2. All curbing shall be constructed of first-class concrete. The 
concrete shall be of such consistency, and be so spaded and worked, 
that a smooth mortar face will be produced. The coarse aggregate 
for concrete curbing shall be approved No. 2 stone or gravel. 

24.3. Curbing shall be moulded in place in sections 6 feet long and 
provision made at each joint for expansion of one-sixteenth inch. 

24.4. All forms shall be set true to line and grade and held rigidly 
in position. They shall be either of metal or of acceptable planed 
and matched lumber, and of such construction that a smooth surface 
will be provided. 

The forms shall be left in place until the concrete has set suffi- 
ciently so that they can in the opinion of the Engineer be removed 
without injury to the curbing. The curbing shall immediately upon 
the removal of the forms be rubbed down to a smooth and uniform 
surface, but no plastering will be allowed. For this work a competent 
and skillful finisher shall be employed. 



COBBLE GUTTERS 



417 



24.5. The Contractor shall protect the curbing and keep it in 
first-class condition until the completion of the contract. Any curb- 
ing which is damaged at any time previous to the final acceptance of 
the work shall be removed and replaced with satisfactory curbing 
at the Contractor's expense. (Also see section 18. 1.) 

24.6. The quantity to be paid for under this item shall be the 
number of linear feet placed in accordance with the plans or directions 
of the Engineer. 

The price bid for concrete curbing shall include the furnishing and 
placing of all concrete, tile, porous filling, forms, and all other ma- 
terials, labor and incidental expenses necessary to complete the work. 

Item 25 — Concrete Edging 

25.1. Under this item the Contractor shall furnish and mould in 
place concrete edging of the type shown on the plans and where 
designated on the plans or ordered by the Engineer. 

25.2. The concrete edging shall be composed of second-class con- 
crete. The top shall be troweled to an even surface and the material 
shall be rammed and spaded so that a dense concrete and a smooth 
surface will result. (Also see section 18.1.) 

25.3. The forms shall be set and held true to line and grade, and 
shall not be removed until the concrete has set sufficiently, in the 
judgment of the Engineer, so that no harm will result therefrom. 
The edging shall be protected from injury until the completion of 
the contract. 

After the removal of the forms, the trenches shall be back-filled 
with earth and thoroughly tamped. 

25.4. The quantity to be paid for under this item shall be the 
number of linear feet of concrete edging completed as shown on the 
plans or ordered by the Engineer. 

The price bid shall include the furnishing and placing of concrete 
and forms, and all other materials, labor and incidentals necessary 
to complete the work. 

Item 26 — Cobble Gutters 

26.1. Under this item the Contractor shall furnish and place 
cobble gutters where shown on the plans or ordered by the Engineer. 

26.2. Cobble gutters shall consist of rounded "hardheads," quarry 
or field stone, and shall be laid on edge. If hardheads are used they 
shall be 4 inches to 8 inches in diameter. The largest stones shall 
be selected and set along the edges of the gutter. All stones except 
where embedded in mortar shall be set in sand, and shall be laid to 
line and grade with close joints by skilled workmen using regular 
paving tools. The whole shall then be thoroughly rammed in place 
and brought to a uniform surface. All joints shall be swept full of 
sand. On grades exceeding 6 per centum, and elsewhere if called for 
by the plans or ordered by the Engineer, cobble gutters shall be laid 
in Portland cement mortar, mixed one to three, as shown upon the 
plans. 



4 i 8 SPECIFICATIONS 

26.3. The quantity of cobble gutter to be paid for under this item 
will be the number of square yards of exposed surface laid in accord- 
ance with the plans and as directed by the Engineer. 

The price bid shall include the furnishing and placing of all stones, 
sand, mortar, and all other materials, labor and incidental expenses 
necessary to complete the work. 

Item 27 — Concrete Gutters 

27.1. Under this item the Contractor shall furnish and place 
concrete gutters where shown upon the plans or ordered by the 
Engineer. 

27.2. Concrete gutters shall be of first-class concrete and shall 
conform to all requirements therefor as elsewhere specified. They 
shall be of the shape and length shown upon the plans, and shall be 
placed true to line and grade as directed. (See section 18. 1.) 

27.3. The quantity for which the Contractor will be paid shall 
be the number of square yards of concrete gutters placed in accordance 
with the plans and ordered by the Engineer. 

The price bid shall include the furnishing and placing of all con- 
crete, the preparation of foundation, together with all other labor 
and incidental expenses necessary to satisfactorily complete the work. 

Item 28 — Brick Gutters 

28.1. Under this item the Contractor shall furnish and place 
brick gutters where shown upon the plans or ordered by the Engineer. 

28.2. Brick gutters shall be constructed of approved brick, shall 
conform to the dimensions shown upon the plans, and shall be laid 
true to lines and grades upon a suitable bed of sand. 

28. 3. Where brick gutters are to be laid next to a curbing in con- 
nection with a pavement having a concrete foundation, they shall 
be constructed in full conformity to the specifications for brick 
pavement, and shall be paid for as such. 

28.4. The quantity for which the Contractor will be paid shall 
be the number of square yards of brick gutters placed in accordance 
with the plans and ordered by the Engineer. 

The price bid shall include the furnishing and placing of all ma- 
terials and the preparation of bed, together with all other labor and 
incidental expenses necessary to satisfactorily complete the work. 

Item 29 — Metal Reinforcement 

29.1. Under this item the Contractor shall furnish and place 
metal bar and metal mesh reinforcing material where shown upon 
the plans or directed by the Engineer. 

29.2. All metal reinforcement shall, when embedded, be free from 
mill scale, grease, injurious rust, dirt or other foreign substance. 

29.3. All metal reinforcement shall be securely held in place so 
that it will be in the prescribed position after the concrete has been 
thoroughly compacted. 



MISCELLANEOUS IRON AND STEEL 419 

29.4. Unless otherwise designated upon the plans, all bar rein- 
forcement shall be of open hearth steel, and shall consist of approved 
"deformed" bars or rods which shall have an elastic limit of not less 
than 30,000 nor more than 45,000 pounds per square inch, and an 
elongation of not less than 20 per centum in a length of 8 inches. 

Deformed bars shall not contain more than T f q of one per centum 
of sulphur nor more than r J T of one per centum of phosphorus. In 
small culverts and other structures of minor importance standard 
commercial deformed bars acceptable to the Engineer may be used. 

All deformed bars shall be uniform in quality, and shall endure 
bending 180 degrees, when cold, around a circle whose diameter is 
equal to the diameter or thickness of the test piece, without fracture 
on the outside of the bent portion. 

Bars shall overlap each other by 30 diameters. 

29.5. Unless otherwise designated upon the plans, all metal mesh 
reinforcement shall be of an approved kind and quality, and of the 
cross-section shown upon the plans and acceptable to the Engineer, 
and equal in all respects to the best standard commercial products. 
Sheets of metal mesh shall overlap each other as directed by the 
Engineer or as shown upon the plans. 

29.6. The quantity of metal reinforcement for which the Contractor 
will be paid shall be the number of pounds incorporated in the work 
in accordance with the plans or directions of the Engineer. 

The bid price shall include all labor, materials, and other expenses 
necessary to satisfactorily complete the work. 

Metal reinforcement used in rails and posts shall not be included 
in this item, but shall be considered as being included in the price 
bid for appropriate items. 

Item 30 — Miscellaneous Iron and Steel 

30.1. Under this item the Contractor shall furnish and place all 
cast iron, wrought iron and steel not especially included in other 
items as shown on the plans and for miscellaneous structures as 
ordered by the Engineer. This item shall include beams, channels, 
and other structural shapes, as well as miscellaneous iron castings, 
wrought iron, etc. 

30.2. All structural steel, bolts, etc., shown on the plans may be 
of stock steel. Stock steel shall be subjected only to surface in- 
spection and cold bending tests. Test pieces cut from finished 
materials shall endure bending cold, without signs of cracking, 180 
degrees around a circle whose diameter is equal to the thickness of 
the test piece. 

Iron castings shall be made of the best tough gray iron of uniform 
quality and shall be free from defects and uneven shrinkage. No 
mill cinder iron, white or burnt iron or scrap of any kind shall be 
used. They shall be clean, out of wind, and true to dimensions. 
Castings having blow holes plugged or filled with putty or crust 
shall not be used. 

Wrought iron shall be tough, fibrous and uniform in quality and 
shall be manufactured by approved methods. Steel scrap shall 



4 20 SPE CIFIC ATIONS 

not be used in its manufacture. Finished material shall be clean, 
smooth, true to shape and free from defects. 

All iron and steel except cast iron shall be given a shop coat of 
red lead and oil, and after being placed shall be given two coats of 
approved paint. 

30.3. The quantity of iron, wrought iron and steel to be paid for 
under this item shall be the number of pounds furnished and placed 
in accordance with the plans or instructions of the Engineer. The 
price bid shall include the furnishing, placing, painting and all other 
labor, materials and incidental expenses necessary to satisfactorily 
complete the work. 

Item 31 — Wooden Guard Railing 

3 1 . 1 . Under this item the Contractor shall furnish and erect wooden 
guard railing of the type indicated, where shown on the plans or 
ordered by the Engineer. 

31.2. The posts shall be of seasoned white oak, cedar, locust, 
tamarack, white pine, or chestnut. They shall be at least 6 inches 
square, or if round they shall be 6 inches in diameter at the smaller 
end after the bark is removed, and 7 feet long. Round posts shall 
be shaved to even surfaces free from bark or skin. The lower part 
of the posts to a point 3 feet from the top shall be dipped while dry 
in suitable bituminous material heated to a temperature of 300 
degrees Fahrenheit, or shall be charred as directed. The posts if 
dipped shall be thoroughly dry before being set in the ground. 

31.3. Rails shall be of seasoned, planed spruce or other satis- 
factory wood, and be properly secured to the posts, all in a workman- 
like manner. 

31.4. The joints of the rails and posts shall be given one coat of 
white lead and linseed oil before being put together; the beveled 
tops of posts shall receive two heavy coats of the same. The entire 
surface exposed above the ground shall be painted with three coats 
of white lead and linseed oil. 

31.5. The white lead and the linseed oil shall be delivered sep- 
arately on the road in original containers; before being mixed and 
used a pint sample of each, covering each lot, shall be forwarded to 
the Bureau of Tests, and neither ingredient shall be used until 
accepted by the Commission. The mixing of the ingredients shall 
be as directed by the Engineer. This specification shall apply to all 
paint used under this contract. 

31.6. The quantity of wooden guard railing to be paid for under 
this item shall be the number of linear feet completed in place. 

The price bid shall include the furnishing and erecting of all posts 
and rail, the excavation, painting, dipping, hardware and all expenses 
and incidentals necessary to complete the work. 

Item 32 — Special Guard Railing 

32.1. Under this item the Contractor shall furnish and erect, true 
to line and grade, guard railing of the special design shown upon the 
plans, at the places indicated by the plans or ordered by the Engineer. 



GUIDE SIGNS 421 

32.2. Except as otherwise provided by the plans, each class of 
work necessitated under this item shall be governed by the clauses 
of other items which are specially applicable thereto. 

32.3. The quantity of guard railing to be paid for under this item 
shall be the number of linear feet placed in accordance with the plans 
and ordered by the Engineer. 

The price bid shall include all excavation, concrete, metal rein- 
forcement, hardware, backfilling and all other materials, labor and 
incidental expenses necessary to satisfactorily complete the work. 

Item 33 — Pipe Railing 

33.1. Under this item the Contractor shall furnish and erect pipe 
railing of the type indicated where shown upon the plans or ordered 
by the Engineer. 

33.2. Pipe railing shall consist of wrought iron pipe, rails, posts 
and pipe rail fittings of the sizes shown on the plans. All threaded 
joints shall be coated with lead and oil before being assembled. All 
parts shall be painted, after being put in place, with two coats of 
white lead and linseed oil. 

2,^-3' The quantity of pipe railing to be paid for under this item 
shall be the number of linear feet placed in accordance with the plans 
and ordered by the Engineer. 

The price bid shall include the furnishing and erecting of all 
materials, the painting and all expenses and incidentals necessary 
to complete the work. 

Item 34 — Guide Signs 

34.1. Under this item the Contractor shall furnish and erect guide 
signs of the type indicated where shown upon the plans or ordered 
by the Engineer. 

34.2. Permanent guide signs shall be for the purpose of furnishing 
permanent directions to traffic after the completion of the contract. 
Permanent guide signs shall be constructed of kiln dried white pine 
and of the dimensions shown on the plans. They shall first be given 
four coats of white lead mixed with linseed oil. After the last coat 
has become thoroughly dried the letters shall be painted with black 
enamel paint, and when this is thoroughly dried they shall be given 
one coat of the finest white shellac. 

34.3. Temporary guide signs shall be for the purpose of guiding 
traffic along a detour during construction. Temporary guide signs 
shall be constructed of kiln dried white pine and of the dimen- 
sions shown on the plans. They shall first be given three coats 
of white lead mixed with linseed oil. After the last coat has 
become thoroughly dried the letters shall be painted with black 
enamel paint. 

34.4. The number of guide signs to be paid for under this item shall 
be the number of signs placed in accordance with the plans and ordered 
by the Engineer. All signs become the property of the State upon 
payment for this item. 



422 SPECIFICATIONS 

The price bid shall include the furnishing of all labor and materials 
necessary to satisfactorily erect permanent guide signs on sign posts 
and temporary guide signs including sign posts, each guide sign com- 
plete in place. 

Item 35 — Highway Number Signs 

35.1. Under this item the Contractor shall paint on the concrete 
sign posts highway number signs of the type indicated where shown 
upon the plans or ordered by the Engineer. 

35.2. Highway number signs shall be painted on all concrete sign 
posts with letters which shall first be formed of two coats of flat 
black mixed in oil and afterward retraced with black enamel. 

35.3. The number of highway number signs to be paid for under 
this item shall be the number placed in accordance with the plans 
and ordered by the Engineer. 

The price bid shall include the furnishing of all labor and materials 
to satisfactorily complete the work. 

Item 36 — Danger Signs 

36.1. Under this item the Contractor shall furnish and erect danger 
signs where shown upon the plans or ordered by the Engineer. These 
shall be of the type called for by the plans. 

36.2. Danger signs shall be constructed of a material and painted 
similar to that specified for guide signs and shall be of the dimensions 
and lettered as shown on the standard plans. These signs shall be 
placed on the standard concrete sign posts and set at an angle of 
forty-five degrees to the center line. When the standard sign is used 
the arrow shall point in the direction of the danger. 

36.3. The number of completed danger signs for which the Con- 
tractor will receive payment will be the number placed in accordance 
with the plans and ordered by the Engineer. 

The price bid shall include the furnishing of all labor and materials 
necessary to complete each danger sign in a satisfactory manner. 

Item 37 — Concrete Sign Posts 

37.1. Under this item the Contractor shall furnish and erect 
concrete sign posts of the type indicated, where shown upon the 
plans or ordered by the Engineer. 

37.2. Concrete sign posts shall be made of first-class concrete and 
of the dimensions and materials shown on the standard plans. To 
these posts shall be securely fastened guide boards and signs. 

37.3. The number of completed concrete sign posts to be paid 
for under this item shall be the number erected in accordance with 
the plans and ordered by the Engineer. 

The price bid shall include all concrete, reinforcement, forms, 
excavation and backfill, and the furnishing of all other labor and 
materials necessary to complete each concrete sign post in a satis- 
factory manner. 



FOUNDATION COURSE 423 



LOOSE STONE 

Item 38 — Screened Gravel — Loose Measure 
Item 39 — Broken Stone — Loose Measure 

38.1. Under these items the Contractor shall furnish and place 
upon the road, as directed by the Engineer, broken stone and gravel 
of the sizes designated on the Itemized Proposal. This stone and 
gravel will be used for general repair work and for miscellaneous work. 

38.2. The stone or gravel delivered shall be of approved quality 
and shall conform to the general requirements for broken stone and 
gravel, and they shall be of the sizes ordered. 

35.3. The quantity to be paid for under Items 38 and 39 respec- 
tively shall be the quantity of broken stone or gravel furnished and 
delivered on the work at the places and in the condition specified by 
the Engineer. When the material is produced by the contractor on 
the work, it shall be measured in cubic yards; it shall be measured 
in tons of 2,000 lbs. when the material is imported and the weight 
is obtainable from reliable sources such as certified quarry or railroad 
figures. 

The price bid shall include furnishing and delivering the stone or 
gravel as directed by the Engineer and all labor, appliances and ex- 
penses incidental thereto; also the spreading, rolling or incorporating 
of the stone or gravel in the work, when required by the Engineer. 



FOUNDATION COURSE 

Item 40 — Foundation Course — "Run of Bank" Gravel 
Item 41 — Foundation Course — Field of Quarry Stone 

40.1. Under these items the Contractor shall furnish and place a 
foundation course of stone or gravel of the depth and in the places 
called for by the plans, or as ordered by the Engineer in accordance 
with section 2.5, " Preparation of Subgrade" of item " Excavation." 

40.2. No stone or gravel shall be placed on the road until the 
culverts are completed and proper drainage provided. 

40.3. When field or quarry stone is used for constructing the 
foundation course it shall be of a hard, sound and durable quality, 
acceptable to the Engineer; the stones shall be placed by hand so 
as to bring them in as close contact as possible. When quarry 
stones are used they shall be placed on edge. The depth of the stone 
shall in no case be greater than the depth specified for the course, 
the width shall not be greater than the depth, nor more than six 
inches; and the length shall not be greater than one and one-half 
times the depth, nor more than 12 inches. The distribution of the 
stone shall be of a uniformity satisfactory to the Engineer. The long 
dimension shall always be placed crosswise the road. After laying, 
this course shall be thoroughly rolled with an approved roller weighing 
not less than ten tons, and shall then be filled with stone or gravel 
as directed and again rolled until the stones are bound together and 



424 SPECIFICATIONS 

thoroughly compacted; but no gravel shall be used for rilling except 
under written permission of the Engineer. All holes or depresssions 
found in rolling shall be filled with material of the same quality and 
the surface shall be re-rolled until it conforms to the lines and grades 
shown on the plans. When field stone is used approved tailings may 
be used for filling. In all cases a sufficient amount of fine material 
shall be used to fill all voids. In limited areas where the use of a 
roller is impracticable heavy tampers may be used to consolidate 
the material. 

40.4. Wherever gravel is used for the foundation course it shall 
conform in all particulars to the gravel specified in section 2 of 
Bottom Course "Run of Bank" Gravel. 

40.5. The quantity to be paid for under this item shall be the 
number of cubic yards of compacted material in place. The amount 
to be estimated shall be computed by multiplying the finished cross- 
section of the foundation course as shown upon the plans or ordered 
by the Engineer, by the length of the foundation course measured 
along the axis of the pavement. 

The price bid shall include the furnishing, placing, filling, rolling 
of the material and all labor and incidental expenses necessary to 
complete the work. 

Item 42 — Foundation Course — Telford Base 

42.1. Under this item the Contractor shall furnish and place a 
foundation course of field or quarry stone laid on edge, in accordance 
with the plans or as ordered by the Engineer. 

42.2. No stone shall be placed on the road until the culverts are 
completed and proper drainage has been provided. 

42.3. Field or quarry stone of approximate rectangular shape 
shall be used. The stone shall be not less than one and one-half 
inches thick, in depth equal to the depth of the course, and in length 
not more than one and one-half times the depth. 

42.4. The pieces shall be placed on edge by hand in as close con- 
tact as possible with long dimension crosswise of the road. After 
being placed, all pieces projecting more than one inch above the 
established plane of the surface shall be broken off flush so as to obtain 
a true and uniform surface. This course shall then be rolled with 
an approved self-propelled roller weighing not less than ten tons, and 
shall then be filled with approved screenings and again rolled until 
the course is thoroughly compacted/ Material other than screen- 
ings for filling this course shall not be used except under the written 
order of the Engineer. 

42.5. The quantity to be paid for under this item shall be the 
number of cubic yards of compacted material in the completed 
course. The amount to be estimated shall be computed by multiply- 
ing the finished cross-section of the foundation course as shown upon 
the plans or ordered by the Engineer, by the length of the founda- 
tion course measured along the axis of the pavement. The price 
bid shall include the furnishing, placing, filling, rolling of the material 
and all labor and incidental expenses necessary to complete the work. 



BOTTOM COURSE 425 

BOTTOM COURSE 

Item 43 — " Run of Bank" Gravel 

43.1. Under this item the Contractor shall furnish and place 
approved "Run of Bank" gravel either upon the properly prepared 
subgrade or upon the foundation course. The work shall be per- 
formed in full conformity to the specifications given under sections 
44.2 to 44.9 inclusive, so far as same are not inconsistent with the 
use of such gravel. 

43.2. All gravel shall be of hard, durable stone satisfactory to 
the Engineer. The particles shall be of such size as will pass through 
a 3J-inch circular hole, and shall be well graded. Gravel shall be 
of such nature that the material passing a J-inch screen shall not be 
more than five per x centum in excess of the voids in the remaining 
material after its separation therefrom. Before using "Run of 
Bank" gravel in the work the same shall be tested to determine its 
suitability. Should at any time during the work and for any reason 
the gravel fail to maintain suitable proportions of the coarse and 
fine particles, the Contractor shall by the addition of selected material 
and satisfactory manipulation produce a material meeting the above 
requirements. 

43.3. The depth of loose stone or gravel in all cases, whether in 
foundation, bottom or top courses, shall be gauged by the use of 
cubical blocks of suitable size. (See page 272.) 

43.4. The spreading of any layer or course of broken stone, gravel 
or filler, whether in foundation, bottom or top courses, shall be done 
from suitable spreader wagons or from piles dumped along the road 
as directed by the Engineer. 

No segregation of large or fine particles will be allowed, but the 
stone as spread shall be well graded with no pockets of fine material. 

43.5. The quantity to be paid for under this item shall be the 
number of cubic yards of compacted material in place in the completed 
course.. The amount to be estimated shall be computed by multi- 
plying the finished cross-section of the bottom course as shown on 
the plans or ordered by the Engineer, by the length of the bottom 
course measured along the axis of the pavement. 

The price bid shall include the furnishing, placing, rolling and filling 
the material, and all other labor, materials and incidental expenses 
necessary to satisfactorily complete the work. 

Item 44 — Bottom Course — Screened Gravel 
Item 45 — Bottom Course — Broken Stone 

44.1. Under these items the Contractor shall furnish and place 
stone or gravel, conforming to the general requirements for same, 
either upon the properly prepared subgrade or upon the foundation 
course. This stone or gravel shall be of sizes specified below. 

44.2. After the subgrade or foundation course shall have been 
properly prepared and proper drainage provided, a course of broken 

1 Not feasible, see page 6g. 



426 SPECIFICATIONS 

stone or gravel of graded No. 3 or No. 4 or a uniform mixture of 
same shall be spread evenly so that it will have after rolling the 
required thickness. If specifically allowed by the Engineer a lim- 
ited amount of No. 2 stone may be used in the bottom course. 

In cases where the finished thickness of the bottom course is to be 
more than 5 inches, the broken stone or gravel for it shall be spread, 
rolled and filled in two separate layers neither of which shall be of 
a greater depth than 6 inches measured loose. 

44.3. The depth of loose sotne or gravel in all cases, whether in 
foundation, bottom or top courses, shall be gauged by the use of 
cubical blocks of suitable size. (See page 272.) 

44.4. The spreading of any layer or course of broken stone, gravel 
or filler, whether in foundation, bottom or top courses, shall be done 
from suitable spreader wagons or from piles dumped along the road 
as directed by the Engineer. 

No segregation of large or fine particles will be allowed, but the 
stone spread shall be well graded with no pockets of fine material. 

44.5. After the bottom course of stone or gravel has been laid 
loose it shall be thoroughly rolled with an approved roller weighing 
not less than ten tons. 

This rolling must begin at the sides and continue toward the center 
and shall continue until there is no disturbance of the stone ahead 
of the roller. After the stone is thoroughly compacted No 1. stone 
or gravel, and screenings or sand, or a mixture of these, shall be uni- 
formly spread upon the surface and swept in with rattan or steel 
brooms and rolled dry. After the completion of the rolling no team- 
ing other than that necessary for bringing material for the next course 
shall be allowed over the rolled material. It is the intention to 
bind this course with the small stone, but not to use so much that a 
good bond will not be secured between the bottom and top courses. 

44.6. When two courses of bottom stone are laid each course shall 
be treated by rolling and adding fine material as described above. 

44.7. If the subgrade material shall become churned up into or 
mixed with the bottom or sub-bottom courses through the Contractor's 
hauling over it or working on it when the subgrade is in a wet con- 
dition, the Contractor shall at his own expense remove such mixture 
of subgrade material and broken stone and replace it with clean 
broken stone of the proper size, and shall roll or otherwise compact 
the material so as to produce a uniform, firm and even bottom course. 

If the above condition occurs through no fault of the Contractor, 
the Contractor shall be paid both for excavating and replacing under 
the items " Excavation" and " Bottom Course" respectively. 

44.8. All filler for top and bottom courses shall be delivered and 
piled alongside the road before the course in which it is to be used 
is placed. 

44.9. The quantity to be paid for under these items respectively 
shall be the number of cubic yards of compacted material in place in 
the completed course. The amount to be estimated shall be computed 
by multiplying the finished cross-section of bottom course as shown 
upon the plans or ordered by the Engineer, by the length of the bottom 
course measured along the axis of the pavement. 



CONCRETE FOUNDATION FOR PAVEMENT 427 

The price bid for the respective items shall include the furnishing, 
placing, filling, rolling of the material and all labor and incidental 
expenses necessary to complete the work. 

Item 46 — Concrete Foundation for pavement 

46.1. Under this item the Contractor shall furnish and place upon 
a properly prepared subgrade, concrete foundation for pavement 
of the thickness shown upon the plans or ordered by the Engineer. 

46.2. Concrete foundation shall not be placed on any subgrade 
until the subgrade has been properly drained, thoroughly rolled and 
compacted, and is true to line and grade in horizontal and transverse 
cross-section. 

46.3. Concrete shall consist of a mixture of Portland cement, No. 2 
or No. 3 sand and broken stone or gravel. The coarse aggregate 
shall consist of a well mixed product of No. 2 and No. 3 stone or 
No. 2 and No. 3 gravel. The fine aggregate shall consist of No. 2 
or No. 3 sand. All of these materials shall conform in all respects 
to the requirements given under "Materials of Construction," 
pages 372 to 377. All specifications relating to second-class concrete 
shall apply to work done under this item, in so far as they are not 
inconsistent with the special specifications given below. 

46.4. The concrete shall be mixed in the proportions of one volume 
of cement to two and one half volumes of sand and five volumes 
of broken stone or gravel. The relative proportions of fine and 
coarse aggregate may be varied slightly, as a result of tests for 
voids by the Engineer, to the end that the resulting concrete shall 
be as dense as possible. The concrete shall in all cases approximate 
a 1: 2 J: 5 mix. 

46.5. The concrete shall be mixed in approved mechanical batch 
mixers. Mixing shall be continued through at least 12 revolutions 
and until every particle is coated with mortar and until the batch is 
of uniform color and consistency. After the materials are once 
wetted the work shall proceed rapidly until the concrete is in place. 
The quantity of water used shall be as directed by the Engineer 
and suitable measuring tanks shall be provided by the Contractor 
so that the same amount of water may be used in the separate 
batches. 

46.6. Before any concrete is placed, the subgrade shall be sprinkled 
sufficiently to dampen it, but a muddy condition shall not be allowed. 
As soon as possible after mixing, the concrete shall be deposited in 
place and thoroughly spaded and rammed so as to bring the mortar 
flush to the surface. Especial care shall be taken to keep the con- 
crete uniform and to prevent pockets of stone or mortar. 

46.7. The surface, when completed, shall conform to the lines and 
grades shown upon the plans, and shall be free from depressions or 
irregularities. No stone shall project above the general surface. 
All ramming and shaping shall be done before the concrete has taken 
its initial set. 

46.8. When the work is stopped for any reason a vertical joint shall 
be put in and the work completed up to this joint. 






428 SPECIFICATIONS 

46.9. No concrete foundation for pavement shall be laid when the 
temperature falls below 35 F. 

46.10. As soon as the concrete has taken its initial set the surface 
shall be covered with a one-inch layer of suitable material and this 
shall be kept moist for a period of at least seven days. For covering 
concrete foundations on which a sand cushion is called for, the sand 
cushion may be used for the cover coat if the contractor so elects; 
in case this is done the sand cushion shall be put in acceptable con- 
dition before preparing for laying the blocks; any portions which 
have become excessively dirty shall be removed and replaced with 
acceptable material to the satisfaction of the Engineer. 

In those cases where material other than sand cushion is used as 
a cover coat it shall be cleaned off after a period of ten days. 

46.11. The quantity to be paid for under this item shall be the 
number of cubic yards of concrete foundation for pavement incor- 
porated in the work in accordance with the plans or as directed by 
the Engineer. 

The price bid shall include the furnishing and placing of all ma- 
terials; all mixing, tamping, finishing, and all labor, appliances and 
incidental expenses necessary to complete the work. The amount 
to be estimated shall be computed by multiplying the cross-section 
of concrete foundation as shown upon the plans or ordered by the 
Engineer by the total length of concrete foundation measured along 
the axis of the pavement. 

TOP COURSE 

Item 47 — Top Course — Water Bound Macadam — Gravel 

47.1 . Under this item the Contractor shall furnish and place upon the 
bottom course, gravel of an approved character to form the top course. 

47.2. The top course shall consist of approved gravel of the char- 
acter hereinbefore specified and of the thickness shown on the plans, 
together with the binder necessary to properly fill and bind the course. 
For this purpose gravel of No. 3 size with, when approved by the 
Engineer, a certain amount of No. 2 size, may be used. Run of 
bank gravel shall not be used except by written permission of the 
Division Engineer; this permit must be given in advance, shall 
specify the locality from which it is to be taken, and contain a proviso 
that if the material should at any time become unsatisfactory its 
use shall at once cease and proper material be furnished without 
additional recompense even if it has to be imported. A copy of 
any such permit must be filed with the State Highway Commission, 
and on this permit must be the written and signed acceptance of 
all the conditions by the Contractor. 

47.3. The gravel shall be spread evenly upon the bottom course, 
using cubical blocks for gauging, to such a depth as to insure the 
required thickness after it shall have been thoroughly rolled and 
compacted with an approved roller weighing 10 to 12 tons. Care 
shall be exercised to prevent any depressions or surface irregularities 
after rolling the gravel and binder. 



WATER BOUND MACADAM 429 

47.4. When the gravel consists of screened material the binder 
shall consist of a mixture of the sand screened out and the No. 1 size, 
with enough clay added when necessary to make a percentage of 12 
to 17, but not to exceed 17 per cent. The binder shall be added as 
directed by the Engineer and thoroughly swept into interstices thereof 
until they are filled. After sprinkling the surface it shall be thoroughly 
rolled. The adding of binder where necessary and the sweeping, 
sprinkling and rolling shall continue until the course is compacted. 
The pavement shall then be opened to traffic and shall be in a 
first-class and satisfactory condition at the time of its acceptance. 

47.5. When the gravel consists of run of the bank the binder shall 
be the fine particles contained in the material in its natural state 
except that when so ordered in writing by the division Engineer a 
small percentage of clay or loam may be added, when necessary to 
properly bind the course. 

The particles shall be of such size as will pass through a 3^-inch 
circular hole, and shall be well graded. Gravel shall be of such nature 
that the material passing a i-inch screen shall not be more than five 
per centum in excess of the voids in the remaining material after its 
separation therefrom. Should at any time during the work and for 
any reason the gravel fail to maintain suitable proportions of the 
coarse and fine particles, the Contractor shall by the addition of 
selected material and satisfactory manipulation produce a top course 
meeting the above requirements. 

Care shall be taken to keep the large stone away from the surface. 

After sprinkling the surface it shall be thoroughly rolled. Addi- 
tional material forbinder shall be added where necessary and the 
sprinkling and rolling shall continue until the course is compacted. 
The pavement shall then be opened to traffic and shall be in a first- 
class and satisfactory condition at the time of its acceptance. 

47.6. The quantity to be paid for under this item shall be the 
number of cubic yards of compacted material in place in the completed 
course. The amount will be computed by multiplying the finished 
cross-section of the top course as shown on the plans or ordered by 
the Engineer, by the length of the top course measured along the 
axis of the pavement. 

The price bid under this item shall include the furnishing, placing, 
roiling, filling, and puddling of the material, and all labor, material 
and incidental expenses necessary to complete the work. 

Gravel or screenings remaining loose on the surface after the work 
is completed shall not be estimated as a part of the depth of the top 
course, but payment therefor shall be included in the price bid for 
this item. 

Item 48 — Top Course — Water Bound Macadam — Broken 

Stone 

48.1. Under this item the Contractor shall furnish and place 
upon the bottom course broken stone to form the top course. 

48.2. The top course shall, except as noted below, consist of No. 
3 broken stone as shown on the plans and of the thickness shown 



43° 



SPECIFICATIONS 



thereon, together with the binder necessary to properly fill and bind 
the course. The binder shall consist of screenings and No. i stone 
mixed. 

48.3. The No. 3 stone shall be spread evenly upon the bottom 
course, using cubical blocks for gauging, to such a depth as to insure 
the required thickness after it shall have been thoroughly rolled and 
compacted. Care shall be used in the reading of the stone that 
no irregularities in the contour shall develop in the rolling; every 
such irregularity that does occur the Contractor shall remove before 
adding the smaller material. The rolling shall be done with a 10 
to 12 ton self-propelled roller of approved pattern, and shall be con- 
tinued until the layer of stone does not creep or wave ahead of the 
roller. 

After the stone has been compacted to the satisfaction of the 
Engineer, a light coating of binder shall be spread on dry by shoveling 
from piles previously placed alongside the pavement, and imme- 
diately swept in and thoroughly rolled. Care must be taken through- 
out to add the binder only in light coatings and to thoroughly sweep 
each coating in order that the maximum amount of binder may be 
worked in to fill the voids. The spreading and sweeping and rolling 
shall be continued until no more binder will go in dry, after which 
the macadam shall be sprinkled until saturated, the sprinkler being 
followed by the roller. If the subgrade should become wet to such 
an extent that the pavement becomes unstable and waves under the 
roller, the roller shall be taken off and this portion left to dry out 
before puddling is resumed. 

More screenings shall be added where necessary, and the sweeping, 
sprinkling, and rolling shall continue until a grout has been formed 
that shall fill all the voids and be pushed into a wave by the wheels 
of the roller. After the wave of grout has been produced over the 
whole section of the macadam this portion shall be left to dry out, 
after which it shall be opened to traffic. The macadam shall be 
repuddled and back-rolled on succeeding days as much as may be 
necessary to secure satisfactory results. The macadam shall then 
be covered with a wearing carpet of screenings at least three-eighths 
of an inch thick; this wearing carpet shall be maintained and renewed 
until the whole road is accepted. During all the working hours 
when the roller is not needed for rohing the fills, subgrade, shoulders, 
and unfinished courses of the pavement, it shall be employed in back- 
rolling the earlier portions of the macadam. 

48.4. The quantity to be paid for under this time shall be the 
number of cubic yards of compacted material in place in the completed 
course. The amount to be estimated shall be computed by multi- 
plying the finished cross-section of the top course as shown on the 
plans or ordered by the Engineer, by the length of the top course 
measured along the axis of the pavement. 

The price bid shall include the furnishing, placing, rolling^ filling 
and puddling of the material, and all labor, material and incidental 
expenses, necessary to complete the work. 

No. 1 stone or gravel, chips or screenings remaining loose on the 
surface after the work is completed shall not be estimated as a part 



CLEANING OLD PAVEMENT 431 

of the depth of the top course, but payment therefor shall be included 
in the price bid for this item. 

Item 49 — Cleaning Old Pavement 

49.1. The purpose of the work called for under this item is to 
prepare an old macadam or old concrete surface for the application 
of a new top course or a wearing carpet. 

49.2. Under this item the Contractor shall clean the old macadam 
or concrete surface by the use of seal hand brooms or by the use of 
mechanical sweepers of approved type, as directed by the Engineer, 
so as to completely uncover but not dislodge the embedded stones 
of the pavement. 

All mud, dust, and other dirt so swept off shall then be removed 
and deposited in such places and in such manner as the Engineer 
may direct. 

49.3. Ruts and depressions of a greater depth than one inch below 
the general surface of the pavement shall be completely swept out 
by hand brooms until all loose material has been removed and the 
embedded stones are fully uncovered. 

This operation of cleaning out the ruts and depressions and filling 
them with thoroughly compacted stone and binder to the general 
level of the surface, shall precede the general operation of cleaning 
the macadam surface. 

49.4. The amount to be paid for under this item shall be the actual 
number of square yards of old macadam or concrete, including ruts 
and depressions, cleaned in accordance with the above sections and 
to the satisfaction of the Engineer. 

The price bid shall include all labor, tools, appliances, the removal 
of material cleaned from the surface, and all other expenses incidental 
thereto. 

Item 50 — Scarifying and Reshaping Old Macadam 

50.1. The purpose of the work under this item is to prepare old 
macadam pavement for the application of a top course. 

50.2. Under this item the Contractor shall thoroughly scarify the 
old macadam by hand picking or by means of a mechanical scarifier 
of approved type. Unless specifically authorized by the Engineer, 
the use of a roller with spiked wheels will not be permitted. 

The loosened stones shall then be forked or raked over as directed 
by the Engineer, after which the macadam shall be compacted by 
rolling with a self-propelled roller weighing not less than 10 tons 
until an even and firm surface is produced. If necessary in order 
to satisfactorily compact the stones, the macadam shall be sprinkled 
during the process of rolling. 

50.3. The quantity to be paid for under this item shall be the 
actual number of square yards, scarified, reshaped, rolled and com- 
pacted to the satisfaction of the Engineer, and the price stipulated 
shall include all labor, appliances and expenses incidental thereto. 



43 2 



SPECIFICATIONS 



Item 51 — Surface Treatments with Bituminous Material 

5 1. 1. Under this item the Contractor shall apply bituminous mate- 
rial and shall apply broken stone or gravel of specified sizes as a wearing 
carpet to a new or old pavement of macadam, concrete, or any other 
substance or type, as shown on the plans or ordered by the Engineer. 

51.2. If the pavement to be treated is a newly built macadam or 
concrete, after it shall have become thoroughly dried and hardened, 
it shall be swept clean of all dust, dirt or other loose material; if 
ordered by the Engineer, the sweeping of the macadam shall be con- 
tinued until the voids are exposed in the surface to a satisfactory 
depth, not exceeding one-half inch. The price bid, under this item, 
shall include the aforesaid cleaning of the pavements. 

If the pavement to be treated is an old macadam or old concrete, 
the cleaning shall be paid for under Item " Cleaning Old Pavement." 

51.3. After the pavement shall have been cleaned to the satis- 
faction of the Engineer, and when dry, the bituminous material shall 
be uniformly sprayed over the surface by means of an approved 
pressure distributor. The bituminous material for hot application 
shall be heated to a temperature between 250 degrees and 350 degrees 
F. as required, and when tar is used, it shall be heated to a tempera- 
ture between 200 degrees and 250 degrees F. as required. 

The amount of bituminous material to be used in any one applica- 
tion shall not be less than one-sixth nor more than one-half gallon 
per square yard, the precise quantity depending upon the character 
of the pavement, the materials and the local conditions. The Con- 
tractor shall, therefore, be subject entirely to the direction of the 
Engineer in this respect. 

51.4. The bituminous material applied as above specified shall 
then be immediately covered, while soft, with a uniform layer of 
approved broken stone of No. 2. or No. 1 size, after which the stone 
shall be rolled with a self-propelled roller of approved weight. If 
ordered by the Engineer another application of bituminous material 
shall then be made to be followed by an application of approved 
No. 2 stone or approved No. 1 stone, and again rolled to the satis- 
faction of the Engineer. 

The quantity of No. 2 stone and of No. 1 stone to be used shall be 
sufficient to completely cover the bituminous- material and shall 
be spread in two or more thin applications, the roller being used 
after each spreading. The total amount of stone to be used after 
each application of the bituminous material being that which will 
become imbedded under the pressure of the roller. The final appli- 
cation of the stone shall be of No. 1 size. 

51.5. Gravel, which has been tested and approved for use, may 
be substituted for broken stone if screened to produce particles cor- 
responding with No. 2 and No. 1 sizes. 

51.6. No bituminous material for surface treatment shall be placed 
between October 15th and May 15th, except by written permission 
of the Engineer, nor when the air temperature on the work is below 
50 degrees F., nor when the pavement is damp or in an otherwise 
unsatisfactory condition. 



BITUMINOUS MACADAM 433 

51.7. Under this item the Contractor shall be paid for the number 
of gallons of bituminous material furnished in and incorporated in the 
work in accordance with these specifications and the orders of the 
Engineer. Bituminous material, that has been wasted or that has 
been rendered unfit for use by over-heating or by long-continued 
heating, shall not be paid for. For purposes of measurement, a 
gallon shall be a volume of 231 cubic inches and measurement shall 
be based on the volume of the bituminous material at a temperature 
of 60 degrees F. 

The price bid shall include the furnishing, hauling, heating and 
applying the bituminous material, and shall also include the spread- 
ing, rolling and incorporation of the stone into the wearing carpet. 

This item shall not include the furnishing of the No. 1 and No. 2 
stone or gravel, nor the delivery of same along the side of the road; 
these will be paid for under Items Screened Gravel or Broken Stone 
Loose Measure, respectively. 

Item 52 — Top Course Bituminous Macadam — Penetration 

Method 

52.1. Under this item the Contractor shall furnish and lay a 
broken stone top course composed of fragments of the specified sizes, 
and incorporate therewith bituminous material introduced from the 
surface by means of an approved pressure distributor. 1 

52.2. After the bottom course shall have been completed to the 
satisfaction of the Engineer, a course of approved No. 3 broken 
stone shall be evenly spread thereon in such quantity that after the 
application of the bituminous material and broken stone of smaller 
sizes, hereafter specified, the final compacted thickness of the top 
course shall be as called for on the plans or ordered by the Engineer. 

The No. 3 stone shall then be smoothed out by passing over it a few 
times a self-propelled roller weighing approximately 10 tons, after 
which bituminous material of the kind specified in the proposal, 
heated to a temperature between 250 degrees and 350 degrees Fah- 
renheit if asphalt is used, and between 200 degrees and 250 degrees 
if tar is used, shall be evenly spreading over the surface. The quan- 
tity of bituminous material to be used in the first application shall 
be the amount ordered by the Engineer, which will approximate if 
gallons per square yard for a top course 3 inches thick, with a pro- 
portional reduction in the quantity for thinner courses. 

The surface shall then be immediately covered with a layer of 
approved No. 2 broken stone, after which it shall be compacted with 
a self-propelled roller weighing approximately 10 tons; during the 
rolling process, additional No. 2 broken stone shall be applied and 
broomed about until the voids in the No. 3 stone are entirely filled. 2 
The rolling shall be continued until the course of stone is thoroughly 

1 Hand spreading from pots or hods is more satisfactory for the first coat but not 
for the flush coat. 

2 Too much rolling is injurious while the oil is hot; better results are obtained by- 
waiting till the next day to compact; the course should be rolled early in the morning 
for 10 days and gradually hardened down. 



434 SPECIFICATIONS ■ 

compacted and its surface is true and even to the established grade 
and conforms in all respects to the requirements specified for finish- 
ing and testing the surface of "Top Course Bituminous Macadam, 
Mixing Method — Type i." 

52.3. After this portion of the work shall have been completed 
to the satisfaction of the Engineer, all loose stone shall be swept 
from the surface and a sealing coat of one-half gallon of bituminous 
material per square yard shall be applied by means of an approved 
pressure distributor. After this it shall be immediately covered 
with approved No. 1 broken stone, spread and broomed about by 
experienced workmen, and again rolled; the rolling shall be continued 
and additional No. 1 stone shall be applied until a smooth, uniform 
surface is produced. 

52.4. Before being opened to traffic a layer of No. 1 broken stone 
approximately one-half inch thick shall be spread loose on the surface 
for wearing course. 

52.5. The quantity to be paid for under this item shall be the 
number of cubic yards of compacted material in place in the com- 
pleted course. The amount to be estimated shall be computed by 
multiplying the finished cross-section of the top course, as shown upon 
the plans or ordered by the Engineer, by the length of the top course 
measured along the axis of the pavement. 

The price bid shall include the heating and placing of the bituminous 
material, the furnishing, placing, rolling and filling of the broken 
stone, and all labor, materials, and incidental expenses necessary 
to complete the top course. 

This item shall not include the furnishing and delivery of the bi- 
tuminous material; such furnishing and delivering will be paid for 
under the item covering such material. 

No. 1 broken stone or gravel, chips or screenings remaining loose 
on the surface after the work is completed shall not be estimated 
as a part of the depth of the top course, but payment for these shall 
be included in the price bid for item 52. 

Item 53 — Top Course — Bituminous Macadam — Mixing 
Method. Type 1 

53.1. Under this item the Contractor shall construct a top course 
of broken stone mixed with a bituminous material, upon a previously 
constructed bottom course of concrete, broken stone, quarry or 
field stone, or gravel. The surface laid shall be in conformity with 
the lines and grades shown upon the plans or ordered by the Engineer. 
A smooth finished surface will be insisted on free from irregularities 
and waviness. The entire top course shall consist of a wearing course 
finished over with a flush or sealing coat. 

53.2. The broken stone used in this course shall be of approved 
material. When the top course is to be 2 inches or less in thickness 
in the completed work, the stone shall be of No. 2 size. When the 
top course is to be over 2 inches in thickness in the completed work, 
No. 2 and No. 3 stone shall be used, proportioned as directed by the 
Engineer. The sealing coat therefor shall be of stone of No. 1 size. 



BITUMINOUS MACADAM 435 

53.3. Gravel of approved quality and corresponding to the same 
sizes as broken stone may be used in the top course. If used, it 
shall conform to the general requirements for broken stone and gravel 
for water-bound and bituminous macadam work. 

53.4. The broken stone for the wearing course shall be heated, 
before entering the mixer, to between 225 degrees Fahrenheit and 
300 degrees Fahrenheit in revolving dryers of an approved type. The 
stone shall be continuously agitated during the heating. 

53.5. The bituminous material to be used in this course shall 
conform with the specifications for "Bituminous Material A for 
Mixing Method — Type I." 

53.6. The bituminous material shall be heated in kettles so 
designed as to admit of even heating of the entire mass, with an 
efficient and positive control of the heat at all times. Bituminous 
material "A" shall be heated as directed to a temperature between 
275 degrees Fahrenheit and 350 degrees Fahrenheit; all material 
heated beyond 350 degrees Fahrenheit, either before or during 
mixing with the broken stone, shall be rejected. Bituminous material 
"T" shall be heated as directed to a temperature between 200 degrees 
Fahrenheit and 275 degrees Fahrenheit; all bituminous material "T" 
heated beyond 275 degrees Fahrenheit either before or during mixing 
with the broken stone, shall be rejected. No tar shall be heated 
in kettles containing any asphalt cement, and no asphalt cement 
shall be heated in kettles containing any tar; before changing from 
one type of material to the other, kettles shall be scrupulously 
cleaned in order to avoid mixtures of the two; any such Mixtures 
shall be rejected. 

53.7. When thoroughly heated to the proper temperatures, the 
bituminous material and the broken stone for the wearing course 
shall be mixed as directed from time to time, using approximately 
18 gallons of bituminous material per cubic yard of loose stone. 
(The amount of bitumen in the completed work shall be from 5 to 

7 J per centum of the total weight of the completed course.) The • 
Contractor shall provide approved means for accurately propor- 
tioning the mixture. Excess of bituminous material shall be pre- 
vented; and any such excess shall be cause for rejection of the course 
unless satisfactorily corrected previous to laying. The mixer used 
shall be of satisfactory design, having revolving blades and efficient 
means for keeping the temperature at the desired point without burn- 
ing the liquid. The mixing shall continue until every particle of 
the broken stone is thoroughly coated with the bituminous material 
and a uniform mixture has been obtained, which when discharged 
shall have a temperature between 200 degrees and 300 degrees 
Fahrenheit for bituminous material "A" and between 200 degrees 
and 250 degrees Fahrenheit for bituminous material "T." 
The use of batteries of small batch mixers will not be allowed. 

53.8. The bituminous mixture, heated and prepared as specified 
above, shall be delivered from the mixer to the point of deposition 
in the pavement, if at a considerable distance, in suitable trucks or 
wagons, provided with canvas covers for retaining the heat. To 
prevent undue compacting on long hauls, partitions may be required 



436 SPECIFICATIONS 

for large truck loads. As delivered, the mixture shall have a tempera- 
ture of at least 150 degrees Fahrenheit. Material having a lower 
temperature than this shall not be laid in the pavement. The mix- 
ture shall be immediately spread over the foundation course by men 
experienced in such work, so that when rolled it shall have the required 
thickness and shall be free from surface depressions and irregularities. 
The paving shall be done as continuously as practicable, to reduce 
to a minimum the number of joints between hot and cold materials. 
Such joints shall be constructed in an approved manner. The hot 
paving mixture shall not be dumped in large masses on the bottom 
course. It shall be dumped upon platforms and shoveled with hot 
shovels into position in the pavement. 

53.9. The wearing course, placed as above specified, shall be 
rolled at once, while the material is still warm and pliable, beginning 
at the edges and working toward the center. Acceptable means 
shall be provided to prevent the asphalt from sticking to the roller. 
Rolling shall continue without interruption until all roller marks 
disappear and the surface shows no further compressibility. Places 
which the roller cannot effectively reach shall be compressed with 
hot iron tamps. 

53.10. As soon as possible after the compacting of the wearing 
course, when the surface is clean and dry, a sealing coat of hot bitu- 
minous material "A" shall be evenly spread over the wearing course 
by means of approved pressure distributors. The bituminous 
material "A" shall be applied at a temperature not less than 275 
degrees Fahrenheit nor more than 350 degrees Fahrenheit, at a rate 
of \ to f gallon per square yard, as directed. A thin and uniform 
layer of dry, clean No. 1 stone shall be immediately spread over the 
bituminous material "A" by machines or skilled workmen, sufficient 
to more than take up all' the excess bituminous material "A." The 
spreading of the No. 1 stone shall not lag more than 20 feet behind 
the placing of the asphalt coating. The pavement shall then be 
again thoroughly rolled. The surface of the wearing course shall be 
kept scrupulously clean until the sealing coat is applied. The Con- 
tractor shall not permit any hauling over the surface before the com- 
pletion of the sealing coat. 

53.11. Before placing the sealing coat, the pavement shall be tested 
with a ten foot straight edge laid parallel with the center line of the 
pavement, and any depressions exceeding one-half inch shall be satis- 
factorily eliminated or the pavement relaid. 

53.12. Rollers used for the bituminous wearing course and the 
sealing coat shall be well balanced, self-propelled rollers of satis- 
factory design, weighing between eight and ten tons. They shall 
give a compression under the rear roller of between 200 and 350 
pounds per linear inch of roll, and shall be provided with an ash pan 
which shall prevent ashes from dropping upon the pavement. 

53.13. No top course bituminous material shall be mixed or placed 
between October 15 and May 15 except by written permission of the 
Engineer, nor when the air temperature in the shade is below 50 
degrees Fahrenheit, nor when the foundation is damp or otherwise 
unsatisfactory. 



BITUMINOUS MACADAM 437 

53.14. The Contractor shall provide a sufficient number of accu- 
rate, efficient thermometers for determining the temperatures of the 
bituminous material and the broken stone at all stages of the work. 

53.15. The quantity to be paid for under this item shall be the 
number of square yards of compacted material in place in the com- 
pleted course. The amount to be estimated shall be computed by 
multiplying the finished width of the top course as shown upon the 
plans or ordered by the Engineer, by the length of the top course 
measured along the axis of the pavement. 

The price bid shall include the furnishing (bituminous material 
excepted), the heating, placing, rolling and compacting of all ma- 
terials, together with all other labor and incidental expenses neces- 
sary to satisfactorily complete the work. 

The furnishing of the bituminous material will be paid for under 
the appropriate item therefor as shown on the proposal sheet. 

Item 54 — Top Course — Bituminous Macadam — Mixing 
Method. Type 2 

54.1. Under this item the Contractor will be required to construct 
a top course consisting of a compacted mixture of broken stone, sand 
and bituminous material "A" laid to conform to the required grade 
and cross-section, as shown on the plans and ordered by the Engineer. 

54.2. Broken stone for this course shall be of the character specified 
all of which shall pass a one-half-inch screen and shall be so graded 
that when combined in a bituminous mixture containing not less 
than thirty (30) per centum of the sand specified in section 54.3 it 
shall produce a bituminous mixture coming within the limits speci- 
fied in section 54.8. 

54.3. The sand shall be clean, hard grained and sharp. It shall 
all pass a ten (10) mesh screen, and shall contain at least fifteen (15) 
per centum of material retained on a forty (40) mesh screen and 
at least twenty (20) per centum of material that will pass an eighty 
(80) mesh screen except as hereinafter provided for. If the sand 
does not contain the required amount of fine material, approved 
stone dust may be added to make up the deficiency. 

54.4. The bituminous material to be used in this course shall 
conform with the specifications for bituminous material "A" for 
Type 2. 

54.5. The broken stone and sand shall be heated as directed, 
before entering the mixer, to between 225 degrees Fahrenheit and 
325 degrees Fahrenheit in revolving dryers of an approved type. 
The broken stone and sand shall be continuously agitated during 
the heating. 

54.6. The bituminous material shall be heated in kettles so designed 
as to produce an even heating of the entire mass, with an efficient 
and positive control of the heat at all times. It shall be heated as 
directed to a temperature between 275 degrees Fahrenheit and 350 
degrees Fahrenheit. If heated beyond 350 degrees Fahrenheit 
either before or during the mixing with the broken stone it shall be 
rejected. 



438 SPECIFICATIONS 

54.7. The Contractor shall provide a sufficient number of accurate, 
efficient, stationary thermometers for determining the temperature 
of the asphalt cement in the kettles. 

54.8. When thoroughly heated to the temperature directed, the 
bituminous material and the broken stone and sand shall be mixed 
in the following proportions by weight : 

Bitumen from 7 to n % 

Mineral aggregate, passing 200 mesh from 7 to n % 

Mineral aggregate, passing 40 mesh from 45 to 55 % 

Mineral aggregate, passing 10 mesh from 16 to 25 % 

Mineral aggregate, passing 4 mesh from 8 to 15 % 

Mineral aggregate, passing 2 mesh less than 10% 

the sieves being used in the order named. A mixer shall be used, 
having revolving blades, and so designed and operated as to produce 
and discharge a thoroughly coated and uniform mixture of non- 
segregated broken stone, sand and bituminous material. When 
discharged the mixture shall have a temperature not more than 325 
degrees Fahrenheit and not less than 225 degrees Fahrenheit as 
directed. 

54.9. All defective areas in the cement concrete foundation shall 
be repaired as directed at least ten (10) days in advance of lay- 
ing the bituminous concrete. Before laying the bituminous 
concrete the surface of the foundation shall be dry and thoroughly 
cleaned. 

54.10. The mixture heated and prepared as specified in section 
54.8, shall be delivered direct from the mixer to the point of deposi- 
tion on the foundation in trucks or wagons, provided with canvas 
covers for retaining the heat. As delivered, the bituminous concrete 
shall have a temperature of at least 200 degrees Fahrenheit: material 
having a lower temperature than this shall not be laid upon the 
foundation. Before the mixture is placed, all contact surfaces of 
curbs, edgings, manholes, etc., shall be well painted with hot asphalt 
cement. The hot mixture shall be dumped upon platforms, con- 
structed as directed, and shoveled with hot shovels into position 
on the foundation. It shall be immediately spread as directed 
over the foundation course by men experienced in such work, 
so that when rolled it shall have at no place less than the required 
thickness and shall be free from surface depressions and irregularities. 
Joints between hot and cold materials shall be constructed as di- 
rected. The paving shall be done as continuously as practicable, to 
reduce to a minimum the number of such joints. 

54.11. Rollers used on the bituminous concrete shall be well 
balanced, self-propelled, tandem rollers, weighing between seven 
(7) and eight (8) tons each. Each shall have a compression under 
the rear roller of between two hundred (200) and three hundred (300) 
pounds per linear inch of roll, and shall be provided with an ash pan 
which shall prevent ashes from dropping into the bituminous con- 
crete or sealing coat. 

54.12. The surface of the top course shall be tested with a ten 
(10) foot straight edge laid parallel with the center line of the road 



BITULITHIC PAVEMENT 439 

upon any portion of the surface, and any depression or other irregu- 
larity exceeding one-half (i) inch \_\" is a better limit] shall be satis- 
factorily eliminated as directed. 

54.13. After the pavement has been satisfactorily finished and has 
thoroughly dried out, Portland cement shall be dusted over the sur- 
face in a quantity sufficient to form a complete film over all parts of 
the pavement. This film shall remain undisturbed by rain or other- 
wise until it has set; in case of disturbance before setting, it shall be 
renewed. 

54.14. No top course material shall be mixed or placed between 
October 15th and May 15th, except by written permission of the 
Engineer, nor when the air temperature in the shade is below 50 
degrees Fahrenheit nor when the foundation is damp or otherwise 
unsatisfactory. 

54.15. The quantity to be paid for under this- item shall be the 
number of square yards of compacted material in place in the com- 
pleted pavement. The amount to be estimated shall be computed 
by multiplying the width of top course as shown on the plans or 
ordered by the Engineer, by the length of the top course measured 
along the axis of the road. 

The price bid for this item shall include the furnishing of the sand; 
the furnishing, crushing and screening of the broken stone; the heat- 
ing, mixing, placing and rolling of the broken stone, sand and bitu- 
minous material, and the cement film and all work and expense in- 
cidental to the completion of the work except the furnishing of the 
bituminous material, which shall be paid for under the item Bitu- 
minous Material "A" for Mixing Method, Type 2. 

Item 55 — Bitulithic Pavement 

55.1. Under this item the Contractor shall furnish the necessary 
stone, bituminous material, machinery, labor and other equipment, 
and shall construct upon a properly prepared foundation a bitulithic 
pavement composed of an accurately proportioned aggregate of 
carefully graded broken stone properly heated and mixed with sep- 
arately heated Warren's Puritan Brand bitulithic cement, placed 
and rolled and covered with Warren's quick drying bituminous flush 
coat composition, followed by two coats of hot stone chips thoroughly 
rolled into the surface. 

55.2. The several grades and sizes of mineral aggregate shall be 
accurately measured in proportions previously determined by labora- 
tory tests to give the best results; that is, the most dense mixture 
of mineral aggregate and one having inherent stability; heated in a 
rotary mechanical heater so designed as to keep each batch by itself 
until heated, or after heating the stone in a rotary mechanical heater 
to a temperature of about 250 degrees Fahrenheit, it shall be ele- 
vated and passed through a rotary screen, having sections with various 
sized openings. The difference in the width of openings in successive 
sections shall not exceed one-fourth (\) inch in sections having open- 
ings smaller than one-half (|) inch, and shall not exceed one-half 
(i) inch, in sections having openings greater than one-half (J) inch. 



440 SPECIFICATIONS 

The several sizes of stone thus separated by the screen sections shall 
pass into a bin containing sections or compartments corresponding 
to screen sections. From these compartments the stone shall be 
drawn into a weighing-box, resting on a scale having seven beams. 
The stone from these compartments shall be accurately weighed, 
using the proportions which have been previously determined by 
laboratory tests to give the best results; that is, the most dense 
mixture of mineral aggregate, and one having inherent stability. 
If the crushed stone in the wearing course does not provide the best 
proportions of fine-grained particles, such deficiency must be sup- 
plied by the use of not to exceed 25 per centum hydraulic cement, 
pulverized stone, or very fine sand. 

55.3. The mineral aggregate, composed of differing sizes accurately 
measured or weighed as above, shall pass into a "twin pug," or other 
approved form of- mixer. In this mixer shall be added a sufficient 
quantity of Warren's Purilan Brand, bituminous water-proof cement, 
or bitulithic cement, to thoroughly coat all the particles of stone and 
to fill all voids in the mixture. The bituminous cement shall, before 
mixing with the stone, be heated to between 200 degrees and 250 
degrees Fahrenheit, and the amount used in each batch shall be 
accurately weighed and used in such proportions as have been pre- 
viously determined by laboratory tests to give the best results — 
that is, to coat all particles of stone and fill the voids in the mineral 
aggregate. The mixing shall be continued until the combination is 
a uniform bituminous concrete. In this condition it shall be hauled 
to the street, and there spread on the prepared foundation to such 
a depth that, after thorough compression with a steam road roller, 
it shall have a thickness of two (2) inches. The proportioning of 
the varying sizes of stone and bituminous cement shall be such, that 
the compressed mixture shall, as closely as practicable, have the 
density of solid stone. 

55.4. After rolling the wearing surface, there shall be spread over 
it, while it is still warm, a thin coating of Warren's Quick Drying 
Bituminous Flush Coat Composition, by means of a suitable flush 
coat spreading machine, so designed as to spread quickly over the 
surface a uniform thickness of flush coat composition. This spread- 
ing machine shall be provided with a flexible spreading band and an 
adjustable device for regulating, to any desired amount, the quantity 
and uniformity of flush coat composition to be spread. 

There shall be spread over the flush coat composition, in at least 
two coats, fine particles of hot crushed stone, in sufficient quantity 
to completely cover the surface of the pavement. These stone chips 
shall be spread by means of a suitable stone spreading machine, so 
designed as to provide a storage receptacle of at least five (5) cubic 
feet capacity and to rapidly and uniformly cover the surface of the 
pavement with the desired quantity of stone. This spreading 
machine shall be provided with an adjustable attachment for regu- 
lating uniformly the quantity of stone spread at each operation. 
The hot stone chips shall be immediately and thoroughly rolled into 
the surface until it has become cool. The purposes of the flush coat 
composition and the fine particles of hot crushed stone are to not 



AMIESITE PAVEMENT 441 

only fill any unevenness in the surface, but also to make the surface 
waterproof and gritty, thus providing a good foothold for horses. 

On grades a mineral flush coat may be used in place of the liquid 
flush coat. 

55.5. Warren Bros., owners of the patents used in the construc- 
tion of Bitulithic pavement, have filed with the State Commission 
of Highways a properly executed binding agreement to furnish any 
contractor to bid for the work all the necessary surface material 
mixed and ready for use, and bituminous flush coating cement 
necessary for coating the wearing surface, delivered on wagons of 
the Contractor at the mixing plant (which will be located within 
three miles of the point of use) at a stipulated price per square yard 
for each contract. Such price for Bitulithic pavement mixture and 
flush coating composition will include a license to use all the patents 
required in the construction of the pavement as herein specified. 

The filing of a bid under these specifications will be construed as 
an acceptance of the terms of the license agreement filed by the 
Warren Bros. Company, at the price fixed in said agreement, which 
is on file with the secretary of the Commission. 

55.6. The quantity of pavement to be paid for under this item 
shall be the number of square yards of Bitulithic pavement placed 
in accordance with the plans, or as directed by the Engineer. The bid 
price shall include the furnishing and placing of all materials, the 
mixing, spreading, rolling and all labor and incidental expenses 
necessary to complete the work. 

GENERAL SPECIFICATIONS FOR AMIESITE 
PAVEMENT 

Foundation. The excavation, filling or embankment, drainage 
and rolling of the sub-base shall be in full accordance with the stand- 
ard specifications for street or highway paving before placing the 
foundation, the depth and nature of which is governed by existing 
conditions of the sub-grade. 

The foundation, whether in re-surfacing or new work, shall be, 
before applying the Amiesite, even and compact and swept clean 
of all loose dirt and foreign material. New stone, if put on, shall 
be thoroughly bonded with screenings, sprinkled and rolled hard 
and uniformly. The foundation must be uniform and be brought 
up to a true and even grade, parallel to and inches below the ele- 
vation of the finished surface of the street or road. 

Application. The bottom course shall be spread in a uniform 
layer, using blocks or strips to insure an even distribution, then 
rolled. (Size) Stone used in Amiesite Bottom Course-Graded — 
|" to ii". If any depressions appear, due to foundation not being 
firm or any other reason, they must be filled with Amiesite and 
rolled until surface is even and to grade desired. 

After the preliminary rolling, the Amiesite top course, made of 
stone graded from \" to \" in size, shall be applied, not less than one 
inch (1") deep, loose measurement, and raked to an even depth so as 
to cover the underlying Amiesite and fill the voids. In no case 



442 SPECIFICATIONS 

shall the bottom course be spread over 300' in advance of the top 
course, nor shall over 50' be left uncovered during the night. 

The compressed depth of finished Amiesite surface shall be: Pref- 
erably not less than 2\ inches. 

Rolling. After the top course has been evenly spread to a true 
grade, the surface shall be rolled with a standard ten ton road roller 
until the material is thoroughly compacted and ceases to creep in 
front of the roller. In rolling the roller must start from the side- 
lines of the street or road and work towards the center. Care must 
be taken that the shoulders are firm and solid, as otherwise the surface 
will iron out to a feather edge and crack. No rolling shall be done 
unless the Amiesite is free from water. 

Surface Finish. After rolling as called for above, clean, sharp sand 
or stone dust (Lines tone where obtainable) shall be spread in a thin 
layer and the road may then be immediately thrown open to traffic. 

General. No Amiesite shall be spread when the road-bed con- 
tains depressions holding water. The Amiesite must at all times 
be kept clean. Dirt or other foreign material must not be allowed to 
mix with, under, or on the Amiesite while being unloaded from cars, 
spread and rolled. 

Should the bottom course become coated or partly coated with 
dust or dirt before the top course can be applied, the part thus coated 
must be swept and then given a light application of bituminous 
cement, that can be applied in a thin coating from a sprinkling pot so 
constructed that a thin and uniform application can easily be applied. 

The Amiesite may be steamed to facilitate its unloading from the 
cars. Steam pressure shall not exceed fifteen pounds to the square 
inch. The Amiesite should not be steamed more than fifteen minutes 
in any one place. This shall be done under the supervision of the 
inspector in charge. 

The Amiesite shall be unloaded from wagons upon iron sheets or 
boards, so as to insure the material being kept clean and being spread 
uniformly. 

Cross rolling shall be done, when ordered, to equalize the bond 
and prevent waves in the surface. Care must be taken that the 
bottom course is not rolled down hard before the top course is applied. 

The finished surface of the Amiesite after rolling shall be kept \" 
higher than any permanent elevation, depending upon the traffic to 
ultimately compress or pound it down to grade. 

Grading slopes or shoulders shall not be carried on after the Amie- 
site course is started until completion of roadway. 

The street or road shall be closed to traffic when the Amiesite 
surface is being applied. 

Item 56 — Hassam Compressed Concrete Pavement 

56.1. Under this item the Contractor shall furnish all materials 
for and place upon a properly prepared sub-grade or sub-bottom 
course Hassam Compressed Concrete Pavement of the thickness 
shown upon the plans or ordered by the Engineer. 

56.2. Hassam Compressed Concrete Pavement will be placed on the 



AMIESITE PAVEMENT 443 

sub-grade or on the sub-bottom course and shall not be placed until 
these are in first-class condition as required for macadam pavement. 

56.3. Hassam Compressed Concrete Pavement shall consist of 
a graded No. 3 and No. 4 stone, of an approved quality, spread evenly 
and gauged by the use of cubical blocks; after rolling and thoroughly 
compacting with a 10-ton roller, it shall have the required depth and 
shall conform to the established lines, grades and cross-sections. 
Where any depressions or irregularities develop in rolling the surface 
shall be forked over and material added or taken away to the end that 
a smooth surface shall be provided after re-rolling. 

56.4. After the rolling has been satisfactorily completed and the 
surface of the broken stone has been brought to the required uni- 
form surface, and before there is any displacement of the stone, the 
voids shall be filled with a grout consisting of one part Portland 
cement and two parts of approved sand. The sand shall be of 
such sizes that it will not separate readily from the cement, when 
placing the grout, and any batch of grout, when being placed, shall 
at all times be of a uniform product and of such consistency that it 
will flow readily but shall not be so wet as to cause a separation of 
the cement and sand. The rolling shall be continued during the 
process of grouting and until all the voids are filled. 

56.5. The grout shall be mixed in a Hassam Grout Mixer or other 
mechanical mixer which will properly mix the ingredients and from 
which they can be deposited without a separation of the cement and 
sand. 

56.6. Immediately after the voids shall have been filled with grout, 
a thin layer of No. 1 broken stone or fine aggregate shall be spread 
over the entire surface and rolled until the grout flushes to the surface. 

56.7. After placing the surface stone the surface shall not be worked 
upon or disturbed for a period of ten days, during which time the 
surface shall be kept thoroughly wet. 

56.8. Any cracks either longitudinal or transverse which develop 
before the acceptance of the work shall be thoroughly cleaned out 
and filled with acceptable bituminous material. 

56.9. The quantity to be paid for, under this item, shall be the 
number of cubic yards of Hassam Compressed Concrete Pavement 
incorporated in the work in accordance with the plans or as directed 
by the Engineer. 

The price bid shall include the furnishing and placing of all 
materials, all grouting, rolling, forms and all labor, appliances, 
royalties and incidental expenses necessary to complete the work. 
The amount to be estimated shall be computed by multiplying the 
cross-section of concrete pavement as shown upon the plans or ordered 
by the Engineer, by the total length of pavement measured along 
the axis of the pavement. 

Item 57 — Cement Concrete Pavement 

57.1. Under this item the Contractor shall furnish and place upon 
a properly prepared sub-grade or sub-bottom course, concrete pave- 
ment of the thickness shown upon the plans or ordered by the 
Engineer. 



444 SPECIFICATIONS 

57.2. Concrete pavement will be placed on the sub-grade or on the 
sub-bottom course, and shall not be placed until these are in first- 
class condition, as required for macadam pavement. 

57.3. Concrete shall consist of a mixture of Portland cement, 
No. 1 sand, and broken stone or gravel. All these materials 
shall conform in all respects to the requirements given under 
"Materials of Construction," and all the specifications relating 
to first-class concrete shall apply to work done under this item, 
in so far as same are not inconsistent with the special specifications 
given below. 

57.4. The concrete shall be mixed in the proportions of one volume 
of cement to four and one-half volumes of sand and broken stone or 
gravel. The volumes of sand and broken stone or gravel, shall be 
measured separately in approved hoppers. The relative proportions 
of fine and coarse aggregate will be varied slightly, as a result of 
tests for voids by the Engineer, to the end that resulting concrete 
shall be as dense as possible. The concrete shall in all cases approxi- 
mate at 1: 1 J: 3 mix. 

57.5. The coarse aggregate shall consist of a well-mixed product 
of No. 2 and No. 3 stone or No. 1 and No. 2 gravel. Gravel shall 
not be used except when it has been submitted by the Division 
Engineer to the Bureau of Tests, has been approved by the Bureau 
of Tests, and its use has been approved by the First Deputy Com- 
missioner in writing, — and then only under the restrictions laid 
down under "Materials of Construction." The fine aggregate shall 
consist of No. 1 sand. 

57.6. The concrete shall be mixed in approved mechanical batch 
mixers. Mixing shall be continued through at least 12 revolutions 
and until every particle is coated with mortar and until the batch is 
of uniform color and consistency. After the materials are once 
wetted the work shall proceed rapidly until the concrete is in place. 
The quantity of water used shall be as directed by the Engineer and 
suitable measuring tanks shall be provided by the Contractor so 
that the same amount of water may be used in the separate batches. 
No concrete pavement shall be laid when the temperature falls 
below 35 F. 

57.7. Substantial forms shall be placed along the edge of the con- 
crete pavement and shall be set and held true to line and grade. 

57.8. Before any concrete is placed, the sub-grade shall be sprinkled 
sufficiently to dampen it but a muddy condition shall not be allowed. 
As soon as possible after mixing, the concrete shall be deposited in 
place and thoroughly spaded and screeded so as to bring the mortar 
flush to the surface. Especial care shall be taken to keep the con- 
crete uniform and to prevent pockets of stone or mortar. 

57.9. Heavy screeds cut to the lines required for the finished 
surface and resting upon the side forms shall be used for consolidat- 
ing and screeding the concrete, and the surface, when completed, 
shall conform to the lines and grades shown upon the plans, and 
shall be free from depressions or irregularities. No stone shall pro- 
ject above the general surface. All shaping and screeding shall be 
done before the concrete has taken its initial set. Any concrete 



CONCRETE PAVEMENT 445 

which has not been shaped and finished previous to the time of initial 
set, shall be removed for the full depth of the roadway and replaced 
with satisfactory concrete. 

57.10. If a satisfactory finish cannot be obtained with the screed, 
the screeding shall be immediately followed, and before the cement 
has taken its initial set, by rubbing down with a wooden float. The 
men employed for this work shall be competent and experienced and 
shall work from a platform which rests on the forms or shoulders. 
The surface, when finished, shall be such that no water will stand on 
the finished pavement. It shall then be slightly roughened by 
brooming. 

57.11. As soon as the concrete has taken its initial set the surface 
shall be covered with a one-inch layer of sand or other suitable 
material of which the shoulders are to be constructed and this shall 
be thoroughly sprinkled every morning and night, and more often 
if necessary, so that it will be kept moist for a period of ten days 
after placing; the material shall then be cleaned from the surface and 
the road may be opened to traffic if so directed by the Engineer. 

57.12. The concrete shall be deposited in sections 30 feet in length, 
and at the end of each section expansion joints of the type shown on 
the plans shall be placed. After starting any section, an effort shall 
be made to complete it at one operation. If for any reason this cannot 
be done, a vertical joint shall be made when the work is stopped and 
the work completed up to this joint. 

57.13. Any cracks, either longitudinal or transverse, which develop 
before the acceptance of the work, shall be thoroughly cleaned out 
and filled with acceptable bituminous material. 

57.14. The quantity to be paid for under this item shall be the 
number of cubic yards of concrete pavement incorporated in the work, 
in accordance with the plans or as directed by the Engineer. 

The price bid shall include the furnishing and placing of all 
materials; all mixing, screeding, finishing, forms, expansion joints 
and all labor, appliances and incidental expenses necessary to com- 
plete the work. The amount to be estimated shall be computed 
by multiplying the cross-section of concrete pavement as shown upon 
the plans or ordered by the Engineer by the total length of pavement 
measured along the axis of the pavement. 

Item 58 — Lignin or Sulphite Liquor 

58.1. Under this item the Contractor shall furnish and apply lignin 
or sulphite binder at the rate of one-half gallon of binder (not of 
the mixture) to the square yard. 

58.2. A quart sample, from each carload of the material to be 
used, shall be submitted to the Bureau of Tests for acceptance before 
it may be used. 

This material shall be a neutral or basic liquor secured by the 
extraction of lignin from organic matter. It shall be concentrated 
by evaporation at a temperature not exceeding 210 degrees Fahren- 
heit until it has a specific gravity at 77 degrees Fahrenheit of not 
less than 1.23. When concentrated to a constant weight at 212 



446 SPECIFICATIONS 

degrees Fahrenheit, it shall have a residue of not less than 45 per 
cent. It shall contain not more than 9 per cent of ash. It shall 
be 99.5 per cent soluble in cold water. 

58.3. After the road has been thoroughly filled and brought to a 
puddle with water, the application of lignin or sulphite binder shall 
commence and the puddle continued, using a mixture of one part 
binder to not less than three parts water. This puddling shall con- 
tinue until the road has received at treatment for its full width of 
one-quarter gallon of the lignin (not of the mixture) to the square 
yard. After the roadway has set, but not entirely dried out, the 
balance of one-quarter gallon of the lignin to the square yard shall 
be applied to 80 per cent of the width of roadway, using a mixture 
of one part lignin to two parts water. 

58.4. Lignin or sulphite binder shall be applied to the roadway 
by means of an improved sprinkler which can be regulated so that a 
uniform distribution is obtained and so that not over one-half of the 
required amount of binder shall be spread to the square yard on each 
trip of the sprinkler. The sprinkler shall be equipped with necessary 
brooms so arranged as to sweep forward any excess material that 
does not immediately penetrate into the surface. 

58.5. The quantity of material to be paid for under this item 
shall be the actual number of gallons of lignin binder, measured 
before dilution, actually applied and incorporated in the work to the 
satisfaction of the Engineer. Binder that has been wasted or that 
has been applied not in accordance with the requirements of this 
specification or the orders of the Engineer, shall not be included 
in this item for payment. The price bid shall include the cost of 
furnishing, hauling, applying and all necessary appliances and 
expenses incidental thereto. 

Item 59 — Wood Block Pavement 

59.1. Under this item the Contractor shall furnish and place upon 
a properly prepared foundation wood block of the quality specified 
where shown upon the plans or ordered by the Engineer. 

This pavement shall be placed upon the old macadam, old concrete 
pavement, new concrete foundation or on other foundation as shown 
on the plans and ordered by the Engineer. 

59.2. The blocks shall be from 6 to 9 inches long and shall average 
8 inches; they shall be 3 inches in depth and from 3 to 4 inches in 
width; but all blocks in one piece of pavement shall be of uniform 
width. No variation greater than -j^-inch shall be allowed in the 
depth and |-inch in the width of the blocks. 

59.3. Blocks shall be made from Southern yellow pine, North 
Carolina pine, Norway pine, black gum or tamarack; only one kind 
of wood, however, shall be used in one piece of pavement. 

Yellow pine block shall be made from what is known as Southern 
yellow pine, well manufactured, full size, saw butted, all square 
edges, and shall be free from the following defects: 

Unsound, loose and hollow knots, worm holes and knot holes, 
through shakes and round shakes that show on the surface. In 



WOOD BLOCK 447 

yellow pine timber the annular rings shall average not less than six 
to the inch and shall be in no case less than four to the inch, measured 
radially. 

Norway pine, gum, North Carolina pine and tamarack block shall 
be cut from timber that is first-class in every respect, and shall be 
of the same grade as that defined for the Southern yellow pine. 

59.4. The creosote oil with which the blocks shall be treated shall 
conform to either of the following specifications, designated as "A" 
and "B." 

The preservative to be used under this specification shall be a 
product of coal gas, water gas or coke oven tar, which shall be free 
from all adulterations and contain no raw or unfiltered tars, petro- 
leum compounds, or tar products obtained from processes other 
than those stated. 

Specification "A" 

The specific gravity shall not be less than one and eight-hundredths 
(1.08) nor more than one and fourteen hundredths (1.14) at a tem- 
perature of thirty-eight (38) degrees centigrade. 

Not more than three and one-half (3^) per centum shall be insol- 
uble by continuous hot extraction with benzol and chloroform. 

On distillation, which shall be made exactly as described in Bul- 
letin 65 of the Railway Engineering and Maintenance of Way As- 
sociation, the distillate, based on water free oil, shall not exceed 
one-half (J) of one (1) per centum at one hundred and fifty (150) 
degrees centigrade, and shall not be less than thirty (30) nor more 
than forty (40) per centum at three hundred and fifteen (315) degrees 
centigrade. 

The oil shall contain not more than three (3) per centum of water. 

Specification "B" 

It shall be completely liquid at thirty-eight (38) degrees centigrade, 
and shall have a specific gravity at that temperature of not less than 
one and three hundredths (1.03) nor more than one and eight hun- 
dredths (1.08). 

It shall contain not more than two (2) per centum of matter in- 
soluble by hot extraction with benzol and chloroform. 

On distillation, which shall be made exactly as described in Bulle- 
tin No. 65 of the American Railway Engineering and Maintenance 
of Way Association, the distillate based on water free oil shall be 
within the following limits: 

At 210 degrees centigrade, not more than 5 per centum. 

At 235 degrees centigrade, not more than 35 per centum. 

At 315 degrees centigrade, not more than 85 per centum. 

The oil shall yield a coke residue not exceeding three (3) per 
centum. 

The distillate, between 210 degrees centigrade and 235 degrees 
centigrade, shall yield solids on cooling to 15 degrees centigrade. 
The preservative shall contain not more than 3 per centum of water. 

59.5. The manufacturer of the oil shall permit full and complete 
inspection and sampling at the factory at which the oil is produced, 



448 SPECIFICATIONS 

of all materials either crude or refined, entering into the manufacture 
of the finished product itself, in order that the materials used can 
be determined to be in accordance with the foregoing requirements. 
He shall also submit satisfactory proof of the origin of all materials 
entering into the composition of the finished product. 

Samples of the preservative taken by the inspector from the treat- 
ing tank during the progress of the work shall at no time show an 
accumulation of more than 2 per centum of foreign matter, such as 
sawdust or dirt. 

59.6. The blocks shall be treated with the preservative above 
described, so that they shall contain at least sixteen pounds of the 
same per cubic foot of timber. 

The manufacturer of the block shall equip his plant with all neces- 
sary gauges, appliances and facilities to enable the inspector to satisfy 
himself that the requirements of the specifications are fulfilled. 

59.7. Upon the foundation shall be spread a bed of cement mortar 
at no place less than one-half inch in thickness, composed of one 
part Portland cement and four parts sand thoroughly mixed dry. 
This mortar bed shall be struck with a template to a true surface 
exactly parallel to the top of the proposed pavement surface and 
three inches below it. This bed shall be sprinkled, immediately in 
advance of the block laying, with hand sprinklers. 

59.8. On the mortar surface prepared as described, the blocks 
shall be laid with grain vertical and at such angles with the curb 
as the Engineer may direct. The blocks shall be laid in straight 
and parallel courses and set snugly together but not driven together. 
Each course of blocks shall be of uniform width and depth, with end 
joints broken by a lap of not less than two and one-half inches. Only 
whole blocks shall be used except in starting courses, cutting closures, 
or where specially permitted by the Engineer. 

Closures shall be carefully cut and trimmed by experienced men, 
the portion of the blocks used shall be free from defects and the cut 
end shall have a surface perpendicular to the top of the block and 
cut at a proper angle to give a close joint. In laying block the pavers 
must stand on the block previously laid. 

After the laying is completed, defective blocks shall be carefully 
culled out, low blocks raised, the courses carefully aligned and the 
blocks spaced up. The pavement shall then be rolled by a steam 
tandem roller weighing not less than two and one-half tons nor more 
than five tons; the pavement being at the same time lightly sprinkled 
and the rolling continued until a uniform surface is obtained. Upon 
the completion of the rolling any defective blocks shall be removed 
and be replaced with sound blocks, and displaced blocks shall be re- 
aligned. The joints in the pavement shall then be immediately 
filled in the manner hereinafter described. If deemed advisable by 
the Engineer, portions of pavement laid with blocks which have 
become "dried out" shall be sprinkled with water at frequent inter- 
vals before joints of same are filled. 

59.9. After rolling, the blocks shall be flushed with an approved 
bituminous filler heated to at least 300 degrees Fahrenheit, which 
shall be poured over the whole surface and well forced into the joints 



ASPHALT BLOCK PAVEMENT 449 

by rubber squeegees. While the bituminous filler is still hot it shall 
be immediately followed with a thin coating of clean dry sand. 
Before turning traffic onto the pavement a coating of one-half inch 
in thickness of dry screened sand shall be spread over the entire 
surface. 

59.10. The quantity to be paid for under this item shall 
be the number of square yards, including expansion joints, of 
pavement laid in accordance with the plans and as directed by the 
Engineer. 

The price bid shall include the furnishing and placing of the mortar 
bed, wood block, bituminous filier and sand surfacing and all other 
labor and incidental expenses necessary to complete the work. 

Item 60 — Asphalt Block Pavement 

60.1. Under this item the Contractor shall furnish and place 
upon a properly prepared foundation asphalt block of the quality 
specified where shown upon the plans or ordered by the Engineer. 
This pavement shall be placed upon the old macadam, old concrete 
pavement, new concrete foundation or on other foundations as 
ordered by the Engineer and shown upon the plans. 

60.2. The blocks shall be five inches in width, by twelve inches in 
length, by two inches in depth, and a variation of more than one- 
fourth of an inch in length and one-eighth of an inch in width or 
depth from these dimensions will be sufficient ground for rejecting 
any block. 

60.3. The blocks shall consist of the following materials: 
Asphaltic cement. 

Crushed trap rock or other approved crushed rock. 

Inorganic dust. 

The rock used in the blocks must be crushed so that every particle 
will pass a screen of one-fourth of an inch mesh. The blocks shall 
receive a compression in the moulds of not less than one ton per 
cubic inch of material in the blocks, and must weigh not less than 
ten and one-half pounds per block. The blocks shall have a specific 
gravity of not less than 2.40, and after having been dried for twenty- 
four hours at a temperature, of 150 degrees Fahrenheit, they shall 
not absorb more than one per centum of moisture when immersed 
in water for seven days. Whatever the character of the asphalt 
used, the block shall yield not less than six and one-half per centum 
of bitumen, when extracted with carbon bisulphide. 

The inorganic dust, or filler, shall be produced from sound lime- 
stone or other approved material, and shall be powdered to such a 
fineness that all of it shall pass a thirty mesh sieve and not less than 
fifty per centum of it shall pass a 200 mesh sieve. Sufficient inor- 
ganic dust shall be used to give a minimum percentage of voids in 
the block, and provide a sufficient medium for absorbing the asphaltic 
cement. 

60.4. The asphaltic cement shall be composed of natural or oil 
asphalt, and asphaltic oil, as approved. This asphaltic cement shall 
be of acceptable consistency and quality. 



45° SPECIFICATIONS 

The material shall have a specific gravity of at least 0.98 at 77 
degrees Fahrenheit. Its penetration shall be not more than ten mm. 
when tested for five seconds at 77 degrees Fahrenheit, with a No. 2 
needle weighted with 100 grams. When twenty grams are heated 
in a hot air oven in a flat-bottom dish two and one-half inches in 
diameter at 325 degrees Fahrenheit for five hours, the loss in weight 
shall not be more than eight per centum. It shall show an open 
flash point not less than 325 degrees Fahrenheit. Its solubility at 
air temperature in chemically pure carbon disulphide shall be at 
least sixty-six per centum. 

60.5. Upon the foundation shall be spread a bed of the thickness 
shown upon the plans, composed of one part Portland cement and 
four parts sand, thoroughly mixed. 

This mortar bed shall be struck with a template to a true surface, 
exactly parallel to the top of the proposed pavement surface and two 
inches below it. 

This bed shall be sprinkled immediately in advance of the block 
laying with hand sprinklers. 

The blocks shall be laid while the mortar is fresh and before it 
has taken its initial set. All depressions and other irregularities in 
the surface shall be corrected by the Contractor immediately. 

The blocks shall be laid by the pavers standing upon the blocks 
already laid and not upon the bed of mortar. 

The blocks shall be laid at right angles with the line of the street, 
and in such a manner that all longitudinal joints shall be broken by 
a lap of at least four inches. The blocks shall be so laid as to make 
the lateral joints as tight as possible, consistent with keeping a 
good alignment of the courses across the street. When thus laid 
the blocks shall be immediately covered with clean, fine sand, per- 
fectly dry, and screened through a one-eighth inch screen. This 
sand shall be spread over the surface and swept into the joints and 
be allowed to remain on the pavement not less than thirty days or 
for such time as the action of the traffic on the street shall have 
thoroughly ground the sand into all the joints. 

60.6. The materials incorporated into blocks shall be approved 
by the Engineer, and samples of all materials shall be sent to the 
Bureau of Tests and they shall pass the tests required by this Bureau 
for these materials. 

60.7. The methods of work and materials used shall at all times 
be subject to the inspection and supervision of the Engineer or his 
representative upon the work. 

60.8. The quantity to be paid for under this item shall be the 
number of square yards of asphalt block laid in accordance with the 
plans or as directed by the Engineer. The price bid shall include 
the furnishing and placing of all materials, mortar bed, and all 
labor and incidental expenses necessary to complete the work. Where 
placed upon old concrete foundation or upon old macadam the 
preparation of the foundation to receive the mortar bed will be paid 
for under item "Cleaning Old Pavement" or item " Scarifying 
and Reshaping Old Macadam." 



BRICK PAVEMENT 451 

Item 61 — Brick Pavement 

6 1. 1. Under this item the Contractor shall furnish and place the 
number of square yards of brick pavement required in accordance 
with the plans or as ordered by the Engineer. The item will include 
the furnishing and placing of all the block, sand cushion, grout, 
expansion joints and all material, labor and other expenses incidental 
thereto but will not include the concrete foundation, edging, curbing, 
manholes, catch basins, etc., which will be paid for under the espe- 
cially designated items therefor. 

61.2. All bricks or blocks used must be vitrified and especially 
burned for street paving and of the very best quality as regards 
hardness, dimensions, toughness, straight lines and non-absorption 
of water. 

61.3. The paving bricks shall be subjected to modulus of rupture 
test and to abrasion tests conducted by the Commission in the 
manner and with rattlers of the type adopted February 7, 191 1, by 
the National Paving Brick Manufacturers Association. One sample 
shall be tested for every two hundred thousand (200,000) bricks 
and less than this when conditions warrant. An average loss in 
weight in a rattler test exceeding twenty-four (24) per centum, or 
an average absorption of three and one-half (3J) per centum of water 
shall cause the rejection of the total quantity that the test represents, 
provided, however, that if permitted the bricks may be carefully 
reculled, and new samples taken and tested. If this second test 
passes the requirements, the bricks represented by it may be used. 
If this second test fails, no further test shall be permitted but the 
entire lot shall be rejected. To ensure the furnishing of bricks of 
uniformly acceptable quality, any " brand" of brick shall be rejected 
and shall not be further considered if three lots, each of ten thousand 
(10,000) bricks or more, offered consecutively for acceptance tests, 
fail to meet the requirements for this section without reculling 
them. 

Modulus of Rupture. When tested on edge as laid on the pave- 
ment, the modulus of rupture shall be not less than two thousand 

WL 

(2,000) pounds per square inch. Computed by formula R = 3-7—^ 

in which R is the modulus of rupture in pounds per square inch, L 
the length between supports in inches ( = 6 inches), b and d the 
breadth and depth in inches, and W the load in pounds, which pro- 
duces rupture. 

All the above tests will be made by the Bureau of Tests of the State 
Commission of Highways. 

61.4. On grades of 5 per centum or over an approved special 
form of block suitable for steep grades shall be used. 

61.5. The size of the brick shall be 3 \ inches in width by four 
inches in depth by 8J inches in length, and shall not vary from these 
dimensions more than one-eighth inch in width or depth nor more than 
one-half inch in length. Bricks of a given brand shall not vary among 
themselves more than J-inch in depth nor more than J-inch in width 
nor more than J-inch in length in any one shipment. If the edges 



452 SPECIFICATIONS 

are rounded the radius shall not be greater than ft of an inch. One 
side shall contain lugs of such dimensions that transverse joints will 
not be less than -f^ of an inch nor more than J-inch in width. Each 
end shall contain a semi-circular groove of J to f-inch radius, or 
a bulge or at least -£6 inch. The grooves shall be horizontal, and shall 
match perfectly when the bricks are laid in the finished pavement. 
Bricks in any course shall not vary in width by more than J-inch. 

61.6. Not less than ten days after the concrete foundation has 
been completed, there shall be laid a bed of clean Cushion Sand as 
described under " Materials of Construction," which shall be one 
and one-half inches thick after being rolled with a roller weighing 
150 pounds per foot of width. Before being rolled this bed of sand 
shall be brought to the proper elevation and crown as shown on 
plans by a template of a shape and size satisfactory to the Engineer. 
After being rolled all irregularities of the surface shall be eliminated 
and the sand cushion shall be brought to the exact form and section 
by the use of lutes or hand templates. 

61.7. Longitudinal expansion joints shall be placed alongside each 
curb or edging, and shall be one of the following types: 

Premolded Type, requiring no heating or pouring at the place of 
insertion. These expansion joints shall be of the proper thickness 
and width, as specified, made in convenient lengths ready for use. 
The joints shall be placed as the paving progresses, and shall rest 
directly on the sand cushion. The expansion joints shall be composed 
entirely of a high grade asphalt, and shall pass the following tests: 

Specific gravity . . . . 985 to 1 . 002 

Melting point 235 to 265 F. 

Loss on heating for 5 hours at 325 F .0 % 

Bitumen soluble in carbon disulphide 99 . 5 % to 99 . 9 % 

Bitumen soluble in carbon tetra-chloride 99.4% to 99.8% 

Bitumen soluble in Be. Naphtha to % 

Penetration at 32 F 25 to 35 

Penetration at 77 F 40 to 50 

Penetration at 115 F 65 to 75 

Poured Type. This type shall be provided for by placing along- 
side each curb or edging wooden strips with metal wedge shape pieces 
dropped over the top of the boards and between the board and the 
curb every three feet apart to facilitate the removal of the boards, 
or, by using two planed wedge-shaped strips so cut that when placed 
together in reverse positions their total section shall be rectangular 
and of a thickness and depth equal to the thickness and depth of 
the required expansion joint. The strip placed next to the curb 
shall be set with the wide edge up. These expansion joint forms 
shall be set next to the curb on a true grade with all end joints tight, 
and be pressed into sand so that their tops shall be one-quarter inch 
below the top surface of the pavement blocks before rolling. The 
two strips comprising the joint form shall break joints. 

The thickness of longitudinal expansion joints shall be as called 
for by the plan. 



BRICK PAVEMENT 453 

61.8. On the sand cushion prepared as in section 61.6 the blocks 
shall be carefully set on edge with the best edge up, shall be laid 
straight at and right angles to the edging line, except at road inter- 
sections, where they shall be laid at such angles as directed by the 
Engineer. All block shall be laid with the lugs in the same direction, 
joints shall be close and at right angles to the tops and sides. Each 
alternate course shall be commenced with a half brick. No half 
bricks or bats shall be used except at the ends of courses. All joints 
shall be broken with a lap of not less than three (3) inches. 

All brick shall be clean when placed in the pavement. Brick 
which in the opinion of the Engineer are not satisfactorily clean, 
shall be washed before being placed. 

In no case shall the sand cushion in front of the pavement be 
disturbed or walked on during the laying of the blocks. 

61.9. After a sufficient number of blocks have been laid, all soft, 
broken or badly misshapen blocks shall be marked by the inspector 
and removed. Any blocks slightly spalled or kiln-marked shall be 
turned over, and should the opposite face be acceptable, it may be 
replaced in the pavement, otherwise, it must be removed. 

In laying block pavement, the inspector shall keep the blocks 
culled, and the Contractor shall make the necessary changes and 
replacements so that the work shall at all times be ready for grouting 
within 300 feet from the block-laying. 

61.10. After all objectionable blocks have been removed from the 
pavement and all replacements have been made, the pavement shall 
be swept clean and thoroughly rolled with a self-propelled tandem 
roller weighing not over five tons and not less than three tons. Horse 
rolling shall not be permitted. This rolling shall start along the 
outside edges and progress toward the center. It shall then be re- 
rolled diagonally both ways until the surface is even. After final 
rolling the pavement shall be tested with a ten-foot straight edge 
laid parallel with the curb, and any depression exceeding one-quarter 
inch shall be corrected and brought to the proper grade. All blocks 
disturbed in making replacements or correcting depressions shall 
be settled into place by ramming or by rerolling. Each section of 
pavement must be acceptable to the Engineer before the grouting 
on that section may be commenced. 

6 1.1 1. Grout for filling the joints of brick or block pavements 
shall be composed of one part Portland cement and one part Grout 
Sand. 

61.12. The box for mixing this grout shall be about four feet 
eight inches long, two feet six inches wide and one foot two inches 
deep, supported on legs of different lengths in order that the mixture 
shall readily flow to the lowest corner, which shall not be more than 
six inches above the pavement. Approved mechanical grout mixers 
may be used. 

61.13. The mixture, not exceeding one sack of cement together 
with a like amount of sand, shall be placed in the box and mixed 
dry, until the mass assumes a uniform color. Water shall then be 
added, forming a liquid mixture of the consistency of thin cream for 
the first coat and slightly thicker for each succeeding coat. From 



454 SPECIFICATIONS 

the time the water is applied until the last drop is removed and 
floated into the joints of the pavement the mixture must be constantly 
agitated. 

61.14. The brick shall be wet to the satisfaction of the Engineer 
before any grout is placed. The grout shall be removed from the 
box to the street surface with a scoop shovel and immediately swept 
into the joints, the mixture in the box being constantly agitated while 
this is being done. 

The work of grouting shall proceed for the entire width of the 
pavement. When sufficient time has elapsed for the grout to thor- 
oughly penetrate all the joints, but before the cement has attained 
its initial set, the section treated shall be gone over a second time in 
the same manner, care being taken to thoroughly fill all joints from 
the bottom flush with the top of the block. If necessary to secure 
flush joints, a third, fourth or fifth coat of the grout shall be swept 
in and smoothed off with a suitable squeegee. 

Care shall be taken to so conduct the grouting that no part of 
any joint will receive an application of the second grout until the 
first is satisfactorily completed, nor of the third until the second is 
completed, etc. To insure this result metal strips 1-16 in. by 6 in. 
by 3 ft. must be inserted, for the full length of the joint, at work 
intervals; all of the several applications of grout must be completed up 
to this joint before any grouting is begun on the other side of it. 

61.15. After the joints are thus filled flush with the top of the blocks 
and sufficient time for hardening has taken place, so that the cover 
coat will not absorb any moisture from the grout, one inch of suitable 
material shall be spread evenly over the entire surface, and be kept 
moist for a period of at least ten days and until the grout has thor- 
oughly set. 

During this period the section grouted must remain absolutely 
free from disturbance or traffic of any kind. After 30 days from the 
spreading, this cover coat shall be completely removed. 

61.16. In case the poured type of expansion joint is used, after 
the grout has set but within thirty-six hours after its application 
the expansion joint forms shall be withdrawn and the space thus 
formed thoroughly cleaned and a bituminous filler having a melting 
point not less than 120 degrees Fahrenheit nor more than 140 
degrees Fahrenheit shall be immediately poured into place at a 
temperature not less than 200 degrees Fahrenheit. 

61.17. If required, transverse expansion joints shall be constructed 
of the materials and in the manner prescribed by the Engineer. 

61.18. The quantity of pavement to be paid for under this item 
shall be the number of square yards placed in accordance with the 
plans or directions of the Engineer. The price bid per square yard 
shall include the sand cushion, paving block, grout, material for 
expansion joint, sand covering, sprinkling, and all other labor, 
materials and incidentals necessary to satisfactorily complete the work. 

The amount to be estimated under this item shall be computed 
by multiplying the actual width of pavement, including expansion 
joints, by the total length of pavement measured along the axis of 
the road and parallel to the surface. 



STONE BLOCK PAVEMENT 455 



Item 62 — Stone Block Pavement 

62.1. Under this item the Contractor shall furnish and place upon 
a properly prepared foundation Stone Block pavement of the quality 
specified below, where shown upon the plans or directed by the 
Engineer. 

The item will include the furnishing and placing of all the block, 
sand cushion, grout, expansion joints and all material, labor and 
other expenses incidental thereto but will not include the concrete 
foundation, edging, curbing, manholes, catch basins, etc., which 
will be paid for under the especially designated items therefor. 

62.2. The dimensions of the blocks shall be as follows: Not less 
than six inches nor more than twelve inches long on top, not less 
than three and one-half inches nor more than four and one-half 
inches wide on top, and not less than four inches nor more than five 
inches deep. They shall be dressed so that after laying, no measure- 
ment of any joint shall show a width of more than one-half inch for 
a depth of one inch, or a width of more than one inch in any part 
of the joint. The head of the block shall be so cut that it shall not 
have a depression in it more than three-eighths inch deep, and the 
edges and corners must be full unchipped and unbroken. All blocks 
shall be sorted and laid in straight courses of uniform width and 
depth. 

62.3. The blocks shall be of stone of medium sized grain showing 
an even distribution of constituent material. They shall be of 
uniform quality and texture, without seams, scales or disintegration, 
and free from an excess of mica or feldspar. They shall be made 
from rock which when tested in the Deval Rattler will show a "co- 
efficient of wear" of more than 7 and less than 14. All blocks for 
any one contract shall be from the same quarry unless otherwise 
directed. 

62.4. On the prepared foundation, sufficient clean Cushion Sand 
as described under "Materials of Construction" on page 375, shall 
be spread to such a thickness that after the pavement has been 
thoroughly rammed or settled the sand under the block shall be 
nowhere less than one inch thick. 

On the sand cushion above specified, the blocks shall be set ver- 
tically on edge in close contact with each other, and in straight rows 
across the road at right angles to the curb, except at intersections, 
where the angle of the rows with the curb shall be varied to meet 
the conditions. Blocks in adjoining rows shall be set to break joints 
not less than three inches. All blocks shall be set so that when 
thoroughly rammed or settled to a firm, unyielding bearing, they 
will then be true to lines, grades and cross sections, and have no 
joints greater than the maximum allowable. All depressions or 
irregularities in the surface shall be corrected to the satisfaction of 
the Engineer. Only practiced and competent pavers shall be em- 
ployed in laying the blocks. 

After the blocks are laid, sufficient approved clean gravel shall be 
spread over the surface and swept into the joints so as to fill the latter 
to a depth of about two inches from the bottom. The blocks shall 



456 SPECIFICATIONS 

then be thoroughly rammed or rolled until firm, even and true to 
the lines, grades and cross sections. 

Approved expansion joints shall be provided along the curb as 
may be required and shall be filled with the same quality of filler 
as is specified for expansion joints in brick pavements. Portland 
cement grout mixed in proportions of one part cement and one part 
sand shall then be poured into the joints until the grout flushes to 
the surface of the pavement. The grout shall be broomed when 
required, and the pouring and brooming shall be continued until all 
the joints are thoroughly filled, and the grout is even with the highest 
part of any and all blocks. Sprinkling or otherwise wetting the 
blocks before grouting shall be done when atmospheric or other 
conditions require this precaution to be taken. 

62.5. After grouting shall have been completed and the grout shall 
have sufficiently hardened, a coating of suitable material about one 
inch deep shall be spread over the whole surface of the grouted 
pavement, and the road shall then be sprinkled with water. This 
covering shall be kept wet, and no travel of any kind shall be allowed 
on the completed pavement for at least seven days thereafter, nor 
until the grout shall have thoroughly set, when the covering shall be 
completely removed. 

62.6. The quantity to be paid for under this item shall be the 
number of square yards, including expansion joints, of pavement 
laid in accordance with the plans and as directed by the Engineer. 

The price bid shall include the furnishing and placing of all 
materials, the spreading of sand cushion, the laying, ramming or 
rolling, grouting, surfacing and all labor and incidental expenses 
necessary to complete ^he work. 

MEDINA SANDSTONE BLOCK PAVEMENT 

(City of Rochester, N.Y., Specifications, 191 1) 

The grading, subwork, and curbs having been completed as herein 
specified under the proper headings, the work of laying the concrete 
foundation and paving will then proceed. 

A concrete foundation six (6) inches thick, of Portland cement, 
as specified in the bidding sheet and shown in plans, will be laid in 
accordance with the specifications herein contained. The surface 
will be eight (8) inches below the finished pavement and parallel 
thereto, or seven (7) inches if a five (5) inch block is specified. 

The surface to be kept wet until covered with sand, and, at least, 
thirty-six (36) hours shall be allowed for the concrete to set before 
the pavement is laid. When connection is to be made with any 
layer set, or partially set, the edge of such layer must be broken down, 
shall be free from dust and properly wet, so as to make the joints 
fresh and close. On this concrete foundation shall be laid a bed of 
clean, sharp sand, perfectly free from moisture (made so by artificial 
heat if deemed necessary), not less than one (1) inch thick, to the 
depth necessary to bring the pavement and crosswalks to the proper 
grade when thoroughly rammed. 



MEDINA SANDSTONE BLOCK PAVEMENT 457 

Upon this bed of sand, the stone blocks and crosswalks must be 
laid. The stone blocks are to be laid in straight courses at right 
angles with the line of the street, except in intersections of streets, 
where the courses shall be laid diagonally, and except in special cases, 
when they shall be laid at such angle, with such crown and at such 
grade as the city engineer may direct. Each course of blocks shall 
be uniform in width and depth, and shall be gauged and selected 
for the pavers on the sidewalks, and so laid that all longitudinal 
joints or end joints shall be close joints and shall be broken by a lap of 
at least three inches, and that joints between courses shall not be more 
than one-half inch in width. The blocks shall then be thoroughly 
rammed by courses at least three times by a rammer weighing not less 
than eighty (80) pounds — no iron of any kind being allowed on its 
lower face to come in contact with the paving, and until brought to 
an unyielding bearing, with a uniform surface, true to the roadway 
on the established grade. The surface of the pavement thus com- 
pleted must be even and smooth throughout and molded to conform 
to the wells of the surface sewers, street and alley intersections, 
drainage details, and the grade lines established by the city engineer. 
During the final ramming the pavement shall be tested with a straight- 
edge and templet, and any unevenness must be taken out and made 
true to the required grade, level, and cross-section. 

If a paving pitch filler is used, the joints shall be filled with clean, 
dry, hot gravel of proper size as herein specified, heated in pans 
especially provided for that purpose, and poured from cans having 
small spouts and thoroughly settled in place with wire picks until 
the level of the gravel is at least two inches below the top of the 
pavement. 

The gravel used between the blocks shall be of such size as will 
pass through a sieve having four meshes per square inch, and be 
retained on a sieve of sixty-four meshes per square inch, and must 
be screened when dry. 

There shall be immediately poured into the joints, while the 
gravel is hot, boiling paving cement as hereinafter described, heated 
to a temperature of 300 F. until the joints and all interstices of 
gravel filling are full and will take no more, and are filled flush with 
the top of the blocks. Dry, hot gravel must then be poured along 
the joints, filled with paving cement, as above described. 

The paving cement to be used in filling the joints as herein provided 
shall be a paving pitch of the best quality, of a brand that has been 
proved by actual use in pavements known to the city engineer to 
be best adapted to the purpose. It shall be delivered on the work 
in lots at least one week before using, in order that the necessary 
analysis and examination may be made by the city engineer. In 
addition to this the contractor must furnish the city engineer with 
the certificate of the manufacturer or refiner that the materials are 
of the kind specified. 

The city engineer may direct that a Portland cement grout filler 
may be used in the joints instead of a paving pitch, in which case 
the pavement shall be thoroughly sprinkled or washed with water 
before grouting. The grout shall be mixed with clean, sharp sand 



458 SPECIFICATIONS 

of approved quality, in the proportion of one to one, the cement and 
sand to be thoroughly mixed together dry, in a box, and then only 
a sufficient amount of water added to make the grout of the proper 
fluidity when thoroughly stirred. 

The grout shall- be prepared only in small quantities at a time, 
and shall be stirred rapidly and constantly in the box and while 
being applied to the pavement, and no settlings or residue will be 
allowed to be used. 

The grout shall be transferred to the pavement in such a way as 
the engineer may think most advantageous and best for the work, 
and shall then be rapidly swept into the joints of the pavement 
with proper brooms. The stones shall be well wet as directed before 
the grout is applied, and the pouring must be continued until the 
joints remain full. 

All teams and traffic of any kind, except on planks, shall be rigidly 
prohibited on the pavement for ten days after the grout is applied, 
or until, in the opinion of the engineer, it has become thoroughly 
set and hardened, so that the bond will not be broken by traffic over 
the pavement. 



CONVERSION TABLE 



459 



Linear Units 



Conversion Table 55 

Old Surveyors' Units 
1 link = 7.92 in. 
100 links = 1 chain = 66 ft. 
25 links = 1 rod = 16.5 ft. 



Ordinary Measure 
12 in. = 1 ft. 
3 ft. = 1 yd. 
5280 ft. = 1 mile 


Square Units 

1 sq.ft. 
1 sq. yd. 

1 acre 

1 sq. mile 


= 144 sq. in. 
= 9 sq. ft. 
= 1296 sq. in, 
= 43>5°° sq. ft. 
= 4840 sq. yds. 
= 27,878,400 sq. ft. 
= 3,097,600 sq. yds. 
= 640 acres 


Volume Units 




1 cu. ft. 

1 cu. yd. 

1 ordinary gal. 
1 Imperial gal. 
1 barrel 


= 1728 cu. in. 

= 7.4805 ordinary gal. 

= 6.232 Imperial gal. 

= 27 cu. ft. 

= 46,656 cu. in. 

= 231 cu. in. 

= 277 cu. in. 

= 3i-5 gal. 
= 4.21 cu. ft. 


Weight Units 

1 pound 
1 ordinary 
1 long ton 


= 16 ounces 
ton = 2000 pounds 
= 2240 pounds 


Temperature Units 
Freezing point of water 


= 32° Fahrenheit 
= o° Centigrade 


Boiling point of water at normal air 

pressure =212° Fahrenheit 

= ioo° Centigrade 


1 degree Fahrenheit 
1 degree Centigrade 


— °-5556 degree Centigrade 
= 1.8 degrees Fahrenheit 



460 



GENERAL REFERENCE TABLES 



Table 56 
Equivalents of Inches and Fractions of Inches in Decimals 

of a Foot 



In. 


In. 


1 In. 


2 In. 


3 In. 


4 In. . 


5 In. 






•0 8 33 


.1667 


.2500 


-3333 


.4167 


A 


.0026 


.0859 


.1693 


.2526 


•3359 


•4193 


ft 


.0052 


.0885 


.1719 


•2552 


.3385 


.4219 


3 
32 


.0078 


.0911 


•1745 


.2578 


•34i 1 


•4245 


i 


.0104 


.0938 


.1771 


.2604 


•3438 


.4271 


5 

32 


.0130 


.0964 


.1797 


.2630 


•3464 


.4297 


A 


.0156 


.0990 


.1823 


.26^6 


•349o 


•4323 


T2 


.0182 


.1016 


.1849 


.2682 


•35i6 


•4349 


1 


.0208 


.1042 


.1875 


.2708 


•3542 


•4375 


9 
32 


.0234 


.1068 


.1901 


.2734 


.3568 


.4401 


5 
16 


.0260 


.1094 


.1927 


.2760 


•3594 


.4427 


11 
32 


.0286 


.1120 


•1953 


.2786 


.3620 


•4453 


I 


•°3I3 


.1146 


.1979 


.2813 


.3646 


•4479 


if 


•°339 


.1172 


.2005 


.2839 


.3672 


•4505 


ft 


•0365 


.1198 


.2031 


.2865 


.3698 


•4531 


II 


.0391 


.1224 


.2057 


.2891 


•3724 


•4557 


1 
2 


.0417 


•1253 


.2083 


.2917 


•375o 


4583 


H 


.0443 


.1276 


.2091 


•2943 


•3776 


.4609 


ft 


.0469 


.1302 


• 2I 35 


.2969 


.3802 


•4635 


U 


•0495 


.1328 


.2161 


•2995 


.3828 


.4661 


f 


.0521 


-1354 


.2188 


.3021 


.3854 


.4688 


21 
32 


•°547 


.1380 


.2214 


•3°47 


.3880 


.4714 


1 1 
T6 


•°573 


.1406 


.2240 


•3°73 


.3906 


.4740 


£3 
32 


•°599 


.1432 


.2266 


•3°99 


•393 2 


.4766 


3 
4 


.0625 


.1458 


.2292 


•3 I2 5 


•3958 


•4792 


25 
3 2 


.0651 


.1484 


.2318 


•3 I 5 I 


•3984 


.4818 


13 
"16 


.0677 


.1510 


.2344 


•3i77 


.4010 


.4844 


21 
32 


.0703 


•1536 


.2370 


•3203 


.4036 


.4870 


1 
8 


.0729 


•1563 


.2396 


.3229 


.4063 


.4896 


2.9 
32 


•o755 


.1589 


.2422 


•3255 


.4089 


.4922 


15 
16 


.0781 


.1615 


.2448 


.3281 


•4115 


.4948 


31 

32 


.0807 


.1641 


.2474 


-33°7 


.4141 


•4974 



EQUIVALENTS OF DECIMALS OF A FOOT 461 



Equivalents of Inches and Fractions of Inches in Decimals 

of a Foot 



In. 


6 In. 


7 In. 


8 In. 


9 In. 


10 In. 


11 In. 




.5000 


.5833 


.6667 


.7500 


•8333 


.9167 


1 
"32 


.5026 


.5859 


.6693 


.7526 


.8359 


•9193 


1 

1 6 


•5°5 2 


.5885 


.6719 


•7552 


.8385 


.9219 


A 


.5078 


•5911 


•6745 


.7578 


.8411 


•9245 


1 

8 


.5104 


.5938 


.6771 


.7604 


.8438 


.9271 


5 
"32 


•513° 


.5964 


.6797 


.7630 


.8464 


.9297 


A 


•5!56 


•599° 


.6823 


.7656 


.S490 


•9323 


J7 
32 


.5182 


.6016 


.6849 


.7682 


.8516 


•9349 


i 


.5208 


.6042 


.6875 


.7708 


.8542 


•9375 


9 

32 


•5 2 34 


.6068 


.6901 


•7734 


.8568 


.9401 


5 

Te- 


.5260 


.6094 


.6927 


.7760 


•8594 


.9427 


ll 

32 


.5286 


.6120 


• 6 953 


.7786 


.8620 


•9453 


1 


•53 J 3 


.6146 


.6979 


.7813 


.8646 


•9479 


13 
32 


•5339 


.6172 


.7005 


.7839 


.8672 


•9505 


A 


•5365 


.6198 


•703 1 


.7865 


.8698 


•953i 


it 


•539i 


.6224 


•7057 


.7891 


.8724 


•9557 


4 


.5417 


.6250 


.7083 


.7917 


.87^0 


.9583 


11 

32 


•5443 


.6276 


.7109 


•7943 


.8776 


.9609 


9 
16 


•5469 


.6302 


•7i35 


.7969 


.8802 


•9635 


19 
32 


•5495 


.6328 


.7161 


•7995 


.8828 


.9661 


5 
S 


•552i 


•6354 


.7188 


.8021 


•8854 


.9688 


21 
¥2 


•5547 


.6380 


.7214 


.8047 


.8880 


.9714 


11 
16 


•5573 


.6406 


.7240 


.8073 


.8906 


.9740 


2 3 
32 


•5599 


.6432 


.7266 


.8099 


•8932 


.9766 


3 
4 


•5625 


.6458 


•7292 


.8125 


.8958 


.9792 


23 
32 


•5651 


.6484 


.73i8 


.81^1 


.8984 


.9818 


13 
1 6 


•5677 


.6510 


•7344 


.8i77 


.9010 


•9844 


27 
32 


•57°3 


.6536 


•737° 


.8203 


.9036 


.9870 


7 

8 


•5729 


•6563 


•7396 


.8229 


.9063 


.9896 


2.9 
32 


•5755 


.6589 


.7422 


•8255 


.9089 


.9922 


1 5 
16 


.578i 


.6615 


.7448 


.8281 


•9115 


.9948 


3 1 
32 


.5807 


.6641 


•7474 


.8307 


.9141 


•9974 



462 



GENERAL REFERENCE TABLES 

Table 57. Areas and Volumes 



Areas 



' 7T 

h 
<--b-->l y k — -b — -> 



-b— >i/ 



Squares, Rectangles, and Parallelograms. Area = bh 




h 



b h 




____*_ 



h-b->| K- 

h 



b *i 



b -—x 



K-b-H 



Triangles Area = ^ bh 



Trapezoids Area = // 




Circles 
Area = n R 2 = - 



D 



Circumference of Circle = 2 n R = tt D 
Commonly used value of n = 3.1416 




Sector of Circle 



Area = n R 2 



A° 

3 6o c 



.A 



Segment of a Circle 

Area ° ( - R2 w) ' ( (i? sin t> (i? cos 1) ) 



Volumes 

Cubes, Rectangular Prisms, Parallelopipeds, Cylinders, etc. All 
solids having parallel bases and a constant cross-section. 

Volume = area of base X perpendicular height between the 
planes of the bases. 




i<i> 



<y 





Wedges. Having parallel ends. 
Volume = area of base X \ the height perpendic- 
ular to the plane of the base. 






AREAS AND VOLUMES 



463 



Cones and Pyramids, whether right or oblique, regular or irreg- 
ular. 

Volume = \ area of the base X height perpendicular to the 
plane of the base 





Frustums of Pyramids or Cones, whether right or oblique, reg- 
ular or irregular provided the base and top are parallel. 




Volume = I perpendicular 
height between base and top 
or by the prismoidal formula 

Volume 
= J perpendicular height X 
between base and top 



X 



area 



\to E 



+ 



area 
base 



+ 






area 
top 



X 



area 
base 



area^area , 4 >< area of section parA 

top+base + fA 61 tc \ and midway) 

between base and top ' 



Prismoidal Formula 

Trautwine defines a prismoid as a solid having for its ends 
two parallel plane figures connected by other plane figures on 
which and through every point of which a straight line may be 
drawn from one of the two parallel ends to the other. These 
connecting planes may be parallelograms or not and parallel to 
each other or not. This includes cubes, all parallelopipeds, 
prisms, cylinders, pyramids, cones, and their frustums, provided 
the top and base are parallel and wedges. 

The prismoidal formula applies to all these solids either alone 
or to any form that can be separated into units of the above 
forms. 



Prismoidal formula 



Volume = h X 



A + a + \M 



h = perpendicular distance between the parallel ends 
A = area of one of the parallel ends 
a = area of the other parallel end 
M = area of a cross-section midway between and parallel to 
the two parallel ends 
Sphere 

Volume = % n R 3 = 4- 1888 R s 

= in D* = O.5236 D 3 

In which R = radius of sphere 

D = diameter of sphere 



464 



GENERAL REFERENCE TABLES 



Table 58 

Squares, Cubes, Square Roots, Cube Roots, Circumferences 

and Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 




Circum. 


Area 


1 


I 


I 


I .OOOO 


I .OOOO 


3.142 


O.7854 


2 


4 


8 


I.4142 


1.2599 


6.283 


3.1416 


3 


9 


27 


I-732I 


1.4422 


9.425 


7.0686 


4 


16 


64 


2 .OOOO 


I-5874 


12.566 


12.5664 


5 


25 


125 


2.2361 


1. 7100 


15.708 


19.6350 


6 


36 


216 


2.4495 


1.8171 


18.850 


28.2743 


7 


49 


343 


2.6458 


1. 91 29 


21.991 


38.4845 


8 


64 


512 


2.8284 


2 .OOOO 


25-I33 


50.2655 


9 


81 


729 


3.OOOO 


2.0801 


28.274 


63.6173 


10 


100 


1000 


3.1623 


2.1544 


31.416 


78.5398 


11 


121 


I33 1 


3.3166 


2.2240 


34.558 


95-°33 


12 


144 


1728 


3.464I 


2.2894 


37-699 


113.097 


1 3 


169 


2197 


3.6056 


2.3513 


40.841 


132.732 


14 


196 


2 744 


3-7417 


2.4101 


43.982 


I53-938 


15 


225 


3375 


3-8730 


2.4662 


47.124 


176.715 


16 


256 


4096 


4.0000 


2.5198 


50.265 


201.062 


17 


289 


49i3 


4-I23I 


2.5713 


53-407 


226.980 


18 


324 


5832 


4.2426 


2.6207 


56.549 


254.469 


19 


361 


6859 


4.3589 


2.6684 


59.690 


283.529 


20 


400 


8000 


44721 


2.7144 


62.832 


3*4-159 


21 


441 


9261 


4.5826 


2.7589 


65^73 


346.361 


22 


484 


10648 


4.6904 


2.8020 


69.115 


380.133 


2 3 


529 


12167 


4.7958 


2.8439 


72.257 


1I5-476 


24 


576 


13824 


4.899O 


2.8845 


75.398 


452.389 


25 


625 


15625 


5.OOOO 


2.9240 


78.540 


490.874 


26 


676 


17576 


5.O99O 


2.9625 


81.681 


530.929 


27 


729 


19683 


5.I962 


3.0000 


84.823 


572.555 


28 


784 


21952 


5-29I5 


3.0366 


87.965 


6i5752 


29 


841 


24389 


5-3852 


3-0723 


91.106 


660.520 


3° 


900 


27000 


5-4772 


3.1072 


94.248 


706.858 


3 1 


961 


29791 


5.5678 


3.1414 


90.389 


754.768 


3 2 


1024 


32768 


5-6569 


3-1748 


100.531 


804.248 


33 


1089 


35937 


5-7446 


3-2075 


103.673 


855-299 


-34 


1156 


39304 


5-83IO 


3.2396 


106.814 


907.920 


35 


1225 


42875 


5.9161 


3-2711 


109.956 


962.113 


36 


1296 


46656 


6.0000 


3-3 OI 9 


113.097 


1017.88 


37 


1369 


50653 


6.0828 


3-3322 


116.239 


1075.21 


38 


1444 


54872 


6.1644 


3.3620 


119.381 


1134.11 


39 


1521 


59319 


6.2450 


3-3912 


122.522 


1194.59 


40 


1600 


64000 


6.3246 


3.4200 


125.660 


1256.64 



SQUARES, CUBES AND ROOTS 



465 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


CnViP Rnnt 


Circle 


V.UUC J\UUl 


Circum. 


Area 


41 


1681 


68921 


6.4031 


3.4482 


128.81 


1320.25 


42 


1764 


74088 


6.4807 


3.4760 


I3I-95 


I385-44 


43 


l849 


795°7 


6-5574 


3-5°34 


I35-09 


1452.20 


44 


1936 


85184 


6.6332 


3-5303 


138.23 


!52o.53 


45 


2025 


91125 


6.7082 


3-5569 


141-37 


i59o-43 


46 


2Il6 


9733 6 


6.7823 


3-5830 


I44oI 


1661.90 


47 


2209 


103823 


6.8557 


3.6088 


I47-65 


1734.94 


48 


2304 


110592 


6.9282 


3-6342 


150.80 


1809.56 


49 


2401 


1 1 7649 


7.0000 


3-6593 


153-94 


1885.74 


5° 


2500 


125000 


7.0711 


3.6840 


157.08 


1963.50 


5 1 


2601 


132651 


7.1414 


3.7084 


160.22 


2042.82 


52 


2704 


140608 


7.2111 


3-7325 


163.36 


2123.72 


53 


2809 


148877 


7.2801 


3-7563 


166.50 


2206.18 


54 


2916 


157464 


7-3485 


3-7798 


169.65 


2290.22 


55 


3° 2 5 


166375 


7.4162 


3.8030 


172.79 


2375-83 


56 


3*36 


175616 


74833 


3-8259 


175-93 


2463.01 


57 


3249 


185193 


7-5498 


3.8485 


179.07 


255I-76 


58 


33 6 4 


195112 


7.6158 


3.8709 


182.21 


2642.08 


59 


348i 


205379 


7.6811 


3-8930 


185.35 


2733-97 


60 


3600 


216000 


7.7460 


3-9149 


188.50 


2827.43 


61 


372i 


226981 


7.8102 


3-9365 


191.64 


2922.47 


62 


3844 


238328 


7.8740 


3-9579 


194.78 


3019.07 


63 


3969 


250047 


7-9373 


3-9791 


197.92 


3II7-25 


64 


4096 


262144 


8.0000 


4.0000 


201.06 


3216.99 


65 


4225 


274625 


8.0623 


4.0207 


204.20 


3318.31 


66 


4356 


287496 


8.1240 


4.0412 


207.35 


3421.19 


67 


4489 


300763 


8.1854 


4.0615 


210.49 


3525-65 


68 


4624 


3 J 443 2 


8.2462 


4.0817 


213.63 


3631.68 


69 


4761 


328509 


8.3066 


4.1016 


216.77 


3739-28 


70 


4900 


343000 


8.3666 


4.1213 


219.91 


384845 


7i 


5°4i 


3579" 


8.4261 


4.1408 


223.05 


3959.19 


72 


5184 


373248 


8.4853 


4.1602 


226.19 


4071.50 


73 


5329 


389017 


8.5440 


4.1793 


229.34 


4185.39 


74 


54/6 


405224 


8.6023 


4.1983 


232.48 


4300.84 


75 


5625 


421875 


8.6603 


4.2172 


235.62 


4417.86 


76 


5776 


438976 


8.7178 


4-2358 


238.76 


453646 


77 


5929 


450533 


8.775o 


4.2543 


241.90 


4656.63 


78 


6084 


474552 


8.8318 


4.2727 


245.04 


4778.36 


■ 79 


6241 


493°39 


8.8882 


4.2908 


248.19 


4901.67 


80 


6400 


512000 


8-9443 


4.3089 


25I-33 


5026.55 



466 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 




Circum. 


Area 


8l 


6561 


53I44I 


9 .OOOO 


4.3267 


2 5447 


5I53.00 


82 


6724 


551368 


9-°554 


4-3445 


257.61 


5281.02 


83 


6889 


571787 


9.IIO4 


4.3621 


260.75 


5410.61 


84 


7056 


592704 


9.1652 


4.3795 


263.89 


5541.77 


85 


7225 


614125 


9- 2I 95 


4.3968 


267.04 


5674.50 


86 


7396 


636056 


9.2736 


4.4140 


270.18 


5808.80 


87 


7569 


658503 


9-3 2 74 


4.4310 


273.32 


5944.68 


88 


7744 


681472 


9.3808 


4.4480 


276.46 


6082.12 


89 


7921 . 


704969 


9.4340 


4.4647 


279.60 


6221.14 


90 


8100 


729000 


9.4868 


4.4814 


282.74 


6361.73 


9i 


8281 


753571 


9-5394 


4.4979 


285.88 


6503.88 


92 


8464 


778688 


9-59I7 


4-5 x 44 


289.03 


6647.61 


93 


8649 


804357 


9.6437 


4.5307 


292.17 


6792.91 


94 


8836 


830584 


9.6954 


4.5468 


295.31 


6939.78 


95 


9025 


857375 


9.7468 


4.5629 


298.45 


7088.22 


96 


9216 


884736 


9.7980 


4.5789 


3 OI -59 


7238.23 


97 


9409 


912673 


9.8489 


4.5947 


304.73 


7389.81 


98 


9604 


941192 


9.8995 


4.6104 


307.88 


7542.96 


99 


9801 


970299 


9.9499 


4.6261 


311.02 


7697.69 


100 


1 0000 


I OOOOOO 


10.0000 


4.6416 


314.16 


7853.98 


IOI 


10201 


1030301 


10.0499 


4.6570 


317.30 


8011.85 


102 


10404 


1061208 


10.0905 


4.6723 


320.44 


8171.28 


103 


10609 


1092727 


10.1489 


4.6875 


323.58 


8332.29 


104 


10816 


I I 24864 


10.1980 


4.7027 


326.73 


8494.87 


105 


11025 


1157625 


10.2470 


47177 


329.87 


8659.OI 


106 


11236 


1191016 


10.2956 


4.7326 


333-OI 


8824.73 


107 


1 1 449 


1225043 


10.3441 


4.7475 


336.15 


8992.02 


108 


1 1 664 


1259712 


10.3923 


4.7622 


339.29 


9160.88 


109 


11881 


1295029 


10.4403 


4.7769 


342.43 


9331.32 


no 


12100 


I 33 I OOO 


10.4881 


4.7914 


345.58 


9503.32 


III 


12321 


1367631 


IO-5357 


4.8059 


348.72 


9676.89 


112 


12544 


1404928 


10.5830 


4.8203 


351.86 


9852.03 


I1 3 


12769 


1442897 


10.6301 


4.8346 


355.oo 


IOO28.7 


114 


12996 


I 48 1 544 


10.6771 


4.8488 


358.14 


IO207.O 


115 


13225 


1520875 


10.7238 


4.8629 


361.28 


10386.9 


116 


13456 


1560896 


10.7703 


4.8770 


364.42 


10568.3 


117 


13689 


1601613 


10.8167 


4.8910 


367.57 


I075L3 


118 


i39 2 4 


1643032 


10.8628 


4.9049 


37o.7i 


I0935.9 


119 


14161 


1 685 1 59 


10.9087 


4.9187 


373^5 


III22.0 


120 


14400 


1728000 


io.9545 


4.9324 


376.99 


II309-7 



SQUARES, CUBES AND ROOTS 



467 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 













ClR<"T TT 


No. 


Square 


Cube 


Sq. Root 


Cube Root 






Circum. 


Area 


121 


14641 


1771561 


1 1 .OOOO 


4.9461 


380.13 


1 1 499.O 


122 


14884 


1815848 


11.0454 


4-9597 


383.2 7 


1 1 689 .9 


123 


15129 


1860867 


11.0905 


4.9732 


386.42 


11882.3 


124 


15376 


1906624 


H-I355 


4.9866 


389.56 


12076.3 


125 


15625 


i953 I2 5 


1 1. 1803 


5 .OOOO 


392.70 


12271.8 


126 


15876 


2000376 


11.2250 


5- OI 33 


395.84 


12469.O 


127 


16129 


2048383 


11.2694 


5.0265 


398.98 


12667.7 


128 


16384 


2097152 


^-3^37 


5-°397 


402.12 


12868.0 


129 


1 664 1 


2146689 


ii-3578 


5.0528 


405.27 


13069.8 


130 


16900 


2197000 


1 1. 401 8 


5.0658 


408.41 


13273.2 


131 


17161 


2248091 


n-4455 


5.0788 


411.55 


13478.2 


132 


17424 


2299968 


1 1. 489 1 


5.0916 


414.69 


13684.8 


*33 


17689 


2352637 


11.5326 


5- io 45 


4I7.83 


13892.9 


134 


17956 


2406104 


n.5758 


5.1172 


420.97 


14102.6 


135 


18225 


2460375 


1 1. 6190 


5.1299 


424.12 


I43I3-9 


136 


18496 


2515456 


1 1. 6619 


5.1426 


427.26 


14526.7 


137 


18769 


2571353 


11.7047 


5.i55i 


430.40 


14741.I 


138 


19044 


2628072 


n-7473 


5.1676 


433-54 


I4957-I 


139 


19321 


2685619 


11.7898 


5.1801 


436.68 


I5I747 


140 


19600 


2744000 


11.8322 


5-!9 2 5 


439.82 


15393.8 


141 


19881 


2803221 


11.8743 


5.2048 


442.96 


I56I4.5 


142 


20164 


2863288 


1 1 .9 1 64 


5-2171 


446.II 


15836.8 


143 


20449 


2924207 


ii-9583 


5-2293 


449.25 


16060.6 


144 


20736 


2985984 


12.0000 


5-2415 


452.39 


16286.O 


145 


21025 


3048625 


12.0416 


5.2536 


455-53 


16513.O 


146 


21316 


3112136 


12.0830 


5-2656 


458.67 


16741.5 


147 


21609 


3176523 


12.1244 


5.2776 


461.81 


16971.7 


148 


21904 


3241792 


12.1655 


5.2896 


464.96 


17203.4 


149 


22201 


33°7949 


12.2066 


5-3 OI 5 


468.10 


17436.6 


150 


22500 


3375°°° 


12.2474 


5-3I33 


471.24 


17671.5 


151 


22801 


344295 1 


12.2882 


5-325 1 


474.38 


17907.9 


J 5 2 


23104 


3511808 


12.3288 


5.3368 


477.52 


18145.8 


i53 


23409 


358i577 


12.3693 


5.3485 


480.66 


18385.4 


i54 


23716 


3652264 


12.4097 


5-36oi 


483.81 


18626.5 


i55 


24025 


3723875 


12.4499 


5.3717 


486.95 


18869.2 


156 


24336 


3796416 


12.4900 


5-3832 


490.09 


19113.4 


157 


24649 


3869893 


12.5300 


5-3947 


493.23 


19359-3 


158 


24964 


39443 1 2 


12.5698 


5.4061 


496.37 


19606.7 


i59 


25281 


4019679 


12.6095 


5-4175 


499.51 


I9855-7 


160 


25600 


4096000 


1 2 .649 1 


5.4288 


502.65 


20106.2 



468 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square 


Roots, Cube Roots, Circumferences 




and Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


161 


25921 


4I7328I 


12.6886 


5.4401 


505.8o 


20358.3 


162 


26244 


4251528 


12.7279 


5-4514 


508.94 


20612.0 


163 


26569 


433°747 


12.7671 


5.4626 


5 1 2 .08 


20867.2 


164 


26896 


4410944 


12.8062 


5-4737 


5 J 5-22 


21124.1 


165 


27225 


4492125 


12.8452 


5.4848 


518.36 


21382.5 


166 


27556 


4574296 


12.8841 


5-4959 


521.50 


21642.4 


167 


27889 


4657463 


12.9228 


•5-5069 


524.65 


21904.0 


168 


28224 


4741632 


12.9,615 


5.5178 


527-79 


22167. 1 


169 


28561 


4826809 


13.0000 


5.5288 


530.93 


22431.8 


170 


28900 


4913000 


13.0384 


5-5397 


534.07 


22698.0 


171 


29241 


500021 1 


13.0767 


5-5505 


537-21 


22965.8 


172 


29584 


5088448 


13.1149 


5-56i3 


540.35 


23235.2 


173 


29929 


5I777I7 


i3- I 5 2 9 


5-5721 


543-5° 


23506.2 


174 


30276 


5268024 


13.1909 


5.5828 


546.64 


23778.7 


175 


30625 


5359375 


13.2288 


5-5934 


549.78 


24052.8 


176 


30976 


5451776 


13.2665 


5.6041 


552.92 


24328.5 


177 


3 J 3 2 9 


5545233 


13-3041 


5-6i47 


556.o6 


24605.7 


178 


31684 


5639752 


I3-34I7 


5-6252 


559-20 


24884.6 


179 


32041 


5735339 


I3-379 1 


5-6357 


562.35 


25164.9 


180 


32400 


5832000 


13.4164 


5.6462 


56549 


25446.9 


181 


32761 


5929741 


I3-4536 


5-6567 


568.63 


25730.4 


182 


33 I2 4 


6028568 


13.4907 


5.6671 


571.77 


26015.5 


183 


33489 


6128487 


I3-5277 


5-6774 


574-9 1 


26302.2 


184 


33856 


6229504 


I3-5647 


5-6877 


578.05 


26^90.4 


185 


34225 


6331625 


13.6015 


5.6980 


581.19 


26880.3 


186 


34596 


6434856 


13.6382 


5-7083 


584.34 


271 7 1. 6 


187 


34969 


6539 20 3 


13.6748 


5-7i85 


587.48 


27464.6 


188 


35344 


6644672 


i3-7ii3 


5-7287 


590.62 


27759.1 


189 


35721 


6751269 


13-7477 


5.7388 


593.76 


28055.2 


190 


36100 


6859000 


15.7840 


5-7489 


596.90 


28352.9 


191 


36481 


6967871 


13.8203 


5-759o 


600.04 


28652.1 


192 


36864 


7077888 


13.8564 


5.7690 


603.19 


28952.9 


193 


37249 


7189057 


13.8924 


5-779° 


606.33 


29255-3 


194 


37636 


73 OI 3 8 4 


13.9284 


5.7890 


609.47 


29559-2 


195 


38025 


7414875 


13.9642 


5-7989 


612.61 


29864.8 


196 


38416 


7529536 


14.0000 


5.8088 


6I5.75 


301 7 1. 9 


197 


38809 


7645373 


14.0357 


5.8186 


618.89 


30480.5 


198 


39204 


7762392 


14.0712 


5.8285 


622.04 


30790.7 


199 


39601 


7880599 


14.1067 


5.8383 


625.18 


31102.6 


200 


40000 


8000000 


14.1421 


5.8480 


628.32 


3 r 4i5-9 



SQUARES, CUBES AND ROOTS 



469 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


201 


40401 


8120601 


14.1774 


5.8578 


631.46 


31730.9 


202 


40804 


8242408 


14.2127 


5.8675 


634.60 


32047.4 


203 


41209 


8365427 


14.2478 


5.8771 


63774 


32365.5 


204 


41616 


8489664 


14.2829 


5.8868 


640.89 


32685.1 


205 


42025 


8615125 


14.3178 


5.8964 


644.03 


33006.4 


206 


42436 


8741816 


14.3527 


5.9059 


647.17 


33329.2 


207 


42849 


8869743 


14.3875 


5.9I55 


650.31 


33653-5 


208 


432 64 


8998912 


14.4222 


5.9250 


65345 


33979-5 


209 


43681 


9129329 


14.4568 


5-9345 


656.59 


34307.0 


210 


44100 


9261000 


14.4914 


5-9439 


65973 


34636.1 


211 


44521 


9393931 


14.5258 


5-9533 


662.88 


34966.7 


212 


44944 


9528128 


14.5602 


5.9627 


666.02 


35298.9 


213 


45369 


9663597 


14.5945 


5.9721 


669.16 


35632.7 


214 


45796 


9800344 


14.6287 


5.9814 


672.30 


35968.1 


215 


46225 


9938375 


14.6629 


5.9907 


67544 


36305.0 


2l6 


46656 


10077696 


14.6969 


6.0000 


678.58 


36643.5 


217 


47089 


10218313 


I47309 


6.00Q2 


681.73 


36983.6 


2l8 


47524 


10360232 


14.7648 


6.O185 


684.87 


37325.3 


219 


47961 


10503459 


14.7986 


6.O277 


688.01 


37668.5 


220 


48400 


10648000 


• 14.8324 


6.O368 


691.15 


38013.3 


221 


48841 


10793861 


14.8661 


6.O459 


694.29 


38359-6 


222 


49284 


10941048 


14.8997 


6.O55O 


69743 


38707.6 


223 


49729 


I10S9567 


I4.9332 


6.064I 


700.58 


39057-I 


2 24 


50176 


11239424 


14.9666 


6.O732 


703.72 


■ 394o8.i 


225 


50625 


11390625 


15.0000 


6.0822 


706.86 


3976o.8 


226 


51076 


ii543!76 


*5-°333 


6.O912 


710.OO 


401 15.0 


227 


51529 


1 1 69 7083 


15.0665 


6.I002 


7 I 3-i4 


40470.8 


228 


51984 


11852352 


15.0997 


6.IOQI 


716.28 


40828.1 


229 


52441 


12008989 


i5-!327 


6.Il8o 


719.42 


41187.1 


23O 


52900 


1 2 167000 


15.1658 


6.I26C) 


722.57 


41547.6 


23I 


5336l 


12326391 


15.1987 


6.I358 


725.71 


41909.6 


232 


53 8 24 


12487168 


15-2315 


6.I446 


728.85 


42273.3 


2 33 


54289 


I2 649337 


15.2643 


6.1534 


73L99 


42638.5 


234 


54756 


12812904 


15.2971 


6.l622 


735.13 


43005-3 


235 


55225 


12977875 


J 5-3297 


6.I7IO 


738.27 


43373-6 


236 


55696 


13144256 


15.3623 


6.1797 


741.42 


43743-5 


237 


56169 


!33i2053 


15.3948 


6.1885 


744.56 


44ii5-o 


238 


56644 


13481272 


15.4272 


6.I972 


747.7o 


44488.1 


239 


57121 


13651919 


154596 


6.2058 


750.84 


44862.7 


240 


57600 


13824000 


15.4919 


6.2145 


753.98 


45238.9 



47° 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 



"NTr» 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


lNO. 


Circum. 


Area 


241 


58081 


I399752I 


15.5242 


6.2231 


757-12 


45616.7 


242 


58564 


14172488 


I5-5563 


6.2317 


760.27 


45996.1 


243 


59°49 


14348907 


15.5885 


6.2403 


76341 


46377.0 


244 


59536 


14526784 


15.6205 


6.2488 


766.55 


46759.5 


245 


60025 


14706125 


I5-6525 


6.2573 


769.69 


47!43-5 


246 


60516 


14886936 


15.6844 


6.2658 


772.83 


47529.2 


247 


61009 


15069223 


15.7162 


6.2743 


775-97 


47916.4 


248 


61504 


15252992 


15.7480 


6.2828 


779.12 


48305.1 


249 


62001 


15438249 


15.7797 


6.2912 


782.26 


48695.5 


250 


62500 


15625000 


15,8114 


6.2996 


78540 


49087.4 


251 


63001 


15813251 


15.8430 


6.3080 


788.54 


49480.9 


252 


635 4 


16003008 


I5-8745 


6.3164 


791.68 


49875-9 


253 


64009 


16194277 


15.9060 


6.3247 


794.82 


50272.6 


254 


64516 


16387064 


15.9374 


6 -333° 


797.96 


50670.7 


255 


65025 


16581375 


15.9687 


6.3413 


801. 11 


5 io 7o-5 


256 


65536 


16777216 


16.0000 


6.3496 


804.25 


5I47L9 


257 


66049 


16974593 


16.0312 


6-3579 


807.39 


51874.8 


258 


66564 


i7i735 J 2 


16.0624 


6.3661 


810.53 


52279.2 


259 


67081 


17373979 


16.0935 


6-3743 


813.67 


52685.3 


260 


67600 


17576000 


16.1245 


6.3825 


816.81 


53092.9 


26l 


68121 


17779581 


I6.I555 


6.3907 


819.96 


53502.1 


262 


68644 


17984728 


16.1864 


6.3988 


823.10 


53912.9 


2 63 


69169 


18191447 


16.2173 


6.4070 


826.24 


54325.2 


264 


69696 


18399744 


16.2481 


6.4151 


829.38 


54739-1 


265 


70225 


18609625 


16.2788 


6.4232 


832.52 


55154.6 


266 


70756 


18821096 


16.3095 


6.4312 


835.66 


55571.6 


267 


71289 


19034163 


16.3401 


6-4393 


838.81 


55990.3 


268 


71824 


19248832 


16.3707 


6-4473 


841.95 


56410.4 


269 


72361 


19465109 


16.4012 


6-4553 


845.09 


56832.2 


270 


72900 


19683000 


16.4317 


6.4633 


848.23 


57255.5 


271 


73441 


19902511 


16.4621 


6.47J3 


85I-37 


57680.4 


272 


73984 


20123648 


16.4924 


6.4792 


854.51 


58106.9 


273 


74529 


20346417 


16.5227 


6.4872 


857.66 


58534.9 


274 


75076 


20570824 


16.5529 


6.4951 


860.80 


58964.6 


275 


75625 


20796875 


16.5831 


6.5030 


863.94 


59395-7 


276 


76176 


21024576 


16.6132 


6.5108 


867.08 


59828.5 


277 


76729 


21253933 


16.6433 


6.5187 


870.22 


60262.8 


278 


77284 


21484952 


16.6733 


6.5265 


873-36 


60698.7 


279 


77841 


21 71 7639 


16.7033 


6.5343 


876.50 


61136.2 


280 


78400 


21952000 


16.7332 


6.5421 


879.65 


6i575-2 



SQUARES, CUBES AND ROOTS 



471 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




and Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


281 


78961 


22188041 


16.7631 


6.5499 


882.79 


62015.8 


282 


79524 


22425768 


16.7929 


6-5577 


885.93 


62458.0 


283 


80089 


22665187 


16.8226 


6.5654 


889.07 


62901.8 


284 


80656 


22906304 


16.8523 


6-573 1 


892.21 


63347.1 


285 


81225 


23149125 


16.8819 


6.5808 


895.35 


63794.0 


286 


81796 


23393656 


16.91 15 


6.5885 


898.50 


64242.4 


287 


82369 


236399 3 


16.9411 


6.5962 


901.64 


64692.5 


288 


82944 


23887872 


16.9706 


6.6039 


904.78 


65144. 1 


289 


83521 


24137569 


1 7 .OOOO 


6.6115 


907.92 


65597.2 


290 


84100 


24389000 


17.0294 


6.6191 


911.06 


66052.O 


291 


84681 


24642171 


17.0587 


6.6267 


914.20 


66508.3 


292 


85264 


24897088 


17.0880 


6.6343 


917.35 


66966.2 


293 


85849 


25153757 


17.1172 


6.6419 


920.49 


67425.6 


294 


86436 


25412184 


17.1464 


6.6494 


923.63 


67886.7 


295 


87025 


25672375 


17.1756 


6.6569 


926.77 


68349-3 


296 


87616 


25934336 


17.2047 


6.6644 


929.91 


68813.5 


297 


88209 


26198073 


17.2337 


6.6719 


933.05 


69279.2 


298 


88804 


26463592 


17.2627 


6.6794 


936.19 


69746.5 


299 


89401 


26730899 


17.2916 


6.6869 


939-34 


70215.4 


300 


90000 


27000000 


17.3205 


6.6943 


942.48 


70685.8 


301 


90601 


27270901 


17.3494 


6.7018 


945.62 


7II57.9 


302 


91204 


27543608 


I7.378I 


6.7092 


948.76 


7I63I.5 


3°3 


91809 


27818127 


17.4069 


6.7166 


951.90 


72106.6 


3°4 


92416 


28094464 


17.4356 


6.7240 


955.04 


725834 


3°5 


93025 


28372625 


17.4642 


6.73 J 3 


958.19 


73061.7 


306 


93636 


28652616 


17.4929 


6.7387 


96i.33 


7354L5 


3°7 


94249 


28934443 


17.5214 


6.7460 


964.47 


74023.0 


308 


94864 


29218112 


17-5499 


6.7533 


967.61 


74506.0 


3°9 


9548i 


29503629 


I7.5784 


6.7606 


97°-75 


74990.6 


310 


96100 


29791000 


17.6068 


6:7679 


973-89 


75476.8 


3 11 


96721 


30080231 


17.6352 


6.7752 


977.04 


75964.5 


312 


97344 


30371328 


17.6635 


6.7824 


980.18 


76453.8 


3*3 


97969 


30664297 


17.6918 


6.7897 


983-32 


76944.7 


314 


98596 


30959144 


17.7200 


6.7969 


986.46 


77437-1 


3i5 


99225 


31255875 


17.7482 


6.8041 


989.60 


7793I- 1 


316 


99856 


31554496 


17.7764 


6.8113 


992.74 


78426.7 


3i7 


100489 


31855013 


17.8045 


6.8185 


995.88 


78923.9 


3i8 


101124 


32157432 


17.8326 


6.8256 


999.03 


79422.6 


3i9 


101761 


32461759 


17.8606 


6.8328 


1002.20 


79922.9 


320 


102400 


32768000 


17.8885 


6.8399 


1005.30 


80424.8 



472 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




and Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


321 


103041 


33076161 


17.9165 


6.8470 


1008.5 


80928.2 


322 


103684 


33386248 


17.9444 


6.8^41 


1011.6 


81433.2 


323 


104329 


33698267 


17.9722 


6.8612 


1014.7 


81939.8 


3 2 4 


104976 


34012224 


18.0000 


6.8683 


1017.9 


82448.O 


325 


105625 


34328125 


18.0278 


6-8753 


1021.0 


82957.7 


326 


106276 


34645976 


18.0555 


6.8824 


1024.2 


83469.0 


32 7 


106929 


34965783 


18.0831 


6.8894 


1027.3 


83981.8 


328 


107584 


35287552 


18.1108 


6.8964 


1030.4 


84496.3 


329 


108241 


35611289 


18.1384 


6.9034 


1033.6 


85012.3 


33° 


108900 


35937000 


18.1659 


6.9104 


1036.7 


85529.9 


33i 


109561 


36264691 


18.1934 


6.9174 


1039.9 


86049.0 


332 


110224 


36594368 


18.2209 


6.9244 


1043.0 


86569.7 


333 


I 10889 


36926037 


18.2483 


6.9313 


1046.2 


87092.O 


334 


III556 


37259704 


18.2757 


6.9382 


1049.3 


87615.9 


335 


112225 


37595375 


18.3030 


6.9451 


1052.4 


88141,3 


336 


112896 


37933056 


I8.3303 


6.9521 


I055-6 


88668.3 


337 


H35 6 9 


38272753 


18.3576 


6.9589 


105.8.7 


89196.9 


33& 


I 14244 


38614472 


18.3848 


6.9658 


1061.9 


89727.O 


339 


114921 


38958219 


18.4120 


6.9727 


1065.0 


90258.7 


34o 


115600 


39304000 


18.4391 


6.9795 


1068. 1 ■ 


90792.O 


34i 


116281 


39651821 


18.4662 


6.9864 


1071.3 


91326.9 


342 


I 16964 


40001688 


18.4932 


6.9932 


1074.4 


91863.3 


343 


1 1 7649 


40353607 


18.5203 


7.0000 


1077.6 


92401.3 


344 


118336 


40707584 


18.5472 


7.0068 


1080.7 


92940.9 


345 


H9 25 


41063625 


18.5742 


7.0136 


1083.8 


93482.O 


346 


119716 


41421736 


18.6011 


7.0203 


1087.0 


94024.7 


347 


120409 


41781923 


18.6279 


7.0271 


1090. 1 


94569.O 


348 


121104 


421.44192 


18.6548 


7-0338 


I093-3 


95114.9 


349 


121801 


42508549 


18.6815 


7.0406 


1096.4 


95662.3 


35o 


122500 


42875000 


18.7083 


7-°473 


1099.6 


96211.3 


35i 


123201 


43243551 


I8.7350 


7.0540 


1102.7 


96761.8 


352 


123904 


43614208 


18.7617 


7.0607 


1105.8 


97314.O 


353 


124609 


43986977 


18.7883 


7.0674 


1 109.0 


978677 


354 


125316 


44361864 


18.8149 


7.0740 


1112.1 


98423.O 


355 


126025 


44738875 


18.8414 


7.0807 


IH5-3 


98979.8 


356 


126736 


45118016 


18.8680 


7.0873 


1118.4 


99538.2 


357 


127449 


45499293 


18.8944 


7.0940 


1121.5 


IOO098 


358 


128164 


45882712 


18.9209 


7.1006 


1124.7. 


100660 


359 


128881 


46268279 


18.9473 


7.1072 


1 127.8 


IOI223 


360 


129600 


46656000 


18.9737 


7.1138 


1131.0 


IO1788 



SQUARES, CUBES AND ROOTS 



473 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 













ClRft-t! 


No. 


Square 


Cube 


Sq. Root 


Cube Root 






Circum. 


Area 


361 


130321 


47045881 


19.0000 


7.1204 


1134*1 


IO2354 


362 


131044 


47437928 


19.0263 


7.1269 


H37-3 


IO2922 


363 


131769 


47832147 


19.0526 


7-1335 


1140.4 


103491 


364 


132496 


48228544 


19.0788 


7.1400 


11430 


IO4062 


365 


133225 


48627125 


19.1050 


7.1466 


1146.7 


IO4635 


366 


133956 


49027896 


19.1311 


7-I53I 


1149.8 


105209 


367 


134689 


49430863 


19.1572 


7.1596 


1153-0 


105785 


368 


135424 


49836032 


19-1833 


7.1661 


1156.1 


106362 


369 


136161 


50243409 


19.2094 


7.1726 


1159-2 


106941 


370 


136900 


50653000 


I9-2354 


7-I79I 


1 1 62 .4 


107521 


371 


137641 


51064811 


19.2614 


7.1855 


1165.5 


108103 


372 


138384 


51478848 


19.2873 


7.1920 


1 1 68.7 


108687 


373 


139129 


5I895II7 


19.3132 


7.1984 


1171.8 


IO9272 


374 


139876 


52313624 


I9-339I 


7.2048 


1175.0 


109858 


375 


140625 


52734375 


19.3649 


7.2 1 12 


1178.1 


I 10447 


376 


141376 


53157376 


19.3907 


7.2177 


1181.2 


IIIO36 


377 


142129 


53582633 


19.4165 


7.224O 


1 184.4 


111628 


378 


142884 


54010152 


19.4422 


7.2304 


1187.5 


II222I 


379 


143641 


54439939 


19.4679 


7.2368 


1190.7 


II28I5 


380 


144400 


54872000 


19.4936 


7.2432 


H93-8 


II34II 


381 


145161 


553 634i 


19.5192 


7-2495 


1 196.9 


I I 4OO9 


382 


145924 


55742968 


19.5448 


7.2558 


1200. 1 


I I4608 


3*3 


146689 


56181887 


19.5704 


7.2622 


1203.2 


II5209 


384 


147456 


56623104 


19-5959 


7.2685 


1206.4 


II5812 


385 


148225 


57066625 


19.6214 


7.2748 


1209.5 


H6416 


386 


148996 


57512456 


19.6469 


7.28ll 


1212.7 


I I 702 I 


3*7 


149769 


57960603 


19.6723 


7.2874 


1215.8 


II7628 


388 


I5 544 


58411072 


19.6977 


7.2936 


1218.9 


H8237 


389 


*5 1 3 21 


58863869 


19.7231 


7.2999 


1222. 1 


I 18847 


39o 


152100 


59319000 


19.7484 


7.3061 


1225.2 


I 19459 


39i 


152881 


59776471 


19-7737 


7-3 I2 4 


1228.4 


120072 


392 


153664 


60236288 


19.7990 


7.3186 


1231-5 


I20687 


393 


154449 


60698457 


19.8242 


7.3248 


1234.6 


I21304 


394 


155236 


61162984 


19.8494 


7.33io 


1237.8 


I2I922 


395 


156025 


61629875 


19.8746 


7.3372 


1240.9 


122542 


396 


156816 


62099136 


19.8997 


7-3434 


1244. 1 


I23163 


397 


157609 


62570773 


19.9249 


7.3496 


1247.2 


I23786 


398 


158404 


63044792 


19.9499 


7.3558 


1250.4 


I244IO 


399 


159201 


63521199 


19.9750 


7.3619 


1253.5 


I25036 


400 


160000 


64000000 


20.0000 


7.3684 


1256.6 


I25664 



474 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square Roots, Cube Roots. Circumferences, 
and Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


401 


I 60801 


64481 201 


20.0250 


7-3742 


1259.8 


126293 


402 


I 61 604 


64964808 


20.0499 


7-3803 


1262.9 


126923 


403 


162409 


6545 o8 27 


20.0749 


7.3864 


1266.1 


127556 


404 


163216 


65939264 


20.0998 


7-3925 


1269.2 


128190 


405 


164025 


66430125 


20.1246 


7.3986 


1272.3 


128825 


406 


164836 


66923416 


20.1494 


7.4047 


1275.5 


129462 


407 


165649 


67419143 


20.1742 


7.4108 


1278.6 


130100 


408 


166464 


67917312 


20.1990 


7.4169 


1281.8 


I3°74I 


409 


167281 


68417929 


20.2237 


7.4229 


1284.9 


131382 


4.10 


168100 


68921000 


20.2485 


7.4290 


1288. 1 


132025 


411 


I 6892 I 


69426531 


20.2731 


7-435° 


1291.2 


132670 


412 


169744 


699345 2 8 


20.2978 


7.4410 


1294.3 


*333*7 


413 


170569 


70444997 


20.3224 


7.4470 


1297.5 


133965 


414 


171396 


70957944 


20.3470 


7-453° 


1300.6 


134614 


415 


172225 


71473375 


20.3715 


7-459° 


l3°3-8 


135265 


416 


I73 56 


71991296 


20.3961 


7.4650 


1306.9 


i359i8 


417 


173889 


72511713 


20.4206 


7.4710 


1310.0 


136572 


418 


174724 


73034632 


20.4450 


7.4770 


i3 I 3- 2 


137228 


419 


I7556I 


73560059 


20.4695 


7.4829 


i3 l6 -3 


137885 


420 


176400 


74088000 


20.4939 


7.4889 


i3 J 9-5 


138544 


421 


177241 


74618461 


20.5183 


7.4948 


1322.6 


139205 


422 


178084 


75151448 


20.5426 


7-5°°7 


1325-8 


139867 


423 


178929 


75686967 


20.5670 


7.5067 


1328.9 


i4°53 x 


424. 


179776 


76225024 


20.5913 


7.5126 


1332.0 


141196 


425 


180625 


76765625 


20.6155 


7-5i85 


1335-2 


141863 


426 


181476 


77308776 


20.6398 


7.5244 


1338.3 


14253 1 


427 


182329 


77854483 


20.6640 


7-53° 2 


I34I-5 


143201 


428 


183184 


78402752 


20.6882 


7-536i 


1344.6 


143872 


429 


184041 


78953589 


20.7123 


7.5420 


1347-7 


144545 


43° 


184900 


79507000 


20.7364 


7-5478 


i35°-9 


145220 


43i 


185761 


80062991 


20.7605 


7-5537 


I354-0 


145896 


432 


186624 


80621568 


20.7846 


7-5595 


1357-2 


146574 


433 


187489 


81182737 


20.8087 


7-5654 


1360.3 


147254 


434 


188356 


81746504 


20.8327 


7-5712 


1363-5 


147934 


435 


189225 


82312875 


20.8567 


7-577° 


1366.6 


148617 


436 


190096 


82881856 


20.8806 


7.5828 


1369.7 


149301 


437 


190969 


83453453 


20.9045 


7.5886 


1372.9 


149987 


438 


191844 


84027672 


20.9284 


7-5944 


1376.0 


150674 


439 


192721 


84604519 


20.9523 


7.6001 


1379.2 


*5 1 3 6 3 


440 


193600 


85184000 


20.9762 


7.6059 


1382.3 


i52°53 



SQUARES, CUBES AND ROOTS 



475 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 













ClRPTTT 


No. 


Square 
194481 


Cube 


Sq. Root 


Cube Root 






Circum. | 


Area 


441 


8^766121 


2 1 .OOOO 


7.6117 


I385-4 


J 5 2 745 


442 


195364 


86350888 


21.0238 


7.6174 


1388.6 


153439 


443 


196249 


86938307 


21.0476 


7.6232 


I39I-7 


I54I34 


444 


197136 


87528384 


21.0713 


7.6289 


1394.9 


154830 


445 


198025 


88121125 


21.0950 


7.6346 


1398.O 


i555 2 8 


446 


198916 


88716536 


21.1187 


7.6403 


1401.2 


156228 


447 


199809 


89314623 


21.1424 


7.6460 


1404.3 


156930 


448 


200704 


89915392 


21.1660 


7-65I7 


1407.4 


157633 


449 


201601 


90518849 


21.1896 


7-6574 


1410.6 


158337 


45° 


202500 


91125000 


21.2132 


7.6631 


I4I3-7 


159043 


45i 


203401 


9i733 8 5i 


21.2368 


7.6688 


1416.9 


i5975i 


45 2 


204304 


92345408 


21.2603 


7.6744 


1420.O 


160460 


453 


205209 


92959677 


21.2838 


7.6801 


I423-I 


161171 


454 


206116 


93576664 


21.3073 


7.6857 


1426.3 


161883 


455 


207025 


94I9 6 375 


21.3307 


7.6914 


1429.4 


162597 


456 


207936 


94818816 


21.3542 


7.6970 


1432.6 


163313 


457 


208849 


95443993 


21.3776 


7.7026 


1435-7 


164030 


458 


209764 


96071912 


2 1 .4OO9 


7.7082 


1438.9 


164748 


459 


210681 


96702579 


2I.4243 


7-7I38 


1442.0 


165468 


460 


21 l6oO 


97336000 


2I.4476 


7-7 J 94 


I445- 1 


166190 


461 


2I252I 


97972181 


2I.4709 


7.7250 


1448.3 


166914 


462 


213444 


98611128 


2I.4942 


7.7306 


i45 x -4 


167639 


463 


214369 


99252847 


21.5174 


7.7362 


1454.6 


168365 


464 


215296 


99897344 


2I.5407 


7.7418 


1457-7 


169093 


465 


216225 


100544625 


2I.5639 


7-7473 


1460.8 


169823 


466 


217156 


101194696 


2I.587O 


7-7529 


1464.0 


170554 


467 


218089 


101847563 


2I.6I02 


7-7584 


1467. 1 


171287 


468 


219024 


102503232 


21.6333 


7-7639 


i47o-3 


172021 


469 


219961 


103161709 


2I.6564 


7-7695 


1473-4 


172757 


470 


2209OO 


103823000 


2I.6795 


7-775o 


1476.5 


173494 


47i 


22184I 


104487111 


21.7025 


7-7805 


1479-7 


174234 


472 


222784 


105154048 


21.7256 


7.7860 


1482.8 


174974 


473 


223729 


105823817 


2I.7486 


7-7915 


1486.0 


175716 


474 


224676 


106496424 


2I.7715 


7.7970 


1489. 1 


176460 


475 


225625 


107171875 


21-7945 


7.8025 


1492.3 


177205 


476 


226576 


107850176 


2I.8174 


7.8079 


1495-4 


177952 


477 


227529 


108531333 


21.8403 


7-8i34 


1498.5 


178701 


478 


228484 


I0 92i535 2 


2I.8632 


7.8188 


1501.7 


i7945i 


479 


22944I 


109902239 


2I.886I 


7.8243 


1504.8 


180203 


480 


2304OO 


110592000 


2I.9089 


7.8297 


1508.0 


180956 



476 



GENERAL REFERENCE TABLES 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
and Circular Areas of Nos. from i to 520 



No 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


J.NV.J. 


Circum. 


Area 


48l 


231361 


111284641 


21.9317 


7.8352 


1511.I 


181711 


482 


2323 2 4 


111980168 


2L9545 


7.8406 


I.5I4.3 


182467 


483 


233289 


112678587 


21.9773 


7.8460 


I5I74 


183225 


484 


234256 


H33799°4 


22.0000 


7.85I4 


1520.5 


183984 


48S 


235225 


114084125 


22.0227 " 


7.8568 


15237 


184745 


486 


236196 


114791256 


22.0454 


7.8622 


1526.8 


185508 


487 


237169 


II 55oi3°3 


22.0681 


7.8676 


I530.0 


186272 


488 


238144 


116214272 


22.0907 


7.8730 


I 533-i 


187038 


489 


239121 


1 1 69301 69 


22.1133 


7.8784 


1536.2 


187805 


490 


240100 


1 1 7649000 


22.1359 


7.8837 


15394 


188574 


491 


241081 


118370771 


22.1585 


7.8891 


1542.5 


189345 


492 


242064 


1 19095488 


22.1811 


7.8944 


1545.7 


190117 


493 


243049 


119823157 


22.2036 


7.8998 


1548.8 


190890 


494 


244036 


120553784 


22.2261 


7.905 1 


I55L9 


191665 


495 


245025 


121287375 


22.2486 


7.9I05 


I555-I 


192442 


496 


246016 


122023936 


22.2711 


7.9158 


1558.2 


193221 


497 


247009 


122763473 


22.2935 


7.921 1 


1561.4 


194000 


498 


248004 


I2 35°5992 


22.3159 


7.9264 


1564.5 


194782 


499 


249001 


124251499 


22.3383 


7.9317 


1567.7 


195565 


500 


250000 


125000000 


22.3607 


7.9370 


1570.8 


196350 


5oi 


251001 


125751501 


22.3830 


7.9423 


1573-9 


197136 


502 


252004 


126506008 


22.4054 


7.9476 


I577-I 


197923 


503 


253009 


127263527 


22.4277 


7.9528 


1580.2 


198713 


5°4 


254016 


128024064 


22.4499 


7.958i 


1583-4 


199504 


505 


255025 


128787625 


22.4722 


7.9634 


1586.5 


200296 


506 


256036 


129554216 


22.4944 


7.9686 


1589.7 


201090 


5o7 


257049 


130323843 


22.5167 


7-9739 


1592.8 


201886 


508 


258064 


131096512 


22.5389 


7.9791 


1595-9 


202683 


5o9 


259081 


131872229 


22.5610 


7-9843 


I599-I 


203482 


5io 


260100 


13 265 1000 


22.5832 


7.9896 


1602.2 


204282 


5ii 


261121 


13343283 1 


22.6053 


7.9948 


1605.4 


205084 


512 


262144 


134217728 


22.6274 


8.0000 


1608.5 


205887 


5i3 


263169 


i35 00 5 6 97 


22.6495 


8.0052 


1611.6 


206692 


5i4 


264196 


135790744 


22.6716 


8.0104 


1614.8 


207499 


5i5 


265225 


136590875 


22.6936 


8.0156 


1617.9 


208307 


5i6 


266256 


137388096 


22.7156 


8.0208 


1621.1 


209117 


5i7 


267289 


138188413 


22.7376 


8.0260 


1624.2 


209928 


5i8 


268324 


138991832 


22.7596 


8.03 1 1 


1627.3 


210741 

21155° 


5i9 


269361 


139798359 


22.7816 


8.0363 


1630.5 


520 


270400 


140608000 


22.8035 


8.0415 


1633.6 


212372 



TRIGONOMETRIC FUNCTIONS 



477 



Table 59. Trigonometric Functions and the Solution of 

Triangles 



In the accompanying figure the trig- 
onometric functions of the angle A 
between the lines B A and A C are 
as follows; 



sin A 

cos A 

tan 

cot 

sec 

cosec 

ex-sec 



= BC 

= AC 

= EF 

= G H 

= A E 

= A H 
= B E 




In the right-angled triangle ABC 
let a equal the side B C opposite the 

angle A; let b equal the side A C opposite the angle B; let 
equal A B, the side opposite the angle C. 

Let C = oo° 

The following formulae apply to right-angled triangles: 



Angles. A+B +C = 180 

A + B = oo° 

A = 90 .- B 
B = go°~A 



Sides. 



sin A 
cos A 

tan A 



A 


rea 


a b 


area 




2 



--c sin A = b tan A 
V(c+b)(c-b$ 

c cos. A = 



tan A 



b = V (c + a) (c — a) 

_ a b 

sin A cos A 

c = V 7 a 2 + b 2 



B 1 



Oblique Triangles. 

Note. Where an angle is 
more than 90 its sine, cosine, 
and tangent are equal to that 
of the angle (180 — the angle 
in question); that is, if the sine 
of 120 is desired take the sine 
of (180 - 120 ) = 6o°. 






B / Let K=Area \ 




478 



GENERAL REFERENCE TABLES 



Given 



A,B, a 



Desired 



A, a, b 



C, a, b 



C,b 
c, K 



B, C 



i(A+B) 

i(A-B) 

A B 



K 



Formulae 



C = 1 80 — (A + B); b 



a 



sin B 



c = 



a 



sin A 



sin (.4 +£);#= 



sin .4 

a 2 sin 5 sin C 
2 sin ^4 



sin 5= ^-^ 6; C = 180 - (A + 5) 



c = 



sin A 



sin C 



Two solutions are possible with B' as an acute angle 
and B as an obtuse angle 



i{A+B) =90° - \C 
tan \{A-B) = 



a + b 
A=l(A+B) + i(A-B) 

B = -\{A+B) - Hi ~B) 
sin i(A+B) 



tan i (A+B) 



c = (a — b) 



sin i (A - B) 



K = h ab sin C 



a, by c 



B 



K 



In the following formula s = \ (a + b + c) 



sin \ B 



- a) - c) 



sin B 



2 y/ s (s — a) (s — b) (s — c) 



ac 



K = V s -a) (s - b) (s - c) 



NATURAL TANGENTS AND CO-TANGENTS 479 



Table 60 









Tan. 


Co-tan. 


.00000 


Infinite. 


.00029 


3437-750 


.00058 


1718.870 


.00087 


1145.920 


.00116 


859-436 


.00145 


687.549 


.00175 


572.957 


.00204 


491.106 


.00233 


429.718 


.00262 


381.971 


.00291 


343-774 


.00320 


312.521 


.00349 


286.478 


•00378 


264.441 


.00407 


245-552 


.00436 


229.182 


.00465 


214.858 


.00495 


202.219 


.00524 


190.984 


•00553 


180.932 


.00582 


171.885 


.00611 


163.700 


.00640 


156.259 


.00669 


149.465 


.00698 


143-237 


.00727 


137-507 


.00756 


132.219 


.00785 


127.321 


.00814 


122.774 


.00844 


118.540 


.00873 


114-589 


.00902 


110.892 


•00931 


107.426 


.00960 


104. 171 


.00989 


101.107 


.01018 


98.2179 


.01047 


95-4895 


.01076 


92.9085 


.01105 


90-4633 


.01135 


88.1436 


.01164 


85-9398 


.01193 


83.8435 


.01222 


81.8470 


.01251 


79-9434 


.01280 


78.1263 


•01309 


76.3900 


•01338 


74.7292 


•01367 


73-I390 


.01396 


71-6151 


.01425 


70.I533 


•01455 


68.7501 


.01484 


67.4019 


•01513 


66.1055 


.01542 


64.8580 


.01571 


63.6567 


.01600 


62.4992 


.01629 


61.3829 


.01658 


60.3058 


.01687 


592659 


.01716 


58.2612 


.01746 


57.2900 


Co-tan. 


Tan. 


1 


$9° 



1 





2 


O 


3 





Tan. 


Co-tax. 


Tan. 


CO -TAN. 


Tan. 


Co-tan. 


.01746 


57.2900 


.03492 


28.6363 


.05241 


19.0811 


.01775 


56-3506 


.03521 


28.3994 


.05270 


18.9755 


.01804 


55-4415 


•03550 


28.1664 


.05299 


18.8711 


.01833 


54-5613 


•03579 


27.9372 


.05328 


18.7678 


.01862 


53.7086 


.03609 


27.7117 


.05357 


18.6656 


.01891 


52.8821 


.03638 


27.4899 


•05387 


18.5645 


.01920 


52.0807 


.03667 


27.2715 


.05416 


18.4645 


.01949 


51-3032 


.03696 


27.0566 


•05445 


18.3655 


.01978 


50.5485 


.03725 


26.8450 


•05474 


18.2677 


.02007 


49.8157 


•03754 


26.6367 


•05503 


18.1708 


.02036 


49.1039 


•03783 


26.4316 


•05533 


18.0750 


.02066 


48.4121 


.03812 


26.2296 


.05562 


17.9802 


.02095 


47-7395 


.03842 


26.0307 


•05591 


17.8863 


.02124 


47-0853 


.03871 


25.8348 


.05620 


17-7934 


.02153 


46.4489 


.03900 


25.6418 


.05649 


17.7015 


.02182 


45.8294 


.03929 


25.45I7 


.05678 


17.6106 


.02211 


45.2261 


.03958 


25.2644 


•05708 


17-5205 


.02240 


44.6386 


.03987 


25.0798 


•05737 


I7-43I4 


.02269 


44.0661 


.04016 


24.8978 


.05766 


17-3432 


.02298 


43-5o8i 


.04046 


24.7I85 


•05795 


17-2558 


.02328 


42.9641 


.04075 


24.5418 


.05824 


17.1693 


•02357 


42-4335 


.04104 


24.3675 


•05854 


17.0837 


.02386 


41.9158 


•04133 


24.1957 


.05883 


16.9990 


.02415 


41.4106 


.04162 


24.0263 


.05912 


16.9150 


.02444 


40.9174 


.04191 


23-8593 


.05941 


16.8319 


.02473 


40.4358 


.04220 


23-6945 


.05970 


16.7496 


.02502 


39-9655 


.04250 


23-5321 


.05999 


16.6681 


•02531 


39.5059 


.04279 


23-37I8 


.06029 


16.5874 


.02560 


39.0568 


.04308 


23.2137 


.06058 


16.5075 


.02589 


38.6177 


•04337 


23-0577 


.06087 


16.4283 


.02619 


38.1885 


•04366 


22.9038 


.06116 


16.3499 


.02648 


37.7686 


•04395 


22.7519 


.06145 


16.2722 


.02677 


37-3579 


.04424 


22.6020 


.06175 


16.1952 


.02706 


36.9560 


•04454 


22.4541 


.06204 


16.1190 


•02735 


36.5627 


•04483 


22.3081 


•06233 


16.0435 


.02764 


36.1776 


.04512 


22.1640 


.06262 


15-9687 


•02793 


35.8006 


.04541 


22.0217 


.06291 


I5-8945 


.02822 


35.43I3 


•04570 


21.8813 


.06321 


15.8211 


.02851 


35-0695 


.04599 


21.7426 


.06350 


I5-7483 


.02881 


34.7I5I 


.04628 


21.6056 


.06379 


15.6762 


.02910 


34-3678 


.04658 


21.4704 


.06408 


15.6048 


.02939 


34-0273 


.04687 


21.3369 


.06437 


I5-5340 


.02968 


33-6935 


.04716 


21.2049 


.06467 


15-4638 


.02997 


33.3662 


•04745 


21.0747 


.06496 


15-3943 


.03026 


33-0452 


•04774 


20.9460 


•06525 


I5.3254 


.03055 


32.7303 


.04803 


20.8188 


•06554 


I5.257I 


.03084 


32.4213 


.04832 


20.6932 


.06584 


I5-I893 


.03114 


32.1181 


.04862 


20.5691 


.06613 


15.1222 


•03143 


31.8205 


.04891 


20.4465 


.06642 


I5-0557 


.03172 


31.5284 


.04920 


20.3253 


.06671 


14.9898 


.03201 


31.2416 


.04949 


20.2056 


.06700 


14.9244 


•03230 


30.9599 


.04978 


20.0872 


•06730 


14.8596 


•03259 


30.6833 


.05007 


19.9702 


•06759 


14-7954 


.03288 


30.4116 


.05037 


19.8546 


.06788 


14.7317 


•03317 


30.1446 


.05066 


19.7403 


.06817 


14.6685 


•03346 


29.8823 


•05095 


19.6273 


.06847 


14-6059 


•03376 


29.6245 


.05124 


I9-5I56 


.06876 


I4.5438 


.03405 


29.3711 


•05153 


19.4051 


.06905 


14-4823 


•03434 


29.1220 


.05182 


19.2959 


.06934 


14.4212 


•03463 


28.8771 


.05212 


19.1879 


.06963 


14.3607 


.03492 


28.6363 


.05241 


19.0811 


.06993 


14.3007 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


I s 


8° 


1 8 


7° 


8 


6° 



480 NATURAL TANGENTS AND CO-TANGENTS 



4 





Tan. 


CO-TAN. 


.06993 


I4.3007 


.07022 


14.24H 


.07051 


14.1821 


.07080 


14-1235 


.07110 


14-0655 


.07139 


14.OO79 


.07168 


I3-9507 


.07197 


13.8940 


.07227 


13.8378 


.07256 


13.7821 


.07285 


13.7267 


.073M 


13.6719 


-07344 


13.6174 


•07373 


I3.5634 


.07402 


13.5098 


.07431 


13.4566 


.07461 


I3-4039 


.07490 


I3.35I5 


.07519 


13.2996 


.07548 


13.2480 


.07578 


13.1969 


.07607 


I3.I46I 


.07636 


13.0958 


.07665 


13.0458 


.07695 


12.9962 


.07724 


12.9469 


.07753 


12.8981 


.07782 


12.8496 


.07812 


12.8014 


.07841 


12.7536 


.07870 


12.7062 


.07899 


I2.659I 


.07929 


12.6124 


.07958 


12.5660 


.07987 


12.5199 


.08017 


12.4742 


.08046 


12.4288 


.08075 


12.3838 


.08104 


12.3390 


.08134 


12.2946 


.08163 


12.2505 


.08192 


12.2067 


.08221 


12.1632 


.08251 


I2.I20I 


.08280 


I2.0772 


.08309 


I2.O346 


•08339 


II.9923 


.08368 


II.9504 


•08397 


II.9087 


.08427 


H.8673 


.08456 


II.8262 


.08485 


H.7853 


.08514 


11.7448 


•08544 


II.7045 


.08573 


II.6645 


.08602 


II.6248 


.08632 


11.5853 


.08661 


II- 546l 


.08690 


H.5072 


.08720 


II.4685 


.08749 


1 1. 43OI 


Co-tan. 


Tan. 


8 


5° 



5 





6 





7 





Tan. 1 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


.08749 


1 1. 4301 


.10510 


9-51436 


.12278 


8.14435 


.08778 


11-3919 


.10540 


9.48781 


.12308 


8.12481 


.08807 


11-3540 


•10569 


9.46141 


.12338 


8.10536 


.08837 


11-3163 


•10599 


9-43515 


.12367 


8.08600 


.08866 


11.2789 


.10628 


9.40904 


.12397 


8.06674 


.08895 


11. 2417 


.10657 


9-38307 


.12426 


8.04756 


.08925 


11.2048 


.10687 


9-35724 


.12456 


8.02848 


.08954 


11.1681 


.10716 


9-33154 


.12485 


8.00948 


.08983 


11.1316 


.10746 


9-30599 


•12515 


7.99058 


.09013 


11.0954 


•10775 


9.28058 


•12544 


7.97176 


.09042 


11.0594 


.10805 


9-25530 


•12574 


7-95302 


.09071 


11.0237 


.10834 


9.23016 


.12603 


7-93438 


.09101 


10.9882 


.10863 


9.20516 


.12633 


7-91582 
7-89734 


.09130 


10.9529 


.10893 


9.18028 


.12662 


.09159 


10.9178 


.10922 


9-15554 


.12692 


7.87895 


.09189 


10.8829 


.10952 


9-I3093 


.12722 


7.86064 


.09218 


10.8483 


.10981 


9.10646 


.12751 


7.84242 


.09247 


10.8139 


.IIOII 


9.08211 


.12781 


7.82428 


.09277 


10.7797 


.11040 


9.05789 


.12810 


7.80622 


.09306 


io.7457 


.11070 


9-Q3379 


.12840 


7.78825 


•09335 


10.7119 


. 1 1099 


9.00983 


.12869 


7-77035 


•09365 


10.6783 


.11128 


8.98598 


.12899 


7-75254 


•09394 


10.6450 


.11158 


8.96227 


.12929 


7.73480 


.09423 


10.6118 


.11187 


8.93867 


.12958 


7-71715 


•09453 


10.5789 


.11217 


8.91520 


.12988 


7-69957 


.09482 


10.5462 


.11246 


8.89185 


.13017 


7.68208 


.09511 


10.5136 


.11276 


8.86862 


.13047 


7.66466 


•09541 


10.4813 


•11305 


8.84551 


.13076 


7.64732 


•09570 


10.4491 


•H335 


8.82252 


.13106 


7.63005 


.09600 


10.4172 


.11364 


8.79964 


•13136 


7.61287 


.09629 


10.3854 


•II394 


8.77689 


.13165 


7.59575 


.09658 


10.3538 


.11423 


8.75425 


•13195 


7.57872 


.09688 


10-3224 


.11452 


8.73172 


.13224 


7.56176 


.09717 


10.2913 


.11482 


8.70931 


.13254 


7-54487 


.09746 


10.2602 


.11511 


8.68701 


•13284 


7.52806 


.09776 


10.2294 


.11541 


8.66482 


.13313 


7-51132 


.09805 


10.1988 


.11570 


8.64275 


•13343 


7-49465 


.09834 


10.1683 


.11600 


8.62078 


.13372 


7.47806 


.09864 


10.1381 


.11629 


8.59893 


.13402 


7.46154 


.09893 


10.1080 


.11659 


8.57718 


•13432 


7-44509 


•09923 


10.0780 


.11688 


8-55555 


.13461 


7.42871 


.09952 


10.0483 


.11718 


8.53402 


•13491 


7.41240 


.09981 


10.0187 


.11747 


8.51259 


•13521 


7.39616 


.10011 


9.98931 


.11777 


8.49128 


•13550 


7-37999 


.10040 


9.96007 


.11806 


8.47007 


, .13580 


7.36389 


.10069 


9.93101 


.11836 


8.44896 


1 .13609 


7.34786 


.10099 


9.902 1 1 


.11865 


8.42795 


1 .13639 


7-33I90 


.10128 


9-87338 


.11895 


8.40705 


.13669 


7.31600 


.10158 


9.84482 


.11924 


8.38625 


.13698 


7.30018 


.10187 


9.81641 


•II954 


8.36555 


1 .13728 


7.28442 


.10216 


9.78817 


•1 1983 


8.34496 


.13758 


7.26873 


.10246 


9.76009 


.12013 


8.32446 


.13787 


7.25310 


.10275 


9.73217 


.12042 


8.30406 


.13817 


7-23754 


.10305 


9.70441 


.12072 


8.28376 


.13846 


7.22204 


.10334 


9.67680 


.12101 


8.26355 


.13876 


7.20661 


•10363 


964935 


.12131 


8-24345 


.13906 


7-I9I25 


.10393 


9.62205 


.12160 


8.22344 


-13935 


7-17594 


.10422 


9.59490 


.12190 


8.20352 


.13965 


7.16071 


.10452 


9.56791 


.12219 


8.18370 


.13995 


7-14553 


.10481 


9.54106 


.12249 


8.16398 


.14024 


7.13042 


.10510 


9-51436 


.12278 


8.14435 


-14054 


7.H537 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


1 


84° 


8 


3° 


8^ 


1° 



NATURAL TANGENTS AND CO-TANGENTS 481 





8 


2> 


9 


3 


10° 


11° 




/ 


Tan. 


CO-TAN. 


Tan. 


CO-TAN. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 





.14054 


7-H537 


.15838 


6.51375 


•17633 


5.67128 


.19438 


5-14455 


60 


I 


.14084 


7.10038 


.15868 


6.30189 


.17663 


5-66165 


.19468 


5.13658 


59 


2 


.14113 


7.08546 


.15898 


6.29007 


.17693 


5-65205 


.19498 


5.12862 


58 


3 


.14143 


7.07059 


.15928 


6.27829 


•17723 


5.64248 


.19529 


5.12069 


57 


4 


.14173 


7-Q5579 


.15958 


6.26655 


•17753 


5-63295 


.19559 


5-11279 


56 


5 


.14202 


7.04105 


.15988 


6.25486 


.17783 


5-62344 


.19589 


5.10490 


55 


6 


.14232 


7.02637 


.16017 


6.24321 


.17813 


5-6i397 


.19619 


5.09704 


54 


7 


.14262 


7-01174 


.16047 


6.23160 


.17843 


5.60452 


.19649 


5.08921 


53 


8 


.14291 


6.99718 


.16077 


6.22003 


.17873 


5-595H 


.19680 


5.08139 


52 


9 


.14321 


6.98268 


.16107 


6.20851 


.17903 


5-58573 


.19710 


5.07360 


51 


10 


•14351 


6.96823 


.16137 


6.19703 


.17933 


5-57638 


.19740 


5.06584 


50 


11 


.14381 


6.95385 


-16167 


6.18559 


.17963 


5.56706 


.19770 


5.05809 


49 


12 


.14410 


6.93952 


.16196 


6.I74I9 


•17993 


5-55777 


.19801 


5-05037 


48 


13 


.14440 


6.92525 


.16226 


6.16283 


.18023 


5.54851 


.19831 


5.04267 


47 


14 


.14470 


6.91104 


.16256 


6.I5I5I 


.18053 


5-53927 


.19861 


5-03499 


46 


15 


.14499 


6.8*9688 


.16286 


6.14023 


.18083 


5-53007 


.19891 


5-02734 


45 


16 


.14529 


6.88278 


.16316 


6.12899 


.18113 


5.52090 


.19921 


5.01971 


44 


17 


.14559 


6-86874 


.16346 


6.II779 


.18143 


5-51176 


.19952 


5.01210 


43 


18 


.14588 


6.85475 


.16376 


6.10664 


.18173 


5.50264 


.19982 


5.00451 


42 


19 


.14618 


6.840S2 


.16405 


6.09552 


.18203 


5.49356 


.20012 


4.99695 


41 


20 


.14648 


6.82694 


.16435 


6.08444 


.18233 


5-48451 


.20042 


4.98940 


40 


21 


.14678 


6.81312 


.16465 


6.07340 


.18263 


5.47548 


.20073 


4.98188 


39 


22 


.14707 


6.79936 


.16495 


6.06240 


.18293 


5.46648 


.20103 


4-97438 


38 


23 


• 14737 


6.78564 


.16525 


6.05143 


.18323 


5.45751 


.20133 


4.96690 


37 


24 


.14767 


6.77199 


•16555 


6.O4051 


.18353 


5.44857 


.20164 


4-95945 


36 


25 


.14796 


6.75838 


.16585 


6.02962 


.18383 


5.43966 


.20194 


4-952QI 


35 


26 


.14826 


6.74483 


.16615 


6.01878 


.18414 


5.43077 


.20224 4.94460 


34 


27 


.14856 


6.73133 


.16645 


6.OO797 


.18444 


5.42192 


.20254 4-93721 


33 


28 


.14886 


6.71789 


.16674 


5.99720 


.18474 


5-41309 


.20285 4.92984 


32 


29 


.14915 


6.70450 


.16704 


5.98646 


.18504 


5.40429 


•20315 


4.92249 


31 


30 


•14945 


6.69116 


•16734 


5.97576 


.18534 


5-39552 


•20345 


4-9i5i6 


30 


3i 


.14975 


6.67787 


.16764 


5.965IO 


.18564 


5.38677 


.20376 


4.90785 


29 


32 


.15005 


6.66463 


.16794 


5.95448 


.18594 


5-37805 


.20406 


4.90056 


28 


33 


.15034 


6.65144 


.16824 


5.94390 


.18624 


5-36936 


.20436 


4.89330 


27 


34 


• 15064 


6.63831 


.16854 


5-93335 


.18654 


5.36070 


.20466 


4.83605 


26 


35 


.15094 


6.62523 


.16884 ' 


5-92283 


.18684 


5-35206 


•20497 


4.87882 


25 


36 


.15124 


6.61219 


.16914 


5.91235 


.18714 


5-34345 


.20527 


4.87162 


24 


37 


•15153 


6.59921 


.16944 


5-90191 


.18745 


5-33487 


.20557 


4.86444 


23 


38 


.15183 


6.58627 


.16974 


5-89151 


.18775 


5-32631 


.20588 


4.85727 


22 


39 


.15213 


6-57339 


.17004 


5.88114 


.18805 


5.3I778 


.20618 


4.85013 


21 


40 


.15243 


6.56055 


.17033 


5.87080 


.18835 


5.30928 


.20648 


4.84300 


20 


4i 


.15272 


6-54777 


.17063 


5.86051 


.18865 


5.30080 


.20679 


4.83590 


19 


42 


.15302 


6.53503 


.17093 


5.85024 


.18895 


5-29235 


.20709 


4.82882 


18 


43 


.15332 


6.52234 


.17123 


5.84001 


.18925 


5-28393 


•20739 


4-82175 


17 


44 


.15362 


6.50970 


.17153 


5.82982 


.18955 


5-27553 


.20770 


4.81471 


16 


45 


• 15391 


6.49710 


.17183 


5.81966 


.18986 


5-26715 


.20800 


4.80769 


15 


46 


.15421 


6.48456 


.17213 


5.80953 


.19016 


5.25880 


.20830 


4.80068 


14 


47 


.15451 


6.47206 


.17243 


5-79944 


.19046 


5.25048 


.20861 


4-79370 


13 


48 


.15481 


6.45961 


.17273 


5.78938 


.19076 


5.24218 


.20891 


4.78673 


12 


49 


•15511 


6.44720 


•17303 


5.77936 


.19106 


5-23391 


.20921 


4.77978 


11 


50 


.15540 


6.43484 


.17333 


5.76937 


.19136 


5.22566 


.20952 


4.77286 


10 


51 


.15570 


6.42253 


.17363 


5-75941 


.19166 


5-21744 


.20982 


4.76595 


9 


52 


.15600 


6.41026 


• 17393 


5-74949 


.19197 


5.20925 


.21013 


4.75906 


8 


53 


.15630 


6.39804 


.17423 


5-7396o 


.19227 


5.20107 


.21043 


4.75219 


7 


54 


.15660 


6.38587 


•17453 


5.72974 


.19257 


5.19293 


.21073 


4-74534 


6 


55 


.15689 


6-37374 


.17483 


5.71992 


.19287 


5.18480 


.21104 


4-73851 


5 


56 


.15719 


6.36165 


•17513 


5-71013 


.19317 


5-17671 


.21134 


4.73I70 


4 


57 


•15749 


6.34961 


• 17543 


5-70037 


.19347 


5-16863 


.21164 


4.72490 


3 


58 


•15779 


6.33761 


• 17573 


5.69064 


•19378 


5.16058 


.21195 


4-71813 


2 


59 


.15809 


6.32566 


.17603 


5.68094 


.19408 


5.15256 


.21225 


4.7II37 


1 


60 


.15838 


6.31375 


.17633 


5.67128 


.19438 


5.14455 


.21256 


4.70463 





/ 


Co-tan. 


Tan. 


Co-tan . 


Tan. 


Co-tan. 


Tan. 


Co~tan. 


Tan. 


/ 




8 


1° 


8 


0° i 


7 


9° I 


7 


3° J 





482 NATURAL TANGENTS AND CO-TANGENTS 





12° 


13° 


14° 


15° 


/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 





.21256 


4.70463 


.23087 


4-33148 


•24933 


4.01078 


.26795 


3-73205 


I 


.21286 


4.69791 


.23117 


4.32573 


.24964 


4.00582 


.26826 


3.72771 


2 


.21316 


4.69121 


.23148 


4.32001 


.24995 


4.00086 


.26857 


3-7233^ 


3 


.21347 


4.68452 


.23179 


4-31430 


.25026 


3-99592 


.26888 


3.71907 


4 


.21377 


4.67786 


.23209 


4.30860 


•25056 


3.99099 


.26920 


3-71476 


5 


.21408 


4.67121 


.23240 


4.30291 


.25087 


3.98607 


.26951 


3-71046 


6 


.21438 


4.66458 


.23271 


4.29724 


.25118 


3-98ii7 


.26982 


3.70616 


7 


.21469 


4-65797 


.23301 


4.29159 


.25149 


3.97627 


.27013 


3.70188 


8 


.21499 


4-65138 


■23332 


4-28595 


.25180 


3-97139 


.27044 


3-69761 


9 


.21529 


4.64480 


-23363 


4.28032 


.25211 


3.96651 


.27076 


3-69335 


10 


.21560 


4-63825 


•23393 


4.27471 


.25242 


3.96165 


.27107 


3.68909 


11 


.21590 


4.631 71 


.23424 


4.26911 


•25273 


3.95680 


.27138 


3.68485 


12 


.21621 


4.62518 


.23455 


4.26352 


•25304 


3-95I96 


.27169 


3.68061 


13 


.21651 


4.61868 


.23485 


4-25795 


•25335 


3-94713 


.27201 


3.67638 


14 


.21682 


4.61219 


.23516 


4-25239 


.25366 


3-94232 


.27232 


3.67217 


15 


.21712 


4.60572 


•23547 


4.24685 


•25397 


3-93751 


.27263 


3.66796 


16 


.21743 


4-59927 


■23578 


4.24132 


.25428 


3-93271 


.27294 


3.66376 


17 


•21773 


4.59283 


.23608 


4.23580 


•25459 


3-92793 


.27326 


3-65957 


18 


.21804 


4.58641 


•23639 


4.23030 


.25490 


3.92316 


.27357 


3-65538 


19 


.21834 


4.58001 


.23670 


4.22481 


.25521 


3-91839 


.27388 


3-65121 


20 


.21864 


4-57363 


.23700 


4-21933 


•25552 


3.91364 


.27419 


3.64705 


21 


.21895 


4.56726 


.23731 


4.21387 


•25583 


3.90890 


.27451 


3.64289 


22 


•21925 


4.56091 


.23762 


4.20842 


.25614 


3.90417 


.27482 


3.63874 


23 


.21956 


4-55458 


•23793 


4.20298 


•25645 


3-89945 


, -27513 


3.63461 


24 


.21986 


4.54826 


.23823 


4.19756 


.25676 


3-89474 


1 -27545 


3.63048 


25 


.22017 


4.54196 


•23854 


4.19215 


.25707 


3.89004 


1 .27576 


3.62636 


26 


.22047 


4.53568 


.23885 


4.18675 


.25738 


3.88536 


1 .27607 


3.62224 


27 


.22078 


4.52941 


.23916 


4-18137 


.25769 


3.88068 


.27638 


3.61814 


28 


.22108 


4.52316 


.23946 


4.17600 


.25800 


3.87601 


.27670 


3.61405 


29 


.22139 


4-51693 


.23977 


4.17064 


.25831 


3-87136 


.27701 


3.60996 


30 


.22169 


4-51071 


.24008 


4.16530 


.25862 


3.86671 


.27732 


3-60588 


3i 


.22200 


4-50451 


.24039 


4-15997 


•25893 


3.86208 


•27764 


3.60181 


32 


.22231 


4.49832 


.24069 


4-I5465 


.25924 


3-85745 


•27795 


3-59775 


33 


.22261 


4.49215 


.24100 


4-14934 


-25955 


3-85284 


.27826 


3.59370 


34 


.22292 


4.48600 


.24131 


4.14405 


.25986 


.3.84824 


.27858 


3.58966 


35 


.22322 


4.47986 


.24162 


4.13877 


.26017 


3-84364 


.27889 


3-58562 


36 


.22353 


4-47374 


.24193 


4-I3350 


.26048 


3.83906 


.27920 


3.58160 


37 


.22383 


4.46764 


.24223 


4.12825 


.26079 


3-83449 


.27952 


3-57758 


38 


.22414 


4-46155 


.24254 


4.12301 


.26110 


3.82992 


.27983 


3-57357 


39 


.22444 


4-45548 


.24285 


4-II778 


.26141 


3-82537 


.28015 


3-56957 


40 


.22475 


4.44942 


.24316 


4.11256 


.26172 


3.82083 


.28046 


3-56557 


4i 


.22505 


4-44338 


•24347 


4.10736 


.26203 


3.81630 


.28077 


3-56i59 


42 


.22536 


4-43735 


•24377 


4.10216 


.26235 


3.8ii77 


.28109 


3-5576i 


43 


.22567 


4-43134 


.24408 


4.09699 


.26266 


3.80726 


.28140 


3-55364 


44 


.22597 


4.42534 


.24439 


4.09182 


.26297 


3.80276 


.28172 


3-54968 


45 


.22628 


4.41936 


.24470 


4.08666 


.26328 


3.79827 


.28203 


3-54573 


46 


.22658 


4.41340 


.24501 


4.08152 


•26359 


3-79378 


.28234 


3-54179 


47 


.22689 


4-40745 


•24532 


4.07639 


.26390 


3-78931 


.28266 


3-53785 


*8 


.22719 


4.40152 


.24562 


4.07127 


.26421 


3-78485 


.28297 


3-53393 


\9 


.22750 


4-3956o 


.24593 


4.06616 


.26452 


3.78040 


.28329 


3-53QOI 


50 


.22781 


4.38969 


.24624 


4.06107 


.26483 


3-77595 


.28360 


3.52609 


;i 


.22811 


4.38381 


.24655 


4-05599 


•26515 


3-77I52 


.28391 


3.52219 


52 


.22842 


4-37793 


.24686 


4.05092 


.26546 


3.76709 


.28423 


3.51829 


53 


.22872 


4.37207 


.24717 


4.04586 


.26577 


3.76268 


.28454 


3-5I44I 


54 


.22903 


4.36623 


.24747 


4.04081 


.26608 


3-75828 


.28486 


3-51053 


>5 


-22934 


4.36040 


.24778 


4-03578 


.26639 


3.75388 


.28517 


3.50666 


;6 


.22964 


4-35459 


.24809 


4-03075 


.26670 


3-7495Q 


.28549 


3-50279 


57 


.22995 


4.34879 


.24840 


4.02574 


.26701 


3-74512 


.28580 


3.49894 


;8 


.23026 


4-34300 


.24871 


4.02074 


.26733 


3-74075 


.28612 


3-49509 


J9 


.23056 


4-33723 


.24902 


4-OI576 


.26764 


3-73640 


.28643 


3-49125 


)0 


.23087 


4-33I48 


•24933 


4.01078 


.26795 


3-73205 


.28675 


3.48741 


/ 


Co-tan. 


Tan. 


CO-TAN. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 




Ti 


TO 


76 


;° 


71 


)° 


7< 


t° 



NATURAL TANGENTS AND CO-TANGENTS 483 





16° 


17° 


| 18° 


19° 




/ 


Tan. 


CO -TAN. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 





.28675 


3.48741 


.30573 


3.27085 


.32492 


3-07768 


•34433 


2.90421 


6 


I 


.28706 


3-48359 


.30605 


3.26745 


•32524 


3.07464 


•34465 


2.90147 


5 


2 


.28738 


3-47977 


.30637 


3.26406 


.32556 


3.07160 


•34498 


2.89873 


5 


3 


.28769 


3-47596 


.30669 


3.26067 


.32588 


3.06857 


.34530 


2.89600 


5 


4 


.28800 


3.47216 


.30700 


3-25729 


.32621 


3-06554 


•34563 


2.89327 


5 


5 


.28832 


3-46837 


•30732 


3-25392 


•32653 


3.06252 


•34596 


2.89055 


5 


6 


.28864 


3-46458 


•30764 


3-25055 


.32685 


3-05950 


.34628 


2.88783 


5 


7 


.28895 


3.46080 


.30796 


3.24719 


•32717 


3-05649 


•34661 


2.88511 


5 


8 


.28927 


3-45703 


.30828 


3-24383 


•32749 


3-Q5349 


•34693 


2.88240 


5 


9 


.28958 


3-45327 


.30860 


3.24049 


•32782 


3-05049 


.34726 


2.87970 


5 


10 


.28990 


3-44951 


.30891 


3-23714 


•32814 


3-04749 


•34758 


2.87700 


5 


11 


.29021 


3-44576 


.30923 


3.23381 


.32846 


3-04450 


•34791 


2.87430 


4 


12 


•29053 


3.44202 


•30955 


3.23048 


.32878 


3.04152 


.34824 


2.87161 


4 


13 


.29084 


3-43829 


•30987 


3.22715 


.32911 


3-03854 


.34856 


2.86892 


4 


14 


.29116 


3-43456 


.31019 


3.22384 


•32943 


3-03556 


.34889 


2.86624 


4 


15 


.29147 


3-43084 


.31051 


3-22053 


•32975 


3.03260 


.34922 


2.86356 


4 


16 


.29179 


3-427I3 


.31083 


3.21722 


•33007 


3.02963 


•34954 


2.86089 


4 


17 


.29210 


3-42343 


•31115 


3-21392 


•33040 


3.02667 


•34987 


2.85822 


4 


18 


.29242 


3-41973 


•3H47 


3.21063 


•33072 


3.02372 


•35019 


2.85555 


4 


19 


.29274 


3.41604 


.31178 


3-20734 


.33104 


3.02077 


•35052 


2.85289 


4 


20 


.29305 


3-41236 


.31210 


3.20406 


•33136 


3-01783 


.35085 


2.85023 


4< 


21 


•29337 


3.40869 


.31242 


3.20079 


.33160 


3.01489 


.35H7 


2.84758 


3< 


22 


.29368 


3.40502 


•31274 


3-19752 


•33201 


3.01196 


•35i5o 


2.84494 


3^ 


23 


.29400 


3.40136 


.31306 


3.19426 


-33233 


3.00903 


.35183 


2.84229 


3 


24 


.29432 


3-39771 


.31338 


3.19100 


.33266 


3.0061 1 


.35216 


2.83965 


3< 


25 


.29463 


3-394o6 


•31370 


3-18775 


•33298 


3.00319 


•35248 


2.83702 


3. 


26 


.29495 


3-39042 


.31402 


3-18451 


-33330 


3.00028 


.35281 


2.83439 


3- 


27 


.29526 


3-38679 


•31434 


3-18127 


•33363 


2.99738 


.35314 


2.83176 


3. 


28 


•29558 


3-383I7 


.31466 


3-17804 


•33395 


2-99447 


•35346 


2.82914 


3- 


29 


.29590 


3-37955 


.31498 


3-17481 


•33427 


2.99158 


•35379 


2.82653 


3^ 


30 


.29621 


3-37594 


.31530 


3-17159 


•3346o 


2.98868 


•35412 


2.82391 


3C 


31 


.29653 


3-37234 


.31562 


3-16838 


•33492 


2.98580 


•35445 


2.82130 


2C 


32 


.29685 


3-36875 


•31594 


3-16517 


•33524 


2.98292 


•35477 


2.81870 


2* 


33 


.29716 


3-36516 


.31626 


3-16197 


•33557 


2.98004 


•355IO 


2.81610 


2; 


34 


.29748 


3-36158 


.31658 


3-15877 


•33589 


2.97717 


•35543 


2.81350 


2t 


35 


.29780 


3-358oo 


.31690 


3-I5558 


•33621 


2.97430 


•35576 


2.81091 


2« 


36 


.29811 


3-35443 


.31722 


3.15240 


•33654 


2.97144 


.35608 


2.80833 


2A 


37 


.29843 


3-35o87 


.31754 


3.14922 


•33686 


2.96858 


•35641 


2.80574 


22 


38 


.29875 


3-34732 


.31786 


3.14605 


.33718 


2-96573 


•35674 


2.80316 


22 


39 


.29906 


3-34377 


.31818 


3.14288 


•33751 


2.96288 


•35707 


2.80059 


21 


40 


.29938 


3-34023 


.31850 


3-13972 


•33783 


2.96004 


.35740 


2.79802 


2C 


4i 


.29970 


3-33670 


.31882 


3-13656 


.33816 


2.95721 


•35772 


2-79545 


IS 


42 


.30001 


3-33317 


.31914 


3-i334i 


•33848 


2-95437 


.35805 


2.79289 


18 


43 


•30033 


3-32965 


.31946 


3.13027 


.33881 


2-95155 


.35838 


2.79033 


17 


44 


.30065 


3-32614 


•31978 


3-12713 


.33913 


2.94872 


.35871 


2.78778 


16 


45 


•30097 


3-32264 


.32010 


3.12400 


•33945 


2.94590 


.35904 


2.78523 


15 


46 


.30128 


3-3I9I4 


.32042 


3.12087 


•33978 


2.94309 


•35937 


2.78269 


14 


47 


.30160 


3-3I565 


•32074 


3.II775 


•34010 


2.94028 


•35969 


2.78014 


13 


48 


•30192 


3-3i2i6 


.32106 


3-11464 


•34043 


2.93748 


.36002 


2.77761 


12 


49 


.30224 


3-30868 


•32139 


3-IH53 


•34075 


2.93468 


•36035 


2.77507 


II 


5o 


•30255 


3-3052I 


.32171 


3.10842 


.34108 


2.93189 


.36068 


2.77254 


10 


5i 


.30287 


3-30I74 


.32203 


3-10532 


.34140 


2.92910 


.36101 


2.77002 


9 


52 


•30319 


3.29829 


•32235 


3.10223 


•34173 


2.92632 


•36134 


2.76750 


S 


53 


•30351 


3-29483 


.32267 


3.09914 


•34205 


2.92354 


.36167 


2.76498 


7 


54 


.30382 


3-29I39 


.32299 


3.09606 


.34238 


2.92076 


.36199 


2.76247 


6 


55 


.30414 


3-28795 


•32331 


3.09298 


.34270 


2.91799 


•36232 


2.75996 


5 


56 


.30446 


3.28452 


.32363 


3.08991 


•34303 


2.91523 


.36265 


2.75746 


A 


57 


.30478 


3.28109 


.32396 


3-08685 


•34335 


2.91246 


.36298 


2.75496 


3 


58 


•30509 


3.27767 


.32428 


3-08379 


.34368 


2.90971 


•36331 


2.75246 


2 


59 


•30541 


3.27426 


.32460 


3.08073 


•34400 


2.90696 


•36364 


2.74997 


I 


60 


•30573 


3-27085 


.32492 


3.07768 


•34433 


2.90421 


•36397 


2.74748 


c 


/ 


Co-tan- 


Tan. 


Co-tan. 


Tan. 


CO-TAN. 


Tan. 


Co-tanJ Tan. 


/ 




7 


3° 


7 


2° 


7 


1° 


1 7 


0° 





484 NATURAL TANGENTS AND CO-TANGENTS 



20° 


21° 


22° 


23° 




Tan. 


Co-tan. 


Tan. 


CO-TAN. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 


.36397 


2.74748 


.38386 


2.60509 


.40403 


2.47509 


.42447 


2-35585 


6c 


•36430 


2-74499 


.38420 


2.60283 


.40436 


2.47302 


.42482 


2-35395 


59 


.36463 


2.74251 


.38453 


2.60057 


•40470 


2.47095 


.42516 


2.35205 


58 


.36496 


2.74004 


.38487 


2.59831 


.40504 


2.46888 


•42551 


2.35015 


57 


•36529 


2.73756 


.38520 


2.59606 


•40538 


2.46682 


•42585 


2.34825 


56 


.36562 


2.73509 


.38553 


2.59381 


.40572 


2.46476 


.42619 


2.34636 


55 


•36595 


2.73263 


.38587 


2.59156 


.40606 


2.46270 


.42654 


2-34447 


54 


.36628 


2.73017 


.38620 


2.58932 


.40640 


2.46065 


.42688 


2.34258 


53 


.36661 


2.72771 


.38654 


2.58708 


.40674 


2.45860 


.42722 


2.34069 


52 


.36694 


2.72526 


.38687 


2.58484 


•40707 


2.45655 


•42757 


2.33881 


5i 


.36727 


2.72281 


.38721 


2.58261 


•40741 


2.45451 


.42791 


2.33693 


50 


.36760 


2.72036 


•38754 


2.58038 


.40775 


2.45246 


.42826 


2.33505 


4Q 


•36793 


2.71792 


.38787 


2.57815 


.40809 


2.45043 


.42860 


2.33317 


48 


.36826 


2.71548 


.38S21 


2-57593 


•40843 


2.44839 


.42894 


2.33130 


47 


.36859 


2.71305 


.38854 


2-57371 


.40877 


2.44636 


.42929 


2-32943 


46 


.36892 


2.71062 


.38888 


2.57I50 


.40911 


2-44433 


.42963 


2.32756 


45 


.36925 


2.70819 


.38921 


2.56928 


•40945 


2.44230 


.42998 


2.32570 


44 


.36958 


2.70577 


•38955 


2.56707 


•40979 


2.44027 


•43032 


2.32383 


43 


.36991 


2.70335 


.38988 


2.56487 


•41013 


2.43825 


•43067 


2.32197 


42 


.37024 


2.70094 


.39022 


2.56266 


.41047 


2.43623 


.43101 


2.32012 


4i 


•37057 


2.69853 


•39055 


2.56046 


.41081 


2.43422 


•43136 


2.31826 


40 


.37090 


2.69612 


.39089 


2.55827 


•41115 


2.43220 


•43170 


2.31641 


39 


•37124 


2.69371 


.39122 


2.55608 


.41149 


2.43019 


■43205 


2.31456 


S^ 


.37157 


2.69131 


•39156 


2.55389 


•41183 


2.42819 


•43239 


2.31271 
2.31086 


37 


.37190 


2.68892 


.39190 


2.55I70 


.4*217 


2.42618 


•43274 


36 


•37223 


2.68653 


.39223 


2.54952 


.41251 


2.42418 


•43308 


2.30902 


35 


•37256 


2.68414 ! 


•39257 


2.54734 


.41285 


2.42218 


•43343 


2.30718 


34 


.37289 


2.S8i75 ! 


.39290 


2.54516 


•41319 


2.42019 


.43378 


2.30534 


33 


•37322 


2.67937 


•39324 


2.54299 


•4*353 


2.41819 


.43412 


2.30351 


32 


•37355 


2.67700 


•39357 


2.54082 


•41387 


2.41620 


•43447 


2.30167 


3i 


.37388 


2.67462 


•39391 


2.53865 


.41421 


2.41421 


.43481 


2.29984 


30 


.37422 


2.67225 


.39425 


2.53648 


•41455 


2.41223 


•43516 


2.29801 


29 


•37455 


2.66989 


.39458 


2.53432 


.41490 


2.41025 


•43550 


2.29619 


28 


.37488 


2.66752 


.39492 


2.53217 


.41524 


2.40827 


•43585 


2.29437 


27 


•37521 


2.66516 


•39526 


2.5300I 


.41558 


2.40629 


.43620 


2.29254 


26 


•37554 


2.66281 


•39559 


2.52786 


.41592 


2.40432 


•43654 


2.29073 


25 


.37588 


2.66046 


•39593 


2.52571 


.41626 


2.40235 


•43689 


2.28891 


24 


.37621 


2.65811 


.39626 


2.52357 


.41660 


2.40038 


•43724 


2.28710 


23 


•37654 


2.65576 


.39660 


2.52142 


.41694 


2.39841 


•43758 


2.28528 


22 


■37687 


2.65342 


•39694 


2.51929 


.41728 


2.39645 


•43793 


2.28348 


21 


.37720 


2.65109 


.39727 


2.5I7I5 


•41763 


2.39449 


.43828 


2.28167 


20 


•37754 


2.64875 


.39761 


2.51502 


•41797 


2.39253 


.43862 


2.27987 


19 


.37787 


2.64642 


•39795 


2.51289 


.41831 


2.39058 


•43897 


2.27806 


18 


•37820 


2.64410 


.39829 


2.51076 


.41865 


2.38862 


•43932 


2.27626 


17 


•37853 


2.64T77 i 


.39862 


2.50864 


.41899 


2.38668 


.43966 


2.27447 


16 


•3738 7 


2.63945 


.39896 


2.50652 


•41933 


2-38473 


.44001 


2.27267 


15 


.37920 


2.63714 


■39930 


2.50440 


.41968 


2.38279 


.44036 


2.27088 


14 


•37953 


2.63483 


•39963 


2.50229 


.42002 


2.38084 


.44071 


2.26909 


13 


.37986 


2.63252 


•39997 


2.50018 


.42036 


2.37891 


.44105 


2.26730 


12 


.38020 


2.63021 


.40031 


2.49807 


.42070 


2.37697 


.44140 


2.26552 


11 


.38053 


2.62791 


.40065 


2-49597 


.42105 


2.37504 


•44175 


2.26374 


10 


.38086 


2.62561 


.40098 


2.49386 


.42139 


237311 


.44210 


2.26196 


9 


.38120 


2.62332 


.40132 


2.49177 


•42173 


2.37118 


•44244 


2.26018 


8 


.38153 


2.62103 


.40166 


2.48967 


.42207 


2.36925 


•44279 


2.25840 


7 


.38186 


2.61874 


.40200 


2.48758 


.42242 


2.36733 


•44314 


2.25663 


6 


.38220 


2.61646 


.40234 


2.48549 


.42276 


2.36541 


•44349 


2.25486 


5 


.38253 


2.61418 


.40267 


2.48340 


.42310 


2.36349 


•44384 


2.25309 


4 


.38286 


2.61190 


.40301 


2.48132 


•42345 


2.36158 


.44418 


2.25132 


3 


.38320 


2.60963 


.40335 


2.47924 


.42379 


2.35967 


•44453 


2.24956 


2 


.38353 


2.60736 


.40369 


2.47716 


.42413 


2.35776 


.44488 


2.24780 


1 


.38386 


2.60509 


.40403 


2.47509 


.42447 


2.35585 


•44523 


2.24604 





CO-TAN. 


Tan. 


CO-TAN. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


/ 


6< 


2° 


6, 


3° 


6' 


7° 


6< 


30 





NATURAL TANGENTS AND CO-TANGENTS 485 



1 


24° 


2 


5° 


26° 


2 


7° 




' 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


CO-TAN. 


Tan. 


CO-TAN. 




- 



•44523 


2.24604 


.46631 


2.14451 


•48773 


2.05030 


•50953 


I.96261 


60 


I 


•44558 


2.24428 


.46666 


2.14288 


.48809 


2.04879 


.50989 


I.96120 


59 


2 


•44593 


2.24252 


.46702 


2.14125 


.48845 


2.04728 


.51026 


1-95979 


58 


3 


.44627 


2.24077 


.46737 


2.13963 


.48881 


2.04577 


.51063 


1.95838 


57 


4 


.44662 


2.23902 


.46772 


2.13801 


.48917 


2.04426 


.51099 


1.95698 


56 


5 


.44697 


2.23727 


.46808 


2.13639 


•48953 


2.04276 


•51 136 


1-95557 


55 


6 


•44732 


2.23553 


•46843 


2.13477 


.48989 


2.04125 


.51173 


I-954I7 


54 


7 


•44767 


2.23378 


.46879 


2.13316 


.49026 


2.03975 


.51209 


1.952-77 


53 


8 


.44802 


2.23204 


.46914 


2.13154 


.49062 


2.03825 


.51246 


I-95I37 


52 


9 


•44837 


2.23030 


•46950 


2.12993 


.49098 


2.03675 


.51283 


1.94997 


51 


10 


.44872 


2.22857 


.46985 


2.12832 


•49134 


2.03526 


•51319 


1.94858 


50 


11 


.44907 


2.22683 


.47021 


2.12671 


.49170 


2.03376 


.51356 


1.94718 


49 


12 


.44942 


2.22510 


•47056 


2.12511 


.49206 


2.03227 


•51393 


1-94579 


48 


13 


•44977 


2.22337 


.47092 


2.12350 


.49242 


2.03078 


•51430 


1.94440 


47 


14 


.45012 


2.22164 


.47128 


2.12190 


.49278 


2.02929 


•51467 


1. 94301 


46 


15 


•45047 


2.21992 


•47163 


2.12030 


•49315 


2.02780 


•51503 


1.94162 


45 


16 


.45082 


2.21819 


.47199 


2.11871 


•49351 


2.02631 


•51540 


1.94023 


44 


17 


.45H7 


2.21647 


•47234 


2.11711 


•49387 


2.02483 


.51577 


1.93885 


43 


18 


■45152 


2.21475 


.47270 


2.11552 


.49423 


2.02335 


.51614 


1.93746 


42 


19 


•45i87 


2.21304 


•47305 


2.11392 


•49459 


2.02187 


•51651 


1.93608 


41 


20 


.45222 


2.21132 


•47341 


2.11233 


•49495 


2.02039 


.51688 


1.93470 


40 


21 


•45257 


2.20961 


•47577 


2.11075 


•49532 


2.01891 


•51724 


1-93332 


39 


22 


.45292 


2.20790 


.47412 


2.10916 


.49568 


2.OI743 


.51761 


I-93I95 


38 


23 


•45327 


2.20619 


.47448 


2.10758 


.49604 


2.01596 


•51798 


I-93057 


31 


24 


•45302 


2.20449 


•47483 


2.10600 


.49640 


2.01449 


.51835 


1.92920 


36 


25 


•45397 


2.20278 


•47519 


2.10442 


.49677 


2.01302 


.51872 


1.92782 


35 


26 


•45432 


2.20108 


•47555 


2.10284 


•49713 


2.OI155 


.51909 


1.92645 


34 


27 


•45467 


2.19938 


•47590 


2.10126 


•49749 


2.OIO08 


.51946 


1.92508 


33 


28 


•45502 


2.19769 


.47626 


2.09969 


.49786 


2.00862 


-51983 


1.92371 


32 


29 


•45537 


2.19599 


.47662 


2.0981 1 


.49822 


2.00715 


.52020 


1.92235 


3i 


30 


•45573 


2.19430 


.47698 


2.09654 


.49858 


2.00569 


•52057 


1.92098 


30 


3i 


.45608 


2.19261 


•47733 


2.09498 


•49894 


2.OO423 


.52094 


1.91962 


29 


32 


.45643 


2.19092 


•47769 


2.09341 


•49931 


2.OO277 


•52131 


1. 9 1 826 


28 


33 


.45678 


2.18923 


•47805 


2.09184 


•49967 


2.OOI31 


.52168 


1. 91690 


27 


34 


•45713 


2.18755 


.47840 


2.09028 


.50004 


I.99986 


.52205 


I-9I554 


26 


35 


•45748 


2.18587 


.47876 


2.08872 


.50040 


1. 99841 


.52242 


1.91418 


25 


36 


•45784 


2.18419 


.47912 


2.08716 


.50076 


I.99695 


.52279 


1.91282 


24 


37 


.45819 


2.18251 


.47948 


2.08560 


•50113 


I -99550 


.52316 


I-9H47 


23 


38 


•45854 


2.18084 


.47984 


2.08405 


•50149 


I.99406 


.52353 


1.91012 


22 


39 


.45889 


2.17916 


.48019 


2.08250 


• 50185 


I.99261 


•52390 


1.90876 


21 


40 


.45924 


2.17749 


•48055 


2.08094 


.50222 


I.99116 


.52427 


1. 90741 


20 


4i 


.45960 


2.17582 


.48091 


2.07939 


.50258 


I.98972 


.52464 


1.90607 


19 


42 


•45995 


2.17416 


.48127 


2.07785 


•50295 


I.98828 


.52501 


1.90472 


18 


43 


.46030 


2.17249 


■48163 


2.07630 


•50331 


I.98684 


.52538 


I-90337 


17 


44 


.46065 


2.17083 


.48198 


2.07476 


.50368 


I.9854O 


•52575 


1.90203 


16 


45 


.46101 


2.16917 


.48234 


2.07321 


.50404 


I.98396 


.52613 


1 .90069 


15 


46 


.46136 


2. 167=51 


.48270 


2.07167 


.50441 


1.98253 


.52650 


1-89935 


14 


47 


.46171 


2.16585 


.48306 


2.07014 


•50477 


I.98110 


.52687 


1. 8980 1 


13 


48 


.46206 


2.16420 


.48342 


2.06860 


•50514 


I.97966 


.52724 


1.89667 


12 


49 


.46242 


2.16255 


•48378 


2.06706 


•50550 


I.97823 


.52761 


1-89533 


11 


50 


.46277 


2.16090 


.48414 


2.06553 


•50587 


I.97680 


.52798 


1 .89400 


10 


5i 


.46312 


2.15925 


•48450 


2.06400 


•50623 


I.97538 


.52836 


1.89266 


9 


52 


.46348 


2.15760 


.48486 


2.06247 


.50660 


1-97395 


.52873 


1-89133 


8 


53 


.46383 


2.15596 


.48521 


2.06094 


.50696 


1-97253 


.52910 


1 .89000 


7 


54 


.46418 


2.15432 


•48557 


2.05942 


•50733 


1.97m 1 


•52947 


1.88867 


6 


55 


.46454 


2.15268 


•48593 


2.05790 


.50769 


1.96969 


.52984 


1.88734 


5 


56 


.46489 


2.15104 


.48629 


2.05637 


! .50806 


1.96827 


.53022 


1.88602 


4 


57 


•46525 


2.14940 


.48665 


2.05485 


! -50843 


1.96685 


.53059 


1.88469 


3 


58 


.46560 


2.14777 


.48701 


2-05333 


1 .50879 


1.96544 


•53096 


1-88337 


2 


59 


•46595 


2.14614 


•48737 


2.051S2 


j 50916 


1.96402 


•53134 


1. 8820 s 


1 


60 


•46631 


2.14451 


•48773 


2.05030 


•50953 


1. 96261 


•53171 


1.88073 





/ 


CO-TAN . 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


CO -TAN. 


Tan. 


/ 




6 


5° 


6 


40 


i 6 


3° 


6 


2° 





486 NATURAL TANGENTS AND CO-TANGENTS 





O 

Ad 


8° 


29° 


30° 


31° 




Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 
1.66428 


o 


.53171 


1.88073 


•5543i 


1.80405 


•57735 


1-73205 


.60086 


I 


.53208 


1. 87941 


•55469 


1. 8028 1 


•57774 


1.73089 


.60126 


1. 663 18 


2 


.53246 


1.87809 


•55507 


1. 80 1 58 


.57813 


1.72973 


.60165 


1. 6209 


3 


.53283 


1.87677 


•55545 


1.80034 


.57851 


1.72857 


.60205 


1.66099 


4 


.53320 


1.87546 


•55583 


1.79911 


.57890 


1.72741 


.60245 


1.65990 


5 


.53358 


1.874^5 


.55621 


1.79788 


•57929 


1.72625 


.60284 


1. 6588 1 


6 


•53395 


1.87283 


•55659 


1.79665 


.57968 


1.72509 


.60324 


1.65772 


7 


-53432 


1.87152 


•55697 


1.79542 


.58007 


1-72393 


.60364 


1.65663 


8 


.53470 


1.87021 


•55736 


1. 79419 


.58046 


1.72278 


.60403 


1-65534 


9 


.53507 


1. 8689 1 


•55774 


1.79296 


.58085 


1. 72163 


.60443 


1.65445 


IO 


•53545 


1.86760 


.55812 


I-79I74 


.58124 


1.72047 


.60483 


1-65337 


ii 


.53582 


1.86630 


.55850 


1-79051 


.58162 


1. 71932 


.60522 


1.65228 


12 


.53620 


1.86499 


.55888 


1.78929 


.58201 


1.71817 


.60562 


1.65120 


13 


.53057 


1.86369 


•55926 


1.78807 


.58240 


1. 71702 


.60602 


1.65011 


14 


•53694 


1.86239 


•55964 


1.78685 


.58279 


1.71588 


.60642 


1.64903 


15 


•53732 


1.86109 


•56003 


1.78563 


.58318 


i-7i473 


.60681 


1.64795 


16 


.53769 


1.85979 


.56041 


1. 78441 


•58357 


i-7i358 


.60721 


1.64687 


17 


.53807 


1.85850 


.56079 


1. 78319 


.58396 


1.71244 


.60761 


1.64579 


18 


•53844 


1.85720 


.56117 


1.78198 


.58435 


1.71129 


.60801 


1. 6447 1 


19 


.53882 


1.85591 


.56156 


1.78077 


•58474 


1-71015 


.60841 


1.64363 


20 


•53920 


1.85462 


.56194 


1.77955 


.58513 


1. 70901 


.60881 


1.64256 


21 


•53957 


1-85333 


.56232 


1.77834 


.58552 


1.70787 


.60921 


1. 64148 


22 


•53995 


1.85204 


•56270 


I-777I3 


.58591 


1.70673 


.60960 


1. 64041 


23 


•54032 


1-85075 


•56309 


1.77592 


.58631 


1.70560 


.61000 


1-63934 


24 


.54070 


1.84946 


•56347 


1. 77471 


•58670 


1.70446 


.61040 


1.63826 


25 


.54107 


1. 84818 


.56385 


I-7735I 


.58709 


1.70332 


.61080 


1.63719 


26 


•54145 


1.84689 


.56424 


1.77230 


.58748 


1. 70219 


.61120 


1.63612 


27 


.54183 


1. 84561 


.56462 


1.77110 


.58787 


1. 70106 


.61160 


1-63505 


28 


.54220 


1-84433 


•56500 


1.76990 


.58826 


1.69992 


.61200 


1.63398 


29 


•54258 


1.84305 


.56539 


1.76869 


.58865 


1.69879 


.61240 


1.63292 


30 


.54296 


1-84177 


•56577 


1.76749 


.58904 


1.69766 


.61280 


1.63185 


31 


•54333 


1.84049 


.56616 


1.76630 


•58944 


1.69653 


.61320 


1.63079 


32 


•54371 


1.83922 


•56654 


1. 76510 


.58983 


1. 69541 


.61360 


1.62972 


33 


•54409 


1.83794 


•56693 


1.76390 


.59022 


1.69428 


.61400 


1.62866 


34 


•54446 


1.83667 


.56731 


1. 76271 


.59061 


1.69316 


.61440 


1.62760 


35 


.54484 


1.83540 


.56769 


1.76151 


.59101 


1.69203 


.61480 


1.62654 


36 


•54522 


1-83413 


.56808 


1*76032 


.59140 


1. 69091 


.61520 


1.62548 


37 


•5456o 


1.83286 


.56846 


I.759I3 


.59179 


1.68979 


.61561 


1.62442 


38 


•54597 


1-83159 


.56885 


1.75794 


.59218 


1.68866 


.61601 


1.62336 


39 


•54635 


1.83033 


.56923 


1.75675 


•59258 


1.68754 


.61641 


1.62230 


40 


•54673 


1.82906 


.56962 


1-75556 


•59297 


1.68643 


.61681 


1.62125 


4i 


•547" 


1.82780 


•57ooo 


1-75437 


■5933^ 


1. 68531 


.61721 


1.62019 


42 


•54748 


1.82654 


•57039 


1. 75319 


•59376 


1. 68419 


.61761 


1.61914 


43 


.54786 


1.82528 


.57078 


1.75200 


•59415 


1.68308 


.61801 


1. 61808 


44 


.54824 


1.82402 


.57116 


1.75082 


•59454 


1.68196 


.61842 


1.61703 


45 


.54862 


1.82276 


•57155 


1.74964 


•59494 


1.68085 


.61882 


1. 6 1 598 


46 


.54900 


1. 82 1 50 


•57193 


1.74846 


•59533 


1.67974 


.61922 


1. 61493 


47 


•54938 


1.82025 


•57232 


1.74728 


•59573 


1.67863 


.61962 


1.61388 


48 


•54975 


1.81899 


•57271 


1. 74610 


.59612 


1.67752 


.62003 


1.61283 


49 


•55013 


1-81774 


•57309 


1.74492 


•59651 


1.67641 


.62043 


1.61179 


50 


•55051 


1. 8 1 649 


.57348 


1-74375 


.59691 


1.67530 


.62083 


1.61074 


5i 


•55089 


1.81524 


.57386 


1-74257 


•59730 


1.67419 


.62124 


1.60970 


52 


•55127 


1.81399 


.57425 


1. 74140 


•59770 


1.67309 


.62164 


1.60865 


53 


•55i65 


1.81274 


.57464 


1.74022 


.59809 


1.67198 


.62204 


1. 60761 


54 


•55203 


1.81150 


•5V503 


I-73905 


•59849 


1.67088 


.62245 


1.60657 


55 


•55241 


1.81025 


•57541 


1.73788 


.59888 


1.66978 


.62285 


1.60553 


56 


•55279 


1. 8090 1 


.5758o 


1.73671 


•59928 


1.66867 


•62325 


1.60449 


57 


•55317 


1.80777 


.57619 


1-73555 


•59967 


1.66757 


.62366 


1.60345 


58 


•55355 


1.80653 


•57657 


I-73438 


.60037 


1.66647 


.62406 


1. 60241 


59 


•55393 


1.80529 


•57696 


1.73321 


.60046 


1.66538 


.62446 


1. 60137 


60 


•55431 


1.80405 


•57735 


1.73205 


.60086 


1.66428 


.62487 


1 .60033 




Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan . 


Tan. 


Co-tan. 


Tan. 




6 


1° 


6 


0° 


5 


9° 


5 


8° 



NATURAL TANGENTS AND CO-TANGENTS 487 



32° 


33° 


34° 


35° 




Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 


.62487 


1.60033 


.64941 


1.53986 


.67451 


1.48256 


; .70021 


1.42815 


60 


.62527 


1.59930 


.64982 


1.53888 


•67493 


1.48163 


1 .70064 


1.42726 


59 


.62568 


1.59826 


.65023 


1.53791 


•67536 


1.48070 


.70107 


1.42638 


58 


.62608 


1-59723 


.65065 


1-53693 


•67578 


1.47977 


.70151 


1.42550 


57 


.62649 


1.59620 


.65106 


1-53595 


.67620 


1.47885 


.70194 


1.42462 


56 


.62689 


I-595I7 


.65148 


1-53497 


.67663 


1.47792 


•70238 


1.42374 


55 


.62730 


1. 59414 


.65189 


1.53400 


: -67705 


1.47699 


.70281 


1.42286 


54 


.62770 


I-593H 


•65231 


I-533Q2 


.67748 


1.47607 


•70325 


1. 42 198 


53 


.62811 


1.59208 


'65272 


1-53205 


.67790 


i-475i4 


.70368 


1.42110 


52 


.62852 


i-59io5 


•65314 


i-53io7 


■67832 


1.47422 


.70412 


1.42022 


5i 


.62892 


1.59002 


.65355 


1. 53010 


.67875 


1-47330 


.70455 


i-4i934 


5o 


.62933 


1 .58900 


•65397 


1-52913 


.67917 


1.47238 


.70499 


1.41847 


49 


•62973 


1.58797 


.65438 


1.52816 


.67960 


1.47146 


•70542 


I-4I759 


48 


.63014 


1.58695 


.65480 


I-527I9 


.68002 


1.47053 


.70586 


1.41672 


47 


•63055 


I-58593 


•65521 


1.52622 


.68045 


1.46962 


.70629 


1.41584 


46 


•63095 


1.58490 


•65563 


1-52525 


.68088 


1.46870 


.70673 


i-4i497 


45 


.63136 


1.58388 


.65604 


1.52429 


.68130 


1.46778 


.70717 


1. 4 1 409 


44 


•63177 


1.58286 


.65646 


1-52332 


.68173 


1.46686 


.70760 


1.41322 


43 


.63217 


1.58184 


.65688 


1.52235 


.68215 


1-46595 


.70804 


1-41235 


42 


.63258 


1.58083 


.65729 


I-52I39 


.68258 


1.46503 


.70848 


1. 41 148 


4i 


•63299 


i.5798i 


•65771 


1.52043 


.68301 


1. 4641 1 


.70891 


1.41061 


40 


•63340 


I-57879 


.65813 


1. 51946 


.68343 


1.46320 


•70935 


1.40974 


39 


.63380 


1.57778 


•65854 


1.51850 


.68386 


1.46229 


•70979 


1.40887 


38 


.63421 


1.57676 


.65896 


I-5I754 


.68429 


1-46137 


.71023 


1 .40800 


37 


.63462 


1-57575 


.65938 


1.51658 


.68471 


1.46046 


.71066 


1.40714 


36 


•63503 


1-57474 


.65980 


1-51562 


.68514 


1-45955 


.71110 


1.40627 


35 


•63544 


1-57372 


.66021 


1.51466 


.68557 


1.45864 


•7ii54 


1.40540 


34 


•63584 


1.57271 


.66063 


i-5i37o 


.68600 


1-45773 


.71198 


1.40454 


33 


•63625 


1.57170 


.66105 


I-5I275 


.68642 


1.45682 


.71242 


1.40367 


32 


.63666 


1.57069 


.66147 


I-5II79 


.68685 


1-45592 


.71285 


1.40281 


3i 


.63707 


1.56969 


.66189 


1.51084 


.68728 


i-455oi 


.71329 


1. 40 1 95 


30 


.63748 


1.56868 


.66230 


1.50988 


.68771 


I.454IO 


•71373 


1. 40 109 


29 


.63789 


1-56767 


.66272 


1.50893 


.68814 


1.45320 


.71417 


1.40022 


28 


.63830 


1.56667 


.66314 


1.50797 


.68857 


1.45229 


.71461 


I.39936 


27 


.63071 


1.56566 


.66356 


1.50702 


.68900 


I-45I39 


.71505 


1.39850 


26 


.63912 


1.56466 


.66398 


1.50607 


.68942 


1.45049 


•71549 


1.39764 


25 


•63953 


1.56366 


.66440 


1.50512 


.68985 


1.44958 


•71593 


1.39679 


24 


.63994 


1.56265 


.66482 


1-50417 


.69028 


1.44868 


•71637 


1-39593 


23 


•6403s 


1.56165 


.66524 


1.50322 


.69071 


1.44778 


.71681 


I-39507 


22 


.64076 


1.56065 


.66566 


1.50228 


.69114 


1.44688 


.71725 


1. 3942 1 


21 


.64117 


1.55966 


.66608 


1-50133 


•69157 


1.44598 


.71769 


1.39336 


20 


•64158 


1.55866 


.66650 


1.50038 


.69200 


1.44508 


.71813 


1.39250 


19 


.64199 


1.55766 


'66692 


1.49944 


.69243 


1. 44418 


.71857 


1-39165 


18 


.64240 


1.55666 


.66734 


1.49849 


.69286 


1.44329 


.71901 


1.39079 


17 


.64281 


I-55567 


.66776 


1-49755 


•69329 


1.44239 


.71946 


1.38994 


16 


.64322 


I-55467 


.66818 


1. 4966 1 


.69372 


1.44149 


.7.1990 


1.38909 


15 


•64363 


1-55368 


.66860 


1.49566 


.69416 


1.44060 


•72034 


1.38824 


14 


.64404 


1.55269 


.66902 


1.49472 


•69459 


1.43970 


.72078 


1.38738 


13 


.64446 


i-55i7o 


.66944 


1.49378 


.69502 


1. 43881 


.72122 


1.38653 


12 


.64487 


1-55071 


.66986 


1.49284 


•69545 


1.43792 


.72166 


1.38568 


11 


.64528 


1.54972 


.67028 


1. 49 1 90 


.69588 


I-43703 


.72211 


1.38484 


10 


•64569 


1.54873 


.67071 


1.49097 


.69631 


1. 43614 


.72255 


I-38399 


9 


.64610 


1-54774 


.67113 


1.49003 


•69675 


1-43525 


.72299 


1-38314 


8 


.64652 


1.54675 


•67155 


1.48909 


.69718 


I-43436 


•72344 


1.38229 


7 


.64693 


1-54576 


.67197 


1. 488 1 6 


.69761 


1-43347 


.72388 


I-38I45 


6 


•64734 


1.54478 


•67239 


1.48722 


.69804 


1.43258 


•72432 


1.38060 


5 


•64775 


1-54379 


.67282 


1.48629 


■69847 


1.43169 


.72477 


1.37976 


4 


.64817 


1.54281 


.67324 


1.48536 


.69891 


1.43080 


•72521 


I-3789I 


3 


.64858 


i-54i83 


•67366 


1.48442 


.69934 


1.42992 


•72565 


1.37807 


2 


.64899 


1.54085 


.67409 


1.48349 


•69977 


1-42903 


.72610 


1.37722 


1 


.64941 


1.53986 


•67451 


1.48256 


.70021 


1.42815 


.72654 


1.37638 





Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


CO -TAN. 


Tan. 


/ 


5 


7° 


5 


6° 


5 


5° 


5 


40 





488 NATURAL TANGENTS AND CO-TANGENTS 





36° 


37° 


38° 


39° 




/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 


o 


.72654 


1-37638 


-75355 


1.32704 


.78129 


1.27994 


.80978 


1-23490 


60 


I 


.72699 


1-37554 


.75401 


1.32624 


.78175 


1.27917 


.81027 


1. 23416 


59 


2 


•72743 


i-3747o 


•75447 


1.32544 


.78222 


1.27841 


.81075 


1-23343 


58 


3 


.72788 


1.37386 


•75492 


1.32464 


.78269 


1.27764 


.81123 


1.23270 


57 


4 


.72832 


1.37302 


.75538 


1.32384 


.78316 


1.27688 


.81171 


1.23196 


56 


5 


.72877 


i-372i8 


.75584 


1.32304 


.78363 


1.27611 


.81220 


1-23123 


55 


6 


.72921 


I-37I34 


.75629 


1.32224 


.78410 


1-27535 


.81268 


1.23050 


54 


7 


.72966 


1.37050 


.75675 


1.32144 


•78457 


1.27458 


.81316 


1.22977 


53 


8 


.73010 


1.36967 


•75721 


1.32064 


.78504 


1.27382 


•81364 


1.22904 


52 


9 


.73055 


1.36883 


•75767 


1-31984 


.78551 


1.27306 


.81413 


1. 22831 


51 


TO 


.73100 


1 .36800 


.75812 


1.31904 


.78598 


1.27230 


.81461 


1.22758 


50 


ii 


•73144 


1.36716 


.75858 


1.31825 


.78645 


I-27I53 


.81510 


1.22685 


49 


12 


.73189 


1-36633 


.75904 


1. 3 1 745 


.78692 


1.27077 


.81558 


1. 22612 


48 


13 


•73234 


I-36549 


•75950 


1. 31666 


.78739 


1. 2 700 1 


.81606 


1.22539 


47 


14 


.73278 


1.36466 


.75996 


1.31586 


.78786 


1.26925 


.81655 


1.22467 


46 


15 


.73323 


1-36383 


.76042 


1-31507 


.78834 


1.26849 


.81703 


1.22394 


45 


16 


.73368 


1.36300 


.76088 


1-31427 


.78881 


1.26774 


.81752 


1. 22321 


44 


17 


.73413 


1.36217 


.76134 


I-3I348 


.78928 


1.26698 


.81800 


1.22249 


43 


18 


•73457 


1.36133 


.76180 


1.31269 


.78975 


1.26622 


.81849 


1. 22176 


42 


19 


.73502 


1-36051 


.76226 


1-31190 


.79022 


1.26546 


.81898 


1. 22104 


4i 


20 


•73547 


1.35968 


.76272 


1.31110 


.79070 


1.26471 


.81946 


1. 22031 


40 


21 


•73592 


1-35885 


.76318 


1-31031 


.79117 


1.26395 


.81995 


1.21959 


39 


22 


•73637 


1.35802 


.76364 


1.30952 


.79164 


1. 26319 


.82044 


1.21886 


38 


23 


.73681 


I-357-I9 


.76410 


1.30873 


.79212 


1.26244 


.82092 


1.21814 


37 


24 


.73726 


1-35637 


.76456 


1-30795 


•79259 


1. 26169 


.82141 


1. 21742 


36 


25 


.73771 


1-35554 


.76502 


1. 30716 


•79306 


1.26093 


.82190 


1. 21670 


35 


26 


.73816 


1-35472 


.76548 


1.30637 


•79354 


1.26018 


.82238 


1. 21598 


34 


27 


.73861 


I-35389 


.76594 


1-30558 


•79401 


1-25943 


.82287 


1. 21526 


33 


28 


•739o6 


I-35307 


.76640 


1.30480 


•79449 


1.25S67 


.82336 


1.21454 


32 


29 


•73951 


1.35224 


.76686 


1. 3040 1 


•79496 


1.25792 


.82385 


1. 21382 


3i 


30 


•73996 


I-35I42 


.76733 


1.30323 


•79544 


I.257I7 


•82434 


1.21310 


30 


3* 


.74041 


1.35060 


.76779 


1.30244 


•79591 


1.25642 


.82483 


1.21238 


29 


32 


.74086 


1.34978 


• 76325 


1.30166 


•79639 


1.25567 


.82531 


1.21166 


28 


33 


.74131 


1 .34896 


.76871 


1.30087 


.79686 


1.25492 


.82580 


1. 21094 


27 


34 


.74176 


1-34814 


.76918 


1.30009 


•79734 


I.254I7 


.82629 


1.21023 


26 


35 


.74221 


1-34732 


.76964 


1-29931 


.7978i 


1.25343 


.82678 


1. 20951 


25 


36 


.74267 


1.34650 


.77010 


1.29853 


.79829 


1.25268 


.82727 


1.20879 


24 


37 


•74312 


1.34568 


'77057 


1.29775 


•79877 


I-25I93 


.82776 


1.20808 


23 


38 


•74357 


1.34487 


•77103 


1.29696 


•79924 


1.25118 


.82825 


1.20736 


22 


39 


.74402 


I-34405 


.77149 


1. 29618 


•79972 


1.25044 


.82874 


1.20665 


21 


40 


•74447 


1-34323 


.77196 


1.29541 


.80020 


1.24969 


.82923 


1.20593 


20 


41 


•74492 


1.34242 


.77242 


1.29463 


.80067 


1.24895 


.82972 


1.20522 


19 


42 


.74538 


1. 34160 


•77289 


1.29385 


.80115 


1.24820 


.83022 


1. 20451 


18 


43 


•74583 


1.34079 


•77335 


1.29307 


.80163 


1.24746 


.83071 


1.20379 


17 


44 


.74628 


I-33998 


.77382 


1.29229 


.80211 


1.24672 


.83120 


1.20308 


16 


45 


•74674 


1.33916 


.77428 


1.-9152 


.80258 


1.24597 


.83169 


1.20237 


15 


46 


.74719 


I-33835 


•77475 


1.29074 


.80306 


1.24523 


.83218 


1. 20166 


14 


47 


.74764 


1-33754 


•77521 


1.28997 


.80354 


1.24449 


.83268 


1.20095 


13 


48 


.74810 


I-33673 


.77568 


1. 28919 


.80402 


1-24375 


-83317 


1.20024 


12 


49 


•74855 


1-33592 


.77615 


1.28842 


.80450 


1. 24301 


.83366 


I-I9953 


11 


SO 


.74900 


I-335H 


.77661 


1.28764 


.80498 


1.24227 


•83415 


1. 1 9882 


10 


5i 


.74946 


I-3343Q 


.777o8 


1.28687 


.80546 


I-24I53 


•83465 


1.19811 


9 


52 


.74991 


1-33349 


•77754 


1. 28610 


.80594 


1.24079 


.83514 


1. 19740 


8 


53 


•75037 


1.33268 


.77801 


1-28533 


.80642 


1.24005 


.83564 


1. 1 9669 


7 


54 


• 75082 


i.33i87 


.77848 


1.28456 


.80690 


I-2393I 


.83613 


1. 1 9599 


6 


55 


.75128 


I-33I07 


.77895 


1.28379 


.80738 


1.23858 


.83662 


1. 19528 


5 


56 


•75173 


1.33026 


.77941 


1.28302 


.80786 


1.23784 


.83712 


1. 19457 


4 


57 


.75219 


1.32946 


.77988 


1.28225 


.80834 


1. 23710 


.83761 


1. 19387 


3 


58 


.75264 


1.32865 


.7S035 


1. 28148 


.80882 


1.23637 


.83811 


1.19316 


2 


59 


•753io 


1-32785 


.78082 


1. 28071 


.80930 


1.23563 


.83860 


1. 19246 


1 


60 


•75355 


1.32704 


.78129 


1.27994 


.80978 


1.23400 


.83910 


I-I9I75 





t 


Co-tan. 


Tan. 


Co-tan. 


Tan. I 


Co-tan 


Tan. 


Co-tan. 


Tan 


t 




5; 


3° 


& 


2° 


5 


1° 


5( 


3° 





NATURAL TANGENTS AND CO-TANGENTS 489 





40° 


41° 


42° 


43° 




1 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 





.83910 


1.19175 


.86929 


1.15037 


.90040 


1.11061 


•93252 


1.07237 


60 


I 


.83960 


1.19105 


.86980 


1. 1 4969 


•90093 


1. 10996 


•93306 


1-07174 


59 


2 


.84009 


1-19035 


.87031 


1. 14902 


.90146 


1.10931 


•93360 


1.07112 


58 


3 


.84059 


1. 1 8964 


.87082 


1. 14834 


.90199 


1. 10867 


•93415 


1.07049 


57 


4 


.84108 


1. 18894 


.87133 


1. 14767 


.90251 


1. 10802 


.93469 


1.06987 


56 


5 


.84158 


1. 18824 


.87184 


1. 1 4699 


.93304 


1. 10737 


•93524 


1.06925 


55 


6 


.84208 


1. 18754 


.87236 


1. 14632 


•90357 


1. 10673 


•93578 


1.06862 


54 


7 


.84258 


1. 1 8684 


.87287 


1-14565 


.90410 


1. 10607 


•93633 


1 .06800 


53 


8 


.84307 


1.18614 


.87338 


1. 1 4498 


•90463 


i- 10543 


.93688 


1.06738 


52 


9 


•84357 


1. 18544 


.87389 


1. 14430 


.90516 


1. 10478 


•93742 


1.06676 


Si 


10 


.84407 


1. 18474 


.87441 


1-14363 | 


.90569 


1.10414 


•93797 


1.06613 


50 


11 


•84457 


1. 18404 


.87492 


1. 14296 


.90621 


1. 10349 


•93852 


1-06551 


49 


12 


.84507 


1-18334 


•87543 


1. 14229 


.90674 


1. 10285 


•939o6 


1.06489 


48 


13 


.84556 


1. 18264 


•87595 


1.14162 


.90727 


1. 10220 


.93961 


1.06427 


47 


14 


.84606 


1.18194 


.87646 


1. 14095 


.90781 


1.10156 


1 .94016 


1.06365 


46 


15 


.84656 


1.18125 


.87698 


1. 14028 | 


•90834 


1.10091 


1 -94071 


1.06303 


45 


16 


.84706 


1. 18055 


.87749 


1.13961 1 


.90887 


1. 10027 


! -94125 


1. 06241 


44 


17 


.84756 


1. 17986 


.87801 


1. 13894 


.90940 


1.09963 


.94180 


1.06179 


43 


18 


.84806 


1.17016 


.87852 


1.1382S 


.90993 


1.09899 


•94235 


1. 061 1 7 


42 


19 


.84856 


1. 1 7846 


.87904 


1.13761 


.91046 


1 .09834 


.94290 


1.06056 


4i 


20 


.84906 


1. 17777 


•87955 


1. 13694 


.91099 


1.09770 


•94345 


1.05994 


40 


21 


•84956 


1*17708 ; 


.88007 


1. 13627 J 


•9H53 


1.09706 


.94400 


1.05932 


39 


22 


.85006 


1. 17638 


.88059 


1-13561 | 


.91206 


1.09642 


•94455 


1.05870 


38 


23 


.85057 


1. 17569 


.88110 


1 .13494 


.91259 


1.09578 


.94510 


1.05809 


37 


24 


.85107 


1-17500 


.88162 


1. 13428 


•91313 


1. 09514 


•94565 


I-05747 


36 


25 


.85157 


1-17430 


.88214 


1-13361 


.91366 


1.09450 


1 .94620 


1.05685 


35 


26 


.85207 


1-17361 


.88265 


1-13295 


.91419 


1.09386 


' .94676 


1.05624 


34 


27 


.85257 


1. 17292 


.88317 


1. 13228 


•91473 


1.09322 


•94731 


1.05562 


33 


28 


.85307 


1. 17223 


.88369 


1.13162 


.91526 


1.09258 


.94786 


1. 05501 


32 


29 


.85358 


1.17154 


.88421 


1. 1 3096 


.91580 


1. 09195 


.94841 


1 -Q5439 


3i 


30 


.85408 


1. 17085 


.88473 


1. 13029 


•91633 


1-09131 


.94896 


1-05378 


30 


3i 


.85458 


1.17016 


.88524 


1. 12963 


.91687 


1.09067 


•94952 


1-05317 


29 


32 


•85509 


1. 16947 


.88576 


1. 12897 


.91740 


1 .09003 


.95007 


1-05255 


28 


33 


.85559 


1. 16878 


.88628 


1.12831 


.91794 


1 .08940 


.95062 


1-05194 


27 


34 


.85609 


1. 1 6809 


.88680 


1. 12765 


.91847 


1.08876 


.95118 


1-05133 


26 


35 


.85660 


1.16741 


.88732 


1. 12699 


.91901 


1. 088 1 3 


•95173 


1.05072 


25 


36 


.85710 


1. 16672 


.88784 


1. 12633 


.91955 


1.08749 


.95229 


1. 05010 


24 


37 


.85761 


1. 1 6603 


.88836 


1. 12567 


.92008 


1.08686 


.95284 


1.04949 


23 


38 


.85811 


1-16535 


.88888 


1.12501 


.92062 


1.08622 


•95340 


1.04888 


22 


39 


.85862 


1. 16466 


.88940 


1.1243s 


.92116 


1.08559 


•95395 


1.04827 


21 


40 


.85912 


1. 16398 


.88992 


1. 12369 


.92170 


1 .08496 


•95451 


1.04766 


20 


41 


.85963 


1. 16329 


.89045 


1. 12303 


.92224 


1.08432 


•95506 


1.04705 


19 


42 


.86014 


1.16261 


.89097 


1. 12238 


.92277 


1.08369 


•95562 


1.04644 


18 


43 


.86064 


1.16192 


.89149 


1.12172 


•92331 


1.08306 


•95618 


1.04583 


17 


44 


.86115 


1.16124 


.89201 


1.12106 


•92385 


1.08243 


•95673 


1.04522 


16 


45 


.86166 


1. 16056 


•89253 


1.12041 


•92439 


1.08179 


•95729 


1. 0446 1 


15 


46 


.86216 


1.15987 


.89306 


I-H975 


.92493 


1.08116 


•95785 


1. 0440 1 


14 


47 


.86267 


1. 15919 


•89358 


1.11909 


•92547 


1.08053 


•95841 


1.04340 


13 


48 


.86318 


1.15851 


.89410 


1.11844 


.92601 


1.07990 


•95897 


1.04279 


12 


49 


.86368 


1-15783 


.89463 


1.11778 


.92655 


1.07927 


•95952 


1.04218 


11 


50 


.86419 


1.15715 


•89515 


1.11713 


.92709 


1.07864 


.96008 


1.04158 


10 


5i 


.86470 


1. 15647 


.89567 


1.11648 


•92763 


1. 0780 1 


.96064 


1.04097 


9 


52 


.86521 


I-I5579 


.89620 


1.11582 


.92817 


1.07738 


.96120 


1.04036 


8 


53 


.86572 


I.I55H 


.89672 


1.11517 


.92872 


1.07676 


.96176 


1.03976 


7 


54 


.86623 


1. 1 5443 


.89725 


1.1 1452 


.92926 


1.07613 


.96232 


1-03915 


6 


55 


.86674 


I-I5375 


.89777 


1.11387 


.92980 


1-07550 


.96288 


1-03855 


5 


56 


.86725 


1-15308 


.89830 


1.11321 


•93034 


1.07487 


•96344 


1.03794 


4 


57 


.86776 


1. 15240 


.89883 


1.11256 


.93088 


1.07425 


.96400 


I-Q3734 


3 


58 


.86827 


1.15172 


•89935 


1.11191 


•93143 


1.07362 


•96457 


1.03674 


2 


59 


.86878 


1.15104 


.89988 


1.11126 


•93197 


1.07299 


.96513 


1-03613 


1 


60 


.86929 


1-15037 


.90040 


i.tio6i 


•93252 


1.07237 


.96569 


I-Q3553 





/ 


Co-tan 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


*• 




4 


3° 


4 


3° 


4 


7° 


4 


6° 





490 NATURAL TANGENTS AND CO-TANGENTS 



44° 
Tan. Co-tan. 



.96569 
.96625 
.96681 
.96738 
.96794 
.96850 
.96907 
.96963 
.97020 
.97076 
•97133 
.97189 
.97246 
.97302 

•97359 
.97416 
.97472 
•97529 
.97586 

•97643 
.97700 



I-Q3553 
1 -03493 
1 -03433 
1.03372 
1-03312 
1.03252 
1.03192 
1.03132 
1.03072 
1.03012 
1.02952 

1.02892 
1.02832 
1.02772 
1 .02713 
1.02653 
1.02593 
1.02533 
1.02474 
1.02414 
1-02355 



Co-tan. Tan. 
45° 



440 
Tan. Co-tan. 



97756 
97813 
97870 
97927 
97984 
98041 
98098 

98155 
98213 
98270 

98327 
98384 
98441 
98499 
98556 
98613 
98671 
98728 
98786 
98843 



1.02295 
1.02236 
1. 02 1 76 
1. 021 17 
1.02057 
1. 01 998 
1.01939 
1.01879 
1.01820 
1.01761 

1. 01 702 
1.01642 
1-01583 
1.01524 
1. 01 465 
1. 01 406 
1.01347 
1. 01 288 
1.01229 
1.01170 



Co-tan. I Tan. 
45° 



/ 


r 


39 
38 


4i 
42 


37 
36 


43 
44 


35 
34 


45 
46 


33 
32 


47 
48 


31 


49 


30 


50 


29 

28 


5i 
52 


27 
26 


53 

54 


25 
24 


55 
56 


23 
22 


57 
58 


21 
20 


59 
60 


' 


/ 



Tan. 



44° 

Co-tan. 



.98901 
.98958 
.99016 
.99073 

•99131 
.99189 
.99247 
.99304 
.99362 
.99420 

•99478 
•99536 
•99594 
.99652 
.99710 
.99768 
.99826 
.99884 
.99942 



1.01112 
1.01053 
1.00994 
1.00935 
1.00876 
1. 008 1 8 
1.00759 
1. 00 70 1 
1.00642 
1.00583 

1.00525 
1.00467 
1 .00408 
1.00350 
1.00291 
1.00233 
1.00175 
1. 001 16 
1.00058 



Co-tan. Tan. 
45° 



NATURAL SINES AND COSINES 



o 

I 

2 

3 
4 
5 
6 
7 
8 

9 

10 

11 
12 
13 
14 
15 
16 

17 

18 

^9 

20 



0° 

Sine Cosine 



.00000 
.00029 
.00058 
.00087 
.00116 
•00145 
.00175 
.00204 
•00233 
.00262 
.00291 

.00320 
.00349 
•00378 
.00407 
.00436 
.00465 
.00495 
.00524 

•00553 
.00582 



.99999 
•99999 
•99999 
•99999 
•99999 
■99999 
•99999 
•99999 
.99998 
•99998 



Cosine Sine 

89° 







c 


>° 






c 


)° 


60 


r 

21 


Sine 


Cosine 


39 


/ 

4i 


Sine 


Cosine 


.00611 


•99998 


.01193 


•99993 


59 


22 


.00640 


•99998 


3^ 


42 


.01222 


•99993 


58 


23 


.00669 


•99998 


37 


43 


.01251 


.99992 


57 


24 


.00698 


•99998 


36 


44 


.01280 


.99992 


56 


25 


.00727 


•99997 


35 


45 


•01309 


.99991 


55 


26 


.00756 


•99997 


34 


46 


•01338 


.99991 


54 


27 


.00785 


•99997 


33 


47 


.01367 


.99991 


53 


28 


.00814 


•99997 


32 


48 


.01396 


•99990 


52 


20 


.00844 


.99996 


3i 


49 


.01425 


•99990 


5i 


30 


.00873 


•99996 


30 


50 


.01454 


.99989 


50 


31 


.00902 


.99996 


29 


51 


.01483 


•99989 


49 


32 


.00931 


.99996 


28 


52 


•01513 


.99989 


48 


33 


.00960 


•99995 


27 


53 


.01542 


.99988 


47 


34 


.00989 


•99995 


26 


54 


.01571 


.99988 


46 


35 


.01018 


•99995 


25 


55 


.01600 


•99987 


45 


36 


.01047 


•99995 


24 


56 


.01629 


•99987 


44 


37 


.01076 


•99994 


23 


57 


.oi6s8 


.99986 


43 


38 


.01105 


•99994 


22 


58 


.01687 


.99986 


42 


39 


.01134 


•99994 


21 


59 


.01716 


•99985 


4i 

40 

r 


40 

/ 


.01164 


•99993 


20 
/ 


60 


•oi745 


•99985 


Cosine 


Sine 


Cosine 


Sine 






8 


3° 






8< 


y> 



17 

TO 
15 
14 
13 
12 

i r 

TO 

9 

8 

7 
6 
5 
4 
3 
2 
1 
o 



NATURAL SINES AND COSINES 



491 








2° 


e 


}° 


40 




Sine 


Cosine | 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


r 


.01745 


.99985 


.03490 


•99939 


•05234 


.99863 


.06976 


•99756 


60 


•01774 


.99984 


■03519 


•99938 


.05263 


.99861 


.07005 


•99754 


59 


.01803 


.99984 


.03548 


•99937 


.05292 


.99860 


•07034 


•99752 


58 


.01832 


.99983 


•03577 


•99936 


.05321 


.99858 


.07063 


•9975o 


57 


.01862 


.99983 


.03606 


•99935 


•05350 


•99857 


.07092 


•99748 


56 


.01891 


.99982 


•03635 


•99934 


•05379 


•99855 


.07121 


•99746 


55 


.01920 


.99982 


.03664 


•99933 


.05408 


.99854 


.07150 


•99744 


54 


.01949 


.99981 


•03693 


.99932 


•05437 


.99852 


.07179 


•99742 


53 


.01978 


.99980 


•03723 


•99931 


•05466 


.99851 


.07208 


•99740 


52 


.02007 


.99980 


•03752 


.99930 


•05495 


•99849 


.07237 


•99738 


5i 


.02036 


.99979 


.03781 


.99929 


.05524 


.99847 


.07266 


.99736 


50 


.02065 


.99979 


.03810 


.99927 


•05553 


.99846 


.07295 


•99734 


49 


.02094 


.99978 


.03839 


.99926 


.05582 


•99844 


.07324 


•99731 


48 


.02123 


.99977 


.03868 


•99925 


.05611 


.99842 


•07353 


.99729 


47 


.02152 


.99977 


.03897 


.99924 


.05640 


.99841 


.07382 


•99727 


46 


.02181 


.99976 


.03926 


.99923 


.05669 


•99839 


.07411 


•99725 


45 


.02211 


.99976 


•03955 


.99922 


.05698 


.99838 


.07440 


•99723 


44 


.02240 


•99975 


.03984 


.99921 


•05727 


.99836 


.07469 


.99721 


43 


.02269 


•99974 


•04013 


.99919 


•05756 


.99834 


.07498 


.99719 


42 


.02298 


•99974 


.04042 


.99918 


.05785 


•99833 


•07527 


.99716 


4i 


.02327 


•99973 


.04071 


.99917 


.05814 


.99831 


.07556 


.99714 


40 


.02356 


.99972 


.04100 


.99916 


.05844 


.99829 


.07585 


.99712 


39 


.02385 


.99972 


.04129 


•99915 


•05873 


.99827 


.07614 


.99710 


38 


.02414 


.99971 


.04159 


•99913 


.05902 


.99826 


.07643 


.99708 


37 


.02443 


.99970 


.04188 


.99912 


•05931 


.99824 


.07672 


•99705 


36 


.02472 


.99969 


.04217 


.99911 


.05960 


.99822 


.07701 


.99703 


35 


.02501 


.99969 


.04246 


.99910 


.05989 


.99821 


.07730 


•99701 


34 


.02530 


.99968 


.04275 


.99909 


.06018 


.99819 


.07759 


•99699 


33 


.02560 


.99967 


•04304 


•9990 7 


.06047 


.99817 


.07788 


.99696 


32 


.02589 


.99966 


•04333 


.99906 


.06076 


.99815 


.07817 


•99694 


31 


.02618 


.99966 


.04362 


•99905 


.06105 


.99813 


.07846 


.99692 


30 


.02647 


.99965 


.04391 


•99904 


•06134 


.99812 


.07875 


.99689 


29 


.02676 


.99964 


.04420 


.99902 


.06163 


.99810 


.07904 


.99687 


28 


.02705 


.99963 


•04449 


.99901 


.06192 


.99808 


.07933 


.99685 


27 


•02734 


.99963 


.04478 


.99900 


.06221 


.99806 


.07962 


.99683 


26 


.02763 


.99962 


.04507 


.99898 


.06250 


.99804 


.07991 


.99680 


25 


.02792 


.99961 


•04536 


.99897 


.06279 


•99803 


.08020 


.99678 


24 


.02821 


.99960 


•04565 


.99896 


.06308 


.99801 


.08049 


.99676 


23 


.02850 


•99959 


•04594 


•99894 


•06337 


•99799 


.08078 


.99673 


22 


.02879 


•99959 


.04623 


•99893 


.06366 


•99797 


.08107 


.99671 


21 


.02908 


.99958 


•04653 


.99892 


•06395 


■99795 


.08136 


.99668 


20 


.02938 


•99957 


.04682 


.99890 


.06424 


•99793 


.08165 


.99666 


19 


.02967 


.99956 


.04711 


.99889 


•06453 


•99792 


.08194 


.99664 


18 


.02996 


•99955 


.04740 


.99S88 


.06482 


•99790 


.08223 


.99661 


17 


•03025 


•99954 


.04769 


.99886 


.06511 


.99788 


.08252 


•99659 


16 


•03054 


•99953 


.04798 


.99885 


.06540 


.99786 


.08281 


•99657 


15 


.03083 


.99952 


.04827 


.99883 


.06569 


•99784 


.08310 


.99654 


14 


.03112 


•99952 


.04856 


.99882 


.06598 


.99782 


•08339 


.99652 


13 


.03141 


•99951 


.04885 


.99881 


.06627 


.99780 


.08368 


-99649 


12 


.03170 


•99950 


.04914 


.99879 


.06656 


•99778 


.08397 


•99647 


11 


.03199 


•99949 


•04943 


.99878 


.06685 


.99776 


.08426 


.99644 


10 


.03228 


.99948 


.04972 


.99876 


.06714 


•99774 


.08455 


.99642 


9 


•03257 


•99947 


.05001 


•99875 


•06743 


.99772 


.08484 


•99639 


8 


.03286 


.99946 


.05030 


•99873 


.06773 


•9977o 


.08513 


•99637 


7 


.03516 


•99945 


.05059 


.99872 


.06802 


.99768 


.08542 


•99635 


6 


•03345 


•99944 


.05088 


.99870 


.06831 


.99766 


.08571 


•99632 


5 


•03374 


•99943 


.05117 


.99869 


.06860 


.99764 


.08600 


.99630 


4 


•03403 


.99942 


.05146 


.99867 


.06889 


.99762 


.08629 


.99627 


3 


•03432 


.99941 


.05175 


.99866 


.06918 


.99760 


.08658 


.99625 


2 


•03461 


•99940 


.05205 


.99864 


.06947 


•99758 


.08687 


.99622 


1 


•03490 


•99939 


•05234 


•99863 


.06976 


•99756 


.08716 


.99619 





Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


Si 


i° 


8' 


7° 


81 


3° 


8 


5° 





49 2 



NATURAL SINES AND COSINES 





5° 


( 


3° 


7° 


8° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


o 


.08716 


.99619 


•10453 


.99452 


.12187 


.99255 


.13917 


.99027 


I 


.08745 


.99617 


.10482 


.99449 


.12216 


.99251 


.13946 


.99023 


2 


.08774 


.99614 


.10511 


•99446 


.12245 


.99248 


•13975 


.99019 


3 


.08803 


.99612 


.10540 


•99443 


.12274 


.99244 


.14004 


.99015 


4 


.08831 


.99609 


.10569 


•99440 


.12302 


.99240 


•14033 


.99011 


5 


.08860 


.99607 


•10597 


•99437 


.12331 


•99237 


.14061 


.99006 


6 


.08889 


.99604 


.10626 


•99434 


.12360 


•99233 


.14090 


.99002 


7 


.08918 


.99602 


.10655 


•99431 


.12389 


.99230 


.14119 


.98998 


8 


.08947 


•99599 . 


.10684 


.99428 


.12418 


.99226 


.14148 


.98994 


9 


.08976 


.99596 


.10713 


•99424 


.12447 


.99222 


.14177 


.98990 


IO 


.09005 


•99594 


.10742 


.99421 


.12476 


.99219 


.14205 


.98986 


ii 


.09034 


•99591 


.10771 


.99418 


.12504 


.99215 


.14234 


.98982 


12 


.09063 


.99588 


.10800 


•99415 


•12533 


.99211 


.14263 


.98978 


13 


.09092 


.99586 


.10829 


.99412 


.12562 


.99208 


.14292 


•98973 


14 


.09121 


•99583 


.10858 


.99409 


.12591 


.99204 


.14320 


.98969 


15 


.09150 


.99580 


.10887 


.99406 


.12620 


.99200 


•14349 


•98965 


16 


.09179 


•99578 


.10916 


.99402 


.12649 


.99197 


•14378 


.98961 


17 


.09208 


•99575 


.10945 


•99399 


.12678 


•99193 


.14407 


•98957 


18 


.09237 


•99572 


.10973 


.99396 


.12706 


.99189 


.14436 


•98953 


19 


.09266 


.99570 


.11002 


•99393 


•12735 


.99186 


.14464 


.98948 


20 


.09295 


.99567 


.11031 


.99390 


.12764 


.99182 


•14493 


•98944 


21 


.09324 


.99564 


.11060 


.99386 


•12793 


.99178 


.14522 


.98940 


22 


•09353 


.99562 


.11089 


•99383 


.12822 


•99175 


.14551 


•98936 


23 


.09382 


•99559 


.11118 


.99380 


.12851 


.99171 


.14580 


.98931 


24 


.09411 


.99556 


.11147 


•99377 


.12880 


.99167 


.14608 


.98927 


25 


.09440 


•99553 


.11176 


•99374 


.12908 


.99163 


.14637 


.98923 


26 


.09469 


.99551 


.11205 


•99370 


•12937 


.99160 


.14666 


.98919 


27 


.09498 


.99548 


.11234 


•99367 


.12966 


.99156 


.14695 


.98914 


28 


.09527 


•99545 


.11263 


•99364 


.12995 


.99152 


•14723 


.98910 


29 


.09556 


•99542 


.11291 


.99360 


.13024 


.99148 


.14752 


.98906 


30 


•09585 


.99540 


.11320 


•99357 


•13053 


.99144 


.14781 


.98902 


31 


.09614 


•99537 


.11349 


•99354 


.13081 


.99141 


.14810 


.98897 


32 


.09642 


•99534 


.11378 


•99351 


.13110 


•99137 


.14838 


.98893 


33 


.09671 


•99531 


.11407 


•99347 


.13139 


•99133 


.14867 


.98889 


34 


.09700 


.99528 


.11436 


•99344 


.13168 


.99129 


.14896 


.98884 


35 


.09729 


.99526 


.11465 


•99341 


•13197 


.99125 


.14925 


.98880 


36 


.09758 


.99523 


.11494 


•99337 


.13226 


.99122 


•14954 


.98876 


37 


.09787 


.99520 


.11523 


•99334 


• 13254 


.99118 


.14982 


.98871 


38 


.09816 


•99517 


.11552 


•99331 


• 13283 


.99114 


.15011 


.98867 


39 


.09845 


•99514 


.11580 


■99327 


.13312 


.99110 


.15040 


.98863 


40 


.09874 


•995H 


.11609 


•99324 


.13341 


.99106 


.15069 


.98858 


4i 


.09903 


.99508 


.11638 


.99320 


•13370 


.99102 


.15097 


.98854 


42 


.09932 


.99506 


.11667 


•99317 


•13399 


.99098 


.15126 


.98849 


43 


.09961 


•99503 


.11696 


•993T4 


• 13427 


.99094 


• 15155 


.98845 


44 


.09990 


.99500 


.11725 


.99310 


•13456 


.99091 


.15184 


.98841 


45 


.10019 


•99497 


.11754 


•99307 


•13485 


.99087 


.15212 


.98836 


46 


.10048 


•99494 


.11783 


•99303 


•T35I4 


.99083 


.15241 


.98832 


47 


.10077 


.99491 


.11812 


.99300 


• 13543 


•99079 


.15270 


.98827 


48 


.10106 


.99488 


.11840 


.99297 


.13572 


•99075 


.15299 


.98823 


49 


.10135 


.99485 


.11869 


.99293 


.13600 


.99071 


•15327 


.98818 


50 


.10164 


.99482 


.11898 


.99290 


.13629 


.99067 


.15356 


.98814 


51 


.10192 


.99479 


.11927 


.99286 


.13658 


.99063 


• 15385 


.98809 


52 


.10221 


.99476 


.11956 


•99283 


.13687 


.99059 


.15414 


.98805 


53 


.10250 


•99473 


.11985 


.99279 


.13716 


•99055 


.15442 


.98800 


54 


.10279 


.99470 


.12014 


.99276 


.13744 


.99051 


•i547i 


.98796 


55 


.10308 


.99467 


.12043 


.99272 


• 13773 


•99047 


.15500 


.98791 


56 


.10337 


.99464 


.12071 


.99269 


.13802 


•99043 


.15529 


.98787 


57 


.10366 


.99461 


.12100 


.99265 


.13831 


.99039 


•15557 


.98782 


58 


•10395 


•99458 


.12129 


.99262 


.13860 


•99035 


.15586 


.98778 


59 


.10424 


•99455 


.T2158 


.99258 


.13889 


.99031 


.15615 


•98773 


60 


•10453 


•99452 


.12187 


•99255 


• 13917 


.99027 


.15643 


.98769 


/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 




& 


t° 


8: 


]° 


& 


jo 


81 






NATURAL SINES AND COSINES 



493 





( 


)° 


1( 


3° 


11° 


12° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 
.19081 


Cosine 


Sine 


Cosine 


t 


o 


•15643 


.98769 


.17365 


.98481 


.98163 


.20791 


•97815 


60 


I 


.15672 


.98764 


•17393 


.98476 


.19109 


•98157 


.20820 


.97809 


59 


2 


.15701 


.98760 


.17422 


.98471 


.19138 


.98152 


.20848 


.97803 


58 


3 


.15730 


•98755 


.i745i 


.98466 


.19167 


.98146 


.20877 


•97797 


57 


4 


.15758 


•98751 


•17479 


.98461 


.19195 


.98140 


.20905 


•97791 


56 


5 


.15787 


.98746 


.17508 


•98455 


.19224 


•98135 


.20933 


.97784 


55 


6 


.15816 


.98741 


•17537 


.98450 


.19252 


.98129 


.20962 


.97778 


54 


7 


-15845 


•98737 


•17565 


•98445 


.19281 


.98124 


.20990 


.97772 


53 


8 


.15873 


.98732 


.17594 


.98440 


.10309 


.98118 


.21019 


•97766 


52 


9 


.15902 


.98728 


.17623 


•98435 


.19338 


.98112 


.21047 


.97760 


5i 


IO 


.15931 


.98723 


.17651 


.98430 


.19366 


.98107 


.21076 


•97754 


5o 


ii 


•15959 


.98718 


.17680 


.98425 


.19395 


.98101 


.21104 


•97748 


49 


12 


.15988 


.98714 


.17708 


.98420 


.19423 


' .98096 


.21132 


•97742 


48 


13 


.16017 


.98709 


•17737 


.98414 


.19452 


.98000 


.21161 


•97735 


47 


14 


.16046 


.98704 


.17766 


.98409 


.19481 


.98084 


.21189 


.97729 


46 


15 


.16074 


.98700 


•17794 


.98404 


.19509 


.98079 


.21218 


•97723 


45 


16 


.16103 


.98695 


.17823 


.98399 


•19538 


.98073 


.21246 


•97717 


44 


i7 


.16132 


.98690 


.17852 


.98394 


.19566 


.98067 


.21275 


.97711 


43 


18 


.16160 


.98689 


.17880 


.98389 


•19595 


.98061 


.21303 


.97705 


42 


19 


.16189 


.98681 


.17909 


•98383 


.19623 


.98056 


.21331 


.97698 


4i 


20 


.16218 


.98676 


•17937 


.98378 


.19652 


.98050 


.21360 


.97692 


40 


21 


.16246 


.98671 


.17966 


•98373 


.19680 


.98044 


.21388 


.97686 


39 


22 


.16275 


.98667 


.•17995 


.98368 


.19709 


.98039 


.21417 


.97680 


38 


23 


.16304 


.98662 


.18023 


.98362 


•19737 


•98033 


.21445 


•97673 


37 


24 


•16333 


■98657 


.18052 


•98357 


.19766 


.98027 


•21474 


.97667 


36 


25 


.16361 


.98652 


.18081 


•98352 


.19794 


.98021 


.21502 


.97661 


35 


26 


.16390 


.98648 


.18109 


•98347 


.19823 


.98016 


.21530 


•97655 


34 


27 


.16419 


.98643 


.18138 


.98341 


.19851 


.98010 


•21559 


.97648 


33 


28 


.16447 


.98638 


.18166 


•98336 


.19880 


.98004 


•21587 


.97642 


32 


29 


.16476 


•98633 


.18195 


•98331 


.19908 


.97987 


.21616 


.97636 


3i 


30 


•16505 


.98629 


.18224 


•98325 


•19937 


.97992 


.21644 


.97630 


30 


31 


•16533 


.98624 


.18252 


•98320 


.19965 


•97987 


.21672 


•97623 


29 


32 


.16562 


.98619 


.18281 


•98315 


.19994 


.97981 


.21701 


•976i7 


28 


33 


.16591 


.98614 


.18309 


.98310 


.20022 


•97975 


.21729 


.97611 


27 


34 


.16620 


.98609 


.18338 


.98304 


.20031 


•97969 


.21758 


.97604 


26 


35 


.16648 


.98604 


.18367 


.98299 


.20079 


•97963 


.21786 


•97598 


25 


36 


.16677 


.98600 


•18395 


.98294 


.20108 


•97958 


.21814 


•97592 


24 


37 


.16706 


•98595 


.18424 


.98288 


.20136 


•97952 


.21843 


•97585 


23 


38 


•16734 


.98590 


.18452 


.98283 


.20165 


.97946 


.21871 


•97579 


22 


39 


.16763 


•98585 


.18481 


.98277 


.20193 


•97940 


.21899 


•97573 


21 


40 


.16792 


.98580 


.18509 


.98272 


.20222 


•97934 


.21928 


•97566 


20 


4i 


.16820 


•98575 


.18538 


.98267 


.20250 


.97928 


•21956 


.97560 


19 


42 


.16849 


.98570 


.18567 


.08261 


.20279 


.97922 


.21985 


•97553 


18 


43 


.16878 


.98565 


•18595 


.98256 


•20307 


.97916 


.22013 


•97547 


17 


44 


.16906 


.98561 


.18624 


.98250 


.20336 


.97910 


.22041 


•97541 


16 


45 


•16935 


.98556 


.18652 


.98245 


.20364 


•97905 


.22070 


•97534 


15 


46 


.16964 


•98551 


.18681 


.98240 


•20393 


.97899 


.22098 


.97528 


14 


47 


.16992 


.98546 


.18710 


•98234 


.20421 


•97893 


.22126 


•97521 


13 


48 


.17021 


.98541 


.18738 


.98229 


.20450 


.97887 


•22155 


•97515 


12 


49 


.17050 


.98536 


.18767 


.98223 


.20478 


.97881 


.22183 


.97508 


11 


50 


.17078 


•98531 


•18795 


.98218 


.20507 


•97875 


.22212 


.97502 


10 


5i 


.17107 


.98526 


.18824 


.98212 


•20535 


.97869 


.22240 


.97496 


9 


52 


.17136 


.98521 


.18852 


.98207 


.20563 


.97863 


.22268 


•97489 


8 


53 


.17164 


.98516 


.18881 


.98201 


.20592 


•97857 


.22297 


•97483 


7 


54 


.17193 


.98511 


.18910 


.98196 


.20620 


•97851 


.22325 


•97476 


6 


55 


.17222 


.98506 


.18938 


.98190 


.20649 


•97845 


•22353 


•97470 


5 


56 


.17250 


.98501 


.18967 


.98185 


.20677 


•97839 


.22382 


•97463 


4 


57 


.17279 


.98496 


.18995 


.98179 


.20706 


•97833 


.22410 


•97457 


3 


58 


.17308 


.98491 


.19024 


•98174 


.20734 


.97827 


.22438 


•97450 


2 


59 


.17336 


.98486 


.19052 


.98168 


.20763 


.97821 


.22467 


•97444 


1 


60 


•17365 


.98481 


.19081 


•9S163 


.20791 


•978i5 


.22495 


•97437 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


r 




8( 


)° 


7< 


)° 


7* 


1° 


Ti 


ro 





494 



NATURAL SINES AND COSINES 





13° 


14° 


15° 


16° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


o 


.22495 


•97437 


.24192 


.97030 


.25882 


•96593 


•27564 


.96126 


I 


.22523 


•97430 


.24220 


.97023 


.25910 


.96585 


.27592 


.96118 


2 


.22552 


•97424 


.24249 


.97015 


•25938 


•96578 


.27620 


.96110 


3 


.22580 


•97417 


•24277 


.97008 


.25966 


.96570 


.27648 


.96102 


4 


.22608 


.97411 


•24305 


.97001 


•25994 


.96562 


.27676 


.96094 


5 


.22637 


.97404 


•24333 


.96994 


.26022 


•96555 


•27704 


.96086 


6 


.22665 


•97398 


.24362 


.96987 


.26050 


•96547 


.27731 


.96078 


7 


.22693 


•97391 


.24390 


.96980 


.26079 


•96540 


•27759 


.96070 


8 


.22722 


•97384 


.24418 


.96973 


.26107 


•96532 


.27787 


.96062 


9 


.22750 


•97378 


.24446 


.96966 


•26135 


.96524 


.27815 


.96054 


IO 


.22778 


•97371 


•24474 


•96959 


.26163 


•96517 


•27843 


.96046 


ii 


.22807 


•97365 


.24503 


•96952 


.26191 


.96509 


.27871 


.96037 


12 


.22835 


•97358 


•24531 


.96945 


.26219 


.96502 


.27899 


.96029 


*3 


.22863 


•97351 


.24559 


•96937 


.26247 


•96494 


.27927 


.96021 


14 


.22892 


•97345 


.24587 


•96930 


.26275 


.96486 


•27955 


•96013 


15 


.22920 


•97338 


.24615 


.96923 


•26303 


•96479 


•27983 


.96005 


16 


.22948 


•97331 


.24644 


.96916 


.26331 


•96471 


.28011 


•95997 


17 


.22977 


.97325 


.24672 


.96909 


.26359 


.96463 


.28039 


•95989 


18 


.23005 


.97318 


.24700 


.96902 


.26387 


.96456 


.28067 


•95981 


IQ 


•23033 


•973H 


.24728 


.96894 


.26415 


.96448 


.28095 


•95972 


20 


.23062 


•97304 


.24756 


.96887 


.26443 


.96440 


.28123 


•95964 


21 


.23090 


.97298 


.24784 


.96880 


.26471 


•96433 


.28150 


•95956 


22 


.23118 


.97291 


.24813 


.96873 


.26500 


.96425 


.28178 


•95948 


23 


.23146 


.97284 


.24841 


.96866 


.26528 


.96417 


.28206 


.95940 


24 


•23175 


.97278 


.24869 


.96858 


.26556 


.96410 


.28234 


•9593i 


25 


.23203 


.97271 


.24897 


.96851 


.26584 


.96402 


.28262 


•95923 


26 


.23231 


.97264 


.24925 


.96844 


.26612 


•96394 


.28290 


•95915 


27 


.23260 


.97257 


•24954 


.96837 


.26640 


.96386 


.28318 


•95907 


28 


.23288 


•97251 


.24982 


.96829 


.26668 


.96379 


.28346 


.95898 


29 


.23316 


•97244 


.25010 


.96822 


.26696 


•96371 


•28374 


.95890 


30 


•23345 


•97237 


.25038 


.96815 


.26724 


•96363 


.28402 


.95882 


31 


•23373 


•97230 


.25066 


.96807 


.26752 


•96355 


.28429 


•95874 


32 


.23401 


.97223 


•25094 


.96800 


.26780 


■96347 


•28457 


.95865 


33 


.23429 


•97217 


.25122 


•96793 


.26808 


•96340 


.28485 


•95857 


34 


•23458 


.97210 


.25151 


.96786 


.26836 


.96332 


.28513 


•95849 


35 


.23486 


.97203 


•25179 


•96778 


.26864 


•96324 


.28541 


.95841 


36 


•23514 


.97196 


.25207 


.96771 


.26892 


.96316 


.28569 


•95832 


37 


•23542 


.97189 


•25235 


.96764 


.26920 


.96308 


.28597 


.95824 


38 


•23571 


.97182 


•25263 


.96756 


.26948 


•96301 


.28625 


.95816 


39 


•23599 


.97176 


.25291 


•96749 


.26976 


.96293 


.28652 


.95807 


40 


•23627 


.97169 


•25320 


.96742 


.27004 


.96285 


.28680 


•95799 


4i 


•23656 


.97162 


.25348 


•96734 


.27032 


.96277 


.28708 


•9579i 


42 


.23684 


•97155 


.25376 


•96727 


.27060 


.96269 


.28736 


.95782 


43 


.23712 


.97148 


.25404 


.96719 


.27088 


.96261 


.28764 


•95774 


44 


.23740 


.97141 


•25432 


.96712 


.27116 


•96253 


.28792 


•95766 


45 


•23769 


•97134 


•25460 


.96705 


.27144 


.96246 


.28820 


•95757 


46 


•23797 


.97127 


.25488 


.96697 


.27172 


.96238 


.28847 


•95749 


47 


•23825 


.97120 


.25516 


.96690 


.27200 


.96230 


.28875 


•95740 


48 


•23853 


•97H3 


•25545 


.96682 


.27228 


.96222 


.28903 


•95732 


49 


.23882 


.97106 


•25573 


•96675 


.27256 


.96214 


.28931 


•95724 


50 


.23910 


.97100 


.25601 


.96667 


.27284 


.96206 


.28959 


•95715 


5i 


•23938 


.97093 


.25629 


.96660 


.27312 


.96198 


.28987 


•95707 


52 


.23966 


.97086 


.25657 


•96653 


•27340 


.96190 


.29015 


.95698 


53 


•23995 


•97079 


.25685 


•96645 


.27368 


.96182 


.29042 


.95690 


54 


.24023 


.97072 


•25713 


.96638 


.27396 


•96174 


.20070 


.95681 


55 


.24051 


.97065 


.25741 


.96630 


.27424 


.96166 


.29098 


.95673 


56 


.24079 


.97058 


•25769 


.96623 


•27452 


.96158 


.29126 


.95664 


57 


.24108 


•97051 


.25798 


.96615 


.27480 


.96150 


•29154 


•95656 


58 


.24136 


.97044 


.25826 


.96608 


.27508 


.96142 


.29182 


•95647 


59 


.24164 


•97037 


•25854 


.96600 


•27536 


.96134 


.29209 


•95639 


60 


.24192 


•97030 


.25882 


•96593 


•27564 


.96126 


.29237 


•95630 


e 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 




76 


>° 


11 


>° 


74 


1° J 


7£ 


s° 



NATURAL SINES AND COSINES 



495 



17° 


18° 


19° 


20° 




Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


f 


.29237 


•95630 


.30902 


.95106 


.32557 


•94552 


.34202 


•93969 


60 


.29265 


.95622 


.30929 


•95097 


•32584 


.94542 


.34229 


•93959 


59 


.29293 


•95613 


•30957 


.95088 


.32612 


•94533 


•34257 


•93949 


58 


.29321 


•95605 


•30985 


•95079 


.32639 


•94523 


.34284 


•93939 


57 


.29348 


•95596 


.31012 


•95070 


.32667 


•94514 


•343 11 


•93929 


56 


.29376 


•95588 


.31040 


.95061 


.32694 


•94504 


•34339 


•93919 


55 


.29404 


•95579 


.31068 


•95052 


.32722 


•94495 


•34366 


•93909 


54 


.29432 


•95571 


•31095 


•95043 


•32749 


•94485 


•34393 


•93899 


53 


.29460 


•95562 


.31123 


•95033 


•32777 


•94476 


•34421 


.93889 


52 


.294S7 


•95554 


■31151 


•95024 


•32804 


.94466 


.34448 


•93879 


51 


.29515 


•95545 


.31178 


•95015 


.32832 


•94457 


•34475 


.93869 


50 


.29543 


•95536 


.31206 


.95006 


•32859 


•94447 


•34503 


•93859 


49 


•29571 


.95528 


.31233 


•94997 


.32887 


.94438 


•34530 


.93849 


48 


•29599 


•95519 


.31261 


.94988 


.32914 


.94428 


•34557 


•93839 


47 


.29626 


•955H 


.31289 


.94979 


.32942 


.94418 


•34584 


•93829 


46 


.29654 


•95502 


.31316 


•94970 


.32969 


•94409 


•34612 


•93819 


45 


.29682 


•95493 


.31344 


.94961 


•32997 


•94399 


.34639 


•93809 


44 


.29710 


•95485 


•31372 


•94952 


•33024 


.94390 


.34666 


•93799 


43 


•29737 


•95476 


•31399 


•94943 


•33051 


•9438o 


.34694 


•93789 


42 


•29765 


•95467 


•31427 


•94933 


•33079 


•94370 


•34721 


•93779 


41 


.29793 


•95459 


•31454 


•94924 


•33106 


•9436i 


•34748 


•93769 


40 


.29821 


•95450 


.31482 


•94915 


•33134 


•94351 


•34775 


•93759 


39 


.29849 


•95441 


•31510 


.94906 


.33161 


•94342 


•34803 


•93748 


38 


.29876 


•95433 


•31537 


•94897 


.33189 


•94332 


•34830 


•93738 


37 


.29904 


.95424 


•31565 


.94888 


.33216 


•94322 


•34857 


•93728 


36 


•29932 


•95415 


•31593 


.94878 


.33244 


•94313 


.34884 


•937i8 


35 


.29960 


•95407 


.31620 


.94869 


•33271 


•94303 


.34912 


•937o8 


34 


.29987 


.95598 


.31648 


.94860 


•33298 


.94293 


•34939 


.93698 


33 


•30015 


•95389 


•31675 


.94851 


■33326 


.94284 


.34966 


.93688 


32 


•30043 


•9538o 


•31703 


.94842 


■33353 


.94274 


•34993 


•93677 


31 


.30071 


•95372 


.31730 


•94832 


•3338i 


.94264 


•3502I 


•93667 


30 


.30098 


•95363 


.31758 


•94823 


•334o8 


.94254 


•35048 


•93657 


29 


.30126 


•95354 


.31786 


.94814 


•33436 


•94245 


•35075 


•93647 


28 


.30154 


•95345 


•31813 


.94805 


•33463 


•94235 


•35I02 


•93637 


27 


.30182 


•95337 


.31841 


•947Q5 


•33490 


•94225 


•35130 


.93626 


26 


.30209 


•95328 


.31868 


.94786 


•335i8 


•94215 


•35157 


•93616 


25 


.30237 


•95319 


.31896 


•94777 


•33545 


.94206 


•35184 


.93606 


24 


.30265 


•953io 


.31923 


.94768 


■33573 


.94196 


•352H 


•93596 


23 


.30292 


•95301 


.31951 


•94758 


•33600 


.94186 


■35239 


•93585 


22 


•30320 


•95293 


•31979 


•94749 


•33627 


.94176 


•35266 


•93575 


21 


•30348 


.95284 


.32006 


•94740 


•33655 


.94167 


•35293 


•93565 


20 


•30376 


•95275 


•32034 


•94730 


.33682 


•94157 


•35320 


•93555 


19 


•30403 


.95266 


.32061 


•94721 


•337IO 


.94147 


•35347 


•93544 


18 


•30431 


•95257 


.32089 


.94712 


•33737 


•94137 


•35375 


•93534 


17 


•30459 


.95248 


.32116 


.94702 


•33764 


.94127 


•35402 


•93524 


16 


.30486 


.95240 


.32144 


•94693 


•33792 


.94118 


•35429 


•93514 


15 


•30514 


•95231 


.32171 


.94684 


•33819 


.94108 


•35456 


•93503 


14 


•30542 


.95222 


.32199 


•94674 


•33846 


.94098 


•35484 


•93493 


13 


•30570 


•95213 


•32227 


.94665 


.33874 


.94088 


•355H 


•93483 


12 


•30597 


.95204 


•32254 


•94656 


•33901 


.94078 


•35538 


•93472 


11 


.30625 


•95195 


.32282 


.94646 


.33929 


.94068 


•35565 


•93462 


10 


.30653 


•95i86 


•32309 


•94637 


•33956 


.94058 


•35592 


•93452 


9 


.30680 


•95177 


•32337 


.94627 


•33983 


•94049 


•35619 


•93441 


8 


•30708 


.95168 


•32364 


.94618 


.34011 


•94039 


•35647 


•93431 


7 


.30736 


•95159 


.32392 


.94609 


•34038 


.94029 


•35674 


.93420 


6 


•30763 


•95i5o 


.32419 


•94599 


•34065 


.94019 


•35701 


.93410 


5 


•30791 


.95142 


•32447 


•94590 


•34093 


.94009 


■35728 


•93400 


4 


.30819 


'95133 


•32474 


.9458o 


.34120 


•93999 


•35755 


•93389 


3 


.30846 


.95124 


.32502 


•94571 


•34147 


'93989 


•35782 


■93379 


2 


•30874 


•95H5 


•32529 


•9456i 


•34175 


•93979 


•358io 


.93368 


1 


.30902 


.95106 


•32557 


•94552 


.34202 


.93969 


•35837 


•93358 





Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


7! 


2° 


7 


1° 


71 


r 


6< 


r 





496 



NATURAL SINES AND COSINES 





2 


L° 


22° 


23° 


24° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


o 


.35837 


•93358 


•3746i 


.92718 


•39073 


.92050 


.40674 


.91355 


I 


^35864 


•93348 


.37488 


.92707 


.39100 


•92039 


.40700 


•91343 


2 


.35891 


•93337 


•37515 


.92697 


•39127 


.92028 


•40727 


•91331 


3 


.35918 


•93327 


•37542 


.92686 


•39153 


.92016 


•40753 


•91319 


4 


•35945 


•933i6 


•37569 


•92675 


.39180 


.92005 


.40780 


•91307 


5 


•35973 


.93306 


•37595 


.92664 


•39207 


.91994 


.40806 


.91295 


6 


.36000 


•93295 


.37622 


•92653 


•39234 


.91982 


•40833 


.91283 


7 


.36027 


•93285 


•37649 


.92642 


.39260 


.91971 


.40860 


.91272 


8 


.36054 


•93274 


•37676 


.92631 


•39287 


•91959 


.40886 


.91260 


9 


.36081 


.93264 


•37703 


.92620 


•39314 


.91948 


.40913 


.91248 


IO 


.36108 


•93253 


•37730 


.92609 


•39341 


.91936 


•40939 


.91236 


n 


•36135 


•93243 


•37757 


.92598 


•39367 


.91925 


.40966 


.91224 


12 


.36162 


.93232 


•37784 


•92587 


•39394 


.91914 


.40992 


.91212 


13 


.36190 


.93222 


.378ii 


.92576 


.39421 


.91902 


.41019 


.91200 


14 


.36217 


.93211 


.37838 


•92565 


•39448 


.91891 


.41045 


.91188 


15 


.36244 


.93201 


.37865 


•92554 


•39474 


.91879 


.41072 


.91176 


16 


.36271 


.93190 


•37892 


•92543 


•39501 


.91868 


.41098 


.91164 


17 


.36298 


.93180 


•37919 


•92532 


•39528 


.91856 


.41125 


.91152 


18 


•36325 


.93169 


•37946 


.92521 


•39555 


.91845 


.41151 


.91140 


19 


•36352 


•93159 


•37973 


.92510 


•3958i 


•91833 


.41178 


.91128 


20 


•36379 


.93148 


•37999 


.92499 


.39608 


.91822 


.41204 


.91116 


21 


.36406 


•93137 


.38026 


.92488 


•39635 


.91810 


. -41231 


.91104 


22 


•36434 


•93127 


.38053 


.92477 


.39661 


.91799 


.41257 


.91092 


23 


•36461 


.93116 


.38080 


.92466 


.39688 


.91787 


.41284 


.91080 


24 


.36488 


.93106 


•38107 


•92455 


•39715 


•91775 


.41310 


.91068 


25 


•36515 


•93095 


•38134 


.92444 


•39741 


.91764 


•41337 


.91056 


26 


•36542 


.93084 


.38161 


•92432 


•39768 


•91752 


.41363 


.91044 


27 


•36569 


•93074 


.38188 


.92421 


•39795 


.91741 


.41390 


.91032 


28 


•36596 


.93063 


•38215 


.92410 


.39822 


.91729 


.41416 


.91020 


29 


.36623 


•93052 


•38241 


•92399 


.39848 


.91718 


.41443 


.91008 


30 


•36650 


.93042 


.38268 


,92388 


•39875 


.91706 


.41469 


.90996 


31 


•36677 


•93031 


•38295 


•92377 


.39902 


.91694 


.41496 


.90984 


32 


.36704 


.93020 


.38322 


.92366 


.39928 


.91683 


.41522 


.90972 


33 


.36731 


.93010 


•38349 


.92355 


•39955 


.91671 


•41549 


.90960 


34 


•36758 


.92999 


•38376 


.92343 


.39982 


.91660 


•41575 


.90948 


35 


.36785 


.92988 


•38403 


•92332 


.40008 


.91648 


> .41602 


.90036 


36 


.36812 


.92978 


•38430 


.92321 


•40035 


.91636 


.41628 


.90924 


37 


.36839 


.92967 


.38456 


.92310 


.40062 


.91625 


•41655 


.90911 


38 


.36867 


.92956 


.38483 


.92299 


.40088 


.91613 


.41681 


.90899 


39 


.36894 


.92945 


.38510 


.92287 


.40115 


.91601 


.41707 


.90887 


P 


.36921 


•92935 


•38537 


.92276 


.40141 


.91590 


.41734 


•90875 


*i 


.36948 


.92924 


•38564 


.92265 


.40168 


.91578 


.41760 


.90863 


*2 


•36975 


.92913 


•38591 


.92254 


•40195 


.91566 


.41787 


•90851 


tf 


.37002 


.92902 


.38617 


•92243 


.40221 


•91555 


.41813 


•90839 


H 


.37029 


.92892 


•38644 


.92231 


.40248 


•91543 


.41840 


.90826 


15 


•37056 


.92881 


.38671 


.92220 


•40275 


•91531 


.41866 


.90814 


tf 


•37083 


.92870 


.38698 


.92209 


.40301 


•91519 


.41892 


.90802 


17 


.37110 


.92859 


•38725 


.92198 


.40328 


.91508 


.41919 


.90790 


*8 


•37137 


.92849 


•38752 


.92186 


.40355 


.91496 


.41945 


.90778 


\9 


.37164 


.92838 


.38778 


•92175 


.40381 


.91484 


.41972 


.90766 


;o 


•37I9I 


.92827 


.38805 


.92164 


.40408 


.91472 


.41998 


•90753 


;i 


.37218 


.92816 


.38832 


.92152 


•40434 


.91461 


.42024 


.90741 


)2 


•37245 


.92805 


.38859 


.92141 


.40461 


.91449 


.42051 


.90729 


;3 


.37272 


.92794 


.38886 


.92130 


.40488 


•91437 


•42077 


.90717 


'4 


.37299 


.92784 


.38912 


.92119 


.40514 


.91425 


.42104 


.90704 


'5 


.37326 


•92773 


.38939 


.92107 


.40541 


.91414 


.42130 


.90692 


6 


•37353 


.92762 


.38966 


.92096 


•40567 


.91402 


.42156 


.90680 


7 


•3738o 


•92751 


•38993 


.92085 


.40594 


.91390 


.42183 


.90668 


8 


•37407 


.92740 


.39020 


.92073 


.40621 


•91378 


.42209 


•90655 


9 


•37434 


.92729 


.39046 


.92062 


.40647 


.91366 


.42235 


•90643 


KD 


•3746i 


.92718 


•39073 


.92050 


.40674 


•91355 


.42262 


.90631 


/ 


Cosine 


Sine 


Cosine 1 


Sine 


Cosine 


Sine 


Cosine 


Sine 




6* 


;° 


6^ 


TO 


66 


>° 


61 


;° 



NATURAL SINES AND COSINES 



497 





25° 


26° 


27° 


28° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 


o 


.42262 


•90631 


•43837 


.89879 


•45399 


.89101 


.46947 


.88295 


60 


I 


.42288 


.90618 


•43863 


.89867 


•45425 


.89087 


•46973 


.88281 


59 


2 


•42315 


.90606 


.43889 


.89854 


•45451 


.89074 


.46999 


.88267 


58 


3 


.42341 


•90594 


.43916 


.89841 


•45477 


.89061 


.47024 


.88254 


57 


4 


.42367 


.90582 


•43942 


.89828 


•45503 


.89048 


•47050 


.88240 


56 


5 


.42394 


.90569 


.43968 


.89816 


•45529 


•89035 


.47076 


.88226 


55 


6 


.42420 


•90557 


•43994 


.89803 


•45554 


.89021 


.47101 


.88213 


54 


7 


.42446 


.90545 


.44020 


.89790 


•4558o 


.89008 


.47127 


.88199 


53 


8 


•42473 


•90532 


.44046 


.89777 


.45606 


.88995 


.47153 


.88185 


52 


9 


•42499 


.90520 


.44072 


.89764 


•45632 


.88981 


.47178 


.88172 


5i 


IO 


•42525 


•90507 


.44098 


•89752 


.45658 


.88968 


.47204 


.88158 


5o 


ii 


•42552 


•90495 


.44124 


•89739 


.45684 


.88955 


.47229 


.88144 


49 


12 


.42578 


.90483 


•44I5I 


.89726 


•457IO 


.88942 


.47255 


.88130 


48 


13 


.42604 


.90470 


•44177 


•89713 


•45736 


.88928 


.47281 


.88117 


47 


14 


.42631 


.90458 


•44203 


.89700 


•45762 


.88915 


.47306 


.88103 


46 


15 


•42657 


.90446 


.44229 


.89687 


•45787 


.88902 


•47332 


.88089 


45 


16 


.42683 


•90433 


•44255 


.89674 


•45813 


.88888 


•47358 


.88075 


44 


17 


.42709 


.90421 


.44281 


.89662 


•45839 


.88875 


•47383 


.88062 


43 


18 


.42736 


.90408 


•44307 


.89649 


.45865 


.88862 


•47409 


.88048 


42 


19 


.42762 


•90396 


•44333 


.89636 


.45891 


.88848 


•47434 


.88034 


41 


20 


.42788 


•90383 


•44359 


.89623 


•45917 


.88835 


.47460 


.88020 


40 


21 


.42815 


•90371 


.44385 


.89610 


•45942 


.88822 


.47486 


.88006 


39 


22 


.42841 


•90358 


.44411 


•89597 


.45968 


.88808 


■475" 


•87993 


38 


23 


.42867 


•90346 


•44437 


.89584 


•45994 


•8S795 


•47537 


.87979 


37 


24 


.42894 


•90334 


•44464 


•89571 


.46020 


.88782 


•47562 


•87965 


36 


25 


.42920 


.90321 


•44490 


•89558 


.46046 


.88768 


.47588 


•87951 


35 


26 


.42946 


.90309 


.44516 


•89545 


.46072 


•88755 


.47614 


•87937 


34 


27 


.42972 


.90296 


•44542 


•89532 


.46097 


.88741 


•47639 


.87923 


33 


28 


•42999 


.90284 


.44568 


.89519 


.46123 


.88728 


•47665 


.87909 


32 


29 


•43025 


.90271 


•44594 


.89506 


.46149 


.88715 


.47690 


.87896 


3i 


30 


•43051 


•90259 


.44620 


89493 


.46175 


.88701 


•477i6 


.87882 


30 


31 


•43077 


.90246 


.44646 


.89480 


.46201 


.88688 


•47741 


.87868 


29 


32 


.43104 


•90233 


.44672 


.89467 


.46226 


.88674 


•47767 


.87854 


28 


33 


•43130 


.90221 


.44698 


•89454 


.46252 


.88661 


•47793 


.87840 


27 


34 


•43156 


.90208 


•44724 


.89441 


.46278 


.88647 


.47818 


.87826 


26 


35 


.43182 


.90196 


•44750 


.89428 


.46304 


.88634 


•47844 


.87812 


25 


36 


•43209 


•90183 


•44776 


.89415 


•46330 


.88620 


.47869 


.87798 


24 


37- 


•43235 


.90171 


.44802 


.89402 


•46355 


.88607 


•47895 


.87784 


23 


38 


.43261 


.90158 


.44828 


.89389 


.46381 


.88593 


.47920 


.87770 


22 


39 


•43287 


.90146 


•44854 


.89376 


.46407 


.88580 


.47946 


.87756 


21 


40 


•43313 


•90133 


.44880 


.89363 


•46433 


.88566 


•47971 


•87743 


20 


4i 


•43340 


.90120 


.44906 


•89350 


.46458 


.88553 


•47997 


•87729 


19 


42 


•43366 


.90108 


•44932 


•89337 


.46484 


.88539 


.48022 


•87715 


18 


43 


•43392 


•90095 


•44958 


.89324 


.46510 


.88526 


.48048 


.87701 


17 


44 


.43418 


.90082 


.44984 


.89311 


•46536 


.88512 


.48073 


.87687 


16 


45 


•43445 


.90070 


.45010 


.89298 


.46561 


.88499 


.48099 


.87673 


15 


46 


•43471 


•90057 


•45036 


.89285 


.46587 


.88485 


.48124 


.87659 


14 


47 


•43497 


.90045 


.45062 


.89272 


•46613 


.88472 


.48150 


•87645 


13 


48 


•43523 


.90032 


.45088 


.89259 


•46639 


.88458 


•48i75 


.87631 


12 


49 


•43549 


.90019 


.45H4 


.89245 


.46664 


.88445 


.48201 


.87617 


11 


50 


•43575 


.90007 


.45140 


.89232 


.46690 


.88431 


.48226 


.87603 


10 


5i 


.43602 


.89994 


.45166 


.89219 


.46716 


.88417 


.48252 


.87589 


9 


52 


.43628 


.89981 


45192 


.89206 


.46742 


.88404 


•48277 


.87575 


8 


53 


•43654 


.89968 


•452i8 


.89193 


•46767 


.88390 


•48303 


.87561 


7 


54 


.43680 


.89956 


•45243 


.89180 


•46793 


.88377 


.48328 


.87546 


6 


55 


•437o6 


•89943 


•45269 


.89167 


.46819 


.88363 


•48354 


.87532 


5 


56 


•43733 


•89930 


•45295 


•89153 


.46844 


.88349 


•48379 


.87518 


4 


57 


•43759 


.89918 


•45321 


.89140 


.46870 


.88336 


.48405 


•87504 


3 


58 


•43785 


.89905 


•45347 


.89127 


.46896 


.88322 


.48430 


.87490 


2 


59 


.43811 


.89892 


•45373 


.89114 


.46921 


.88308 


.48456 


.87476 


1 


60 


•43837 


.89879 


•45399 


.89101 


•46947 


.88295 


.48481 


.87462 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




6^ 


[° 


6c 


1° 


65 


1° 


6] 








49 8 



NATURAL SINES AND COSINES 





29° 


30° 




31° 


32° 




/ 


Sine 


Cosine 


Sine ( 


"OSINE 


Sine 


Cosine 


Sine 


Cosine 


f 


o 


.48481 


.87462 


.50000 


86603 


•51504 


•85717 


.52992 


.84805 


60 


I 


.48506 


.87448 


.50025 


86588 


•51529 


.85702 


•53017 


.84789 


59 


2 


•48532 


.87434 


.50050 


86573 


•51554 


.85687 


•53041 


•84774 


58 


3 


.48557 


.87420 


.50076 


86559 


•51579 


.85672 


•53066 


•84759 


57 


4 


.48583 


.87406 


.50101 


86544 


.51604 


.85657 


•53091 


.84743 


56 


5 


.48608 


.87391 


.50126 


86530 


.51628 


.85642 


•531 15 


.84728 


55 


6 


.48634 


.87377 


•50151 


86515 


.51653 


.85627 


•53140 


.84712 


54 


7 


.48659 


.87363 


.50176 


86501 


.51678 


.85612 


•53164 


.84697 


53 


8 


.48684 


.87349 


.50201 


86486 


•51703 


•85597 


•53189 


.84681 


52 


9 


.48710 


•87335 


.50227 


86471 


.51728 


.85582 


•53214 


.84666 


51 


IO 


•48735 


.87321 


.50252 


86457 


•51753 


.85567 


•53238 


.84650 


50 


ii 


.48761 


.87306 


•50277 


86442 


•51778 


.85551 


•53263 


•84635 


49 


12 


.48786 


.87292 


•50302 


86427 


•51803 


.85536 


.53288 


.84619 


48 


13 


.48811 


.87278 


•50327 


86413 


.51828 


.85521 


.53312 


.84604 


47 


14 


•48837 


.87264 


•50352 


86398 


.51852 


.85506 


•53337 


.84588 


46 


15 


.48862 


.87250 


•50377 


86384 


.51877 


.85491 


•53361 


•84573 


45 


16 


.48888 


•87235 


•50403 


86369 


.51902 


.85476 


.53386 


•84557 


44 


17 


.48913 


.87221 


.50428 


86354 


•51927 


.85461 


.53411 


.84542 


43 


18 


.48938 


.87207 


•50453 


86340 


•51952 


•85446 


•53435 


.84526 


42 


19 


.48964 


•87193 


•50478 


86325 


•51977 


•85431 


.53460 


.84511 


41 


20 


.48989 


.87178 


•50503 


86310 


.52002 


.85416 


.53484 


.84495 


40 


21 


.49014 


.87164 


.50528 


86295 


.52026 


.85401 


•53509 


.84480 


39 


22 


.49040 


•87150 


•50553 


86281 


.52051 


.85385 


•53534 


.84464 


38 


23 


.49065 


.87136 


•50578 


86266 


.52076 


.85370 


.53558 


.84448 


37 


24 


.49090 


.87121 


.50603 


86251 


.52101 


•85355 


.53583 


•84433 


36 


25 


.49116 


.87107 


.50628 


86237 


.52126 


•85340 


•53607 


.84417 


35 


26 


.49141 


•87093 


•50654 


86222 


•52151 


•85325 


•53632 


.84402 


34 


27 


.49166 


•87079 


•50679 


86207 


.52175 


•85310 


•53656 


.84386 


33 


28 


.49192 


.87064 


.50704 


86192 


.52200 


•85294 


•5368i 


.84370 


32 


29 


.49217 


•87050 


.50729 


86178 


•52225 


•85279 


•53705 


•84355 


3i 


30 


.49242 


.87036 


•50754 


86163 


♦52250 


.85264 


•53730 


•84339 


30 


31 


.49268 


.87021 


.50779 


86148 


•52275 


.85249 


•53754 


•84324 


29 


32 


.49293 


.87007 


.50804 


86133 


.52299 


•85234 


•53779 


.84308 


28 


33 


.49318 


.86993 


.50829 


86119 


•52324 


.85218 


•53804 


.84292 


27 


34 


•49344 


.86978 


.50854 


86104 


•52349 


•85203 


.53828 


.84277 


26 


35 


.49369 


.86964 


•50879 


86089 


•52374 


.85188 


•53853 


.84261 


25 


36 


•49394 


.86949 


.50904 


86074 


•52399 


.85173 


•53877 


.84245 


24 


37 


.49419 


.86935 


.50929 


86059 


.52423 


•85157 


•53902 


.84230 


23 


38 


•49445 


.86921 


•50954 


86045 


.52448 


.85142 


•53926 


.84214 


22 


39 


.49470 


.86906 


•50979 


86030 


•52473 


.85127 


•53951 


.84198 


21 


40 


•49495 


.86892 


.51004 


86015 


.52498 


.85112 


•53975 


.84182 


20 


41 


•49521 


.86878 


.51029 


86000 


.52522 


.85096 


.54000 


.84167 


19 


42 


.49546 


.86863 


.51054 


85985 


•52547 


.85081 


.54024 


.84151 


18 


43 


•49571 


.86849 


.51079 


85970 


•52572 


.85066 


•54049 


•84135 


17 


44 


.49596 


.86834 


.51104 


85956 


•52597 


•85051 


•54073 


.84120 


16 


45 


.49622 


.86820 


.51129 


85941 


.52621 


•85035 


•54097 


.84104 


15 


46 


.49647 


.86805 


•5H54 


85926 


.52646 


.85020 


.54122 


.84088 


14 


47 


.49672 


.86791 


•5ii79 


859TI 


.52671 


.85005 


.54146 


.84072 


13 


48 


.49697 


.86777 


.51204 


85896 


.52696 


.84989 


•54I7I 


.84057 


12 


49 


•49723 


.86762 


.51229 


8s88i 


.52720 


•84974 


•54195 


.84041 


11 


50 


•49748 


.86748 


.51254 


85866 


.52745 


.84959 


.54220 


.84025 


10 


51 


•49773 


•86733 


.51279 


85851 


.52770 


.84943 


•54244 


.84009 


9 


52 


.49798 


.86719 


•51304 


85836 


•52794 


.84928 


.54269 


•83994 


8 


53 


.49824 


.86704 


•51329 


85821 


.52819 


.84913 


•54293 


•83978 


7 


54 


.49849 


.86690 


•51354 


85806 


.52844 


.84897 


•54317 


.83962 


6 


55 


•49874 


.86675 


•51379 


85792 


.52869 


.84882 


•54342 


.83946 


5 


56 


.49899 


.86661 


.51404 


85777 


.52893 


.84866 


.54366 


•83930 


4 


57 


.49924 


.86646 


.51429 


85762 


.52918 


.84851 


•54391 


.83915 


3 


58 


.49950 


.86632 


•51454 


85747 


.52943 


.84836 


•54415 


.83899 


2 


59 


•49975 


.86617 


•51479 


85732 


.52967 


.84820 


•54440 


.83883 


1 


60 


.50000 


.86603 


•51504 


85717 


.52992 


.84805 


•54464 


.83867 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


t 




6( 


)° 


59° 




5£ 


*° 


51 


to 





NATURAL SINES AND COSINES 



499 





33° 


34° 


35° 


36° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosnie 


/ 


o 


.54464 


.83867 


.55919 


.82904 


.57358 


.81915 


•58779 


.80902 


60 


I 


.54488 


.83851 


•55943 


.82887 


.57381 


.81899 


.58802 


.80885 


59 


2 


•54513 


.83835 


.55968 


.82871 


•57405 


.81882 


.58826 


.80867 


58 


3 


•54537 


.83819 


.55992 


.82855 


•57429 


.81865 


.58849 


.80850 


57 


4 


•5456i 


.83804 


.56016 


.82839 


•57453 


.81848 


.58873 


.80833 


56 


5 


•54586 


.83788 


.56040 


.82822 


•57477 


.81832 


.58896 


.80816 


55 


6 


.54610 


•83772 


.56064 


.82806 


.57501 


.81815 


.58920 


..80799 


54 


7 


•54635 


•83756 


.56088 


.82790 


.57524 


.81798 


•58943 


.80782 


53 


8 


•54659 


.83740 


.56112 


.82773 


•57548 


.81782 


.58967 


.80765 


52 


9 


•54683 


•83724 


.56136 


.82757 


•57572 


.81765 


.58990 


.80748 


5i 


IO 


.54708 


.83708 


.56160 


.82741 


.57596 


.81748 


.59014 


.80730 


5o 


ii 


•54732 


83692 


.56184 


.82724 


•57619 


.81731 


•59037 


.80713 


49 


12 


•54756 


.83676 


.56208 


.82708 


•57643 


.81714 


.59061 


.80696 


48 


13 


•5478i 


.83660 


.56232 


.82692 


•57667 


.81698 


.59084 


.80679 


47 


14 


•54805 


.83645 


.56256 


.82675 


.57691 


.81681 


.59108 


.80662 


46 


15 


.54829 


.83629 


.56280 


.82659 


•57715 


.81664 


•59131 


.80644 


45 


16 


•54854 


.83613 


•56305 


.82643 


.57738 


.81647 


•59154 


.80627 


44 


17 


•54878 


.83597 


•56329 


.82626 


.57762 


.81631 


•59178 


.80610 


43 


18 


.54902 


.83581 


.56353 


.82610 


.57786 


.81614 


.59201 


.80593 


42 


19 


•54927 


.83565 


.56377 


•82593 


.57810 


•81597 


•59225 


.80576 


4i 


20 


•54951 


.83549 


.56401 


.82577 


.57833 


.81580 


.59248 


.80558 


40 


21 


•54975 


.83533 


•56425 


.82561 


•57857 


.81563 


.59272 


.80541 


39 


22 


•54999 


.83517 


•56449 


.82544 


.57881 


.81546 


•59295 


.80524 


38 


23 


•55024 


•83501 


•56473 


.82528 


.57904 


•81530 


•59318 


•80507 


37 


24 


•55048 


.83485 


•56497 


.82511 


.57928 


.81513 


•59342 


.80489 


36 


25 


•55072 


•83469 


.56521 


.82495 


•57952 


.81496 


•59365 


.80472 


35 


26 


•55097 


.83453 


.56545 


.82478 


•57976 


.81479 


•59389 


•80455 


34 


27. 


•55121 


•83437 


•56569 


.82462 


•57999 


.81462 


.59412 


.80438 


33 


28 


•55145 


.83421 


•56593 


.82446 


.58023 


•81445 


•59436 


.80420 


32 


29 


•55169 


•83405 


.56617 


.82429 


•58047 


.81428 


•59459 


.80403 


3i 


30 


•55194 


.83389 


.56641 


.82413 


.58070 


.81412 


.59482 


.80386 


30 


31 


.55218 


.83373 


.56665 


.82396 


.58094 


•81395 


•595o6 


.80368 


29 


32 


•55242 


.83356 


.56689 


.82340 


.58118 


.81378 


.59529 


.80351 


28 


33 


.55266 


•83340 


.56713 


.82363 


.58141 


.81361 


•59552 


•80334 


27 


34 


•55291 


•83324 


.56736 


.82347 


.58165 


.81344 


.59576 


.80316 


26 


35 


•55315 


.83308 


.56760 


•82330 


.58189 


.81327 


•59599 


.80299 


25 


36 


•55339 


•83292 


.56784 


.82314 


.58212 


.81310 


.59622 


.80282 


24 


37 


•55363 


.83276 


.56808 


.82297 


.5S236 


.81293 


•59646 


.80264 


23 


38 


.55388 


.83260 


.56832 


.82281 


.58260 


.Si 176 


.59669 


.80247 


22 


39 


•55412 


.83244 


.568=16 


.82264 


•58283 


.81259 


•59693 


.80230 


21 


40 


•55436 


.83228 


.56880 


.82248 


.58307 


.81242 


•597i6 


.80212 


20 


4i 


•5546o 


.83212 


.56904 


.82231 


•58330 


.81225 


•59739 


.80195 


19 


42 


.55484 


•83195 


.56928 


.82214 


•58354 


.81208 


•59763 


.80178 


18 


43 


•55509 


•83179 


•56952 


.82198 


.58378 


.81191 


.59786 


.80160 


17 


44 


•55533 


.83163 


.56976 


.82181 


.58401 


.81174 


.59809 


•80143 


16 


45 


•55557 


•83147 


.57000 


.82165 


•58425 


.81157 


•59832 


.80125 


15 


46 


.55581 


•83131 


.57024 


.82148 


•58449 


.81140 


•59856 


.80108 


14 


47 


•55605 


•83115 


•57047 


.82132 


.58472 


.81123 ! 


•59879 


.80091 


13 


48 


■55630 


.83098 j 


•57071 


.82115 


.58496 


.81106 


.59902 


.80073 


12 


49 


•55654 


.83082 ! 


•57095 


.82098 


•58519 


.81089 [ 


•59926 


.80056 


11 


5o 


.55678 


.83066 


•57H9 


.82082 


•58543 


.81072 


•59949 


.80038 


10 


5i 


•55702 


.83050 


•57143 


.82065 


.58567 


.81055 


•59972 


.80021 


9 


52 


•55726 


•83034 


•57167 


.82048 


.58590 


.81038 


•59995 


.80003 


8 


53 


•55750 


.83017 


•57191 


.82032 


.58614 


.81021 


.60019 


.79986 


7 


54 


•55775 


.83001 


•57215 


.82015 


.58637 


.81004 


.60042 


.79968 


6 


55 


•55799 


.82985 


•57238 


.81999 


.58661 


.80987 ! 


.60065 


•79951 


5 


56 


•55823 


.82969 


•57262 


.81982 


.58684 


.80970 


.60089 


•79934 


4 


57 


•55847 


•82953 


.57286 


.81965 


.58708 


•80953 


.60112 


.79916 


3 


58 


•55871 


.82936 


.57310 


.81949 


•58731 


.80936 


•60135 


•79899 


2 


59 


•55895 


.82920 


•57334 


.81932 


.58755 


.80919 


.60158 


.79881 


1 


60 


•55919 


.82904 


•57358 


.81915 


.58779 


.80902 


.60182 


.79864 





/ 


Cosine 


Sine 


Cosine 


Sine 


Corine 


Sine 1 


Cosine 


Sine 


/ 




5( 


)° 


51 


)° 


54 


t° 1 


5c 


;° 





5°° 



NATURAL SINES AND COSINES 





37° 


38° 


39° 


40° 




f 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 


o 


.60182 


.79864 


.61566 


.78801 


.62932 


.77715 


.64279 


.76604 


60 


I 


.60205 


.79846 


.61589 


.78783 


.62955 


.77696 


.64301 


.76586 


59 


2 


.60228 


.79829 


.61612 


.78765 


.62977 


.77678 


•64323 


.76567 


58 


3 


.60251 


.79811 


.61635 


•78747 


.63000 


.77660 


.64346 


.76548 


57 


4 


.60274 


•79793 


.61658 


.78729 


.63022 


.77641 


.64368 


•76530 


56 


5 


.60298 


.79776 


.61681 


.78711 


.63045 


.77623 


.64390 


.76511 


55 


6 


.6032 1« 


•79758 


.61704 


.78694 


.63068 


.77605 


.64412 


.76492 


54 


7 


.60344 


•79741 


.61726 


.78676 


.63090 


.77586 


.64435 


•76473 


53 


8 


.60367 


.79723 


•61749 


.78658 


•63113 


•77568 


.64457 


•76455 


52 


9 


.60390 


.79706 


.61772 


.78640 


•63135 


•77550 


.64479 


.76436 


5i 


IO 


.60414 


.79688 


•61795 


.78622 


.63158 


.77531 


.64501 


.76417 


50 


ii 


.60437 


•79671 


.61818 


.78604 


.63180 


•77513 


.64524 


.76398 


49 


12 


.60460 


.79653 


.61841 


.78586 


.63203 


•77494 


•64546 


.76380 


48 


13 


.60483 


•79635 


.61864 


.78568 


.63225 


•77476 


.64568 


.76361 


47 


14 


.60506 


.79618 


.61887 


•78550 


.63248 


•77458 


.64590 


•76342 


46 


15 


.60529 


.79600 


.61909 


•78532 


•63271 


•77439 


.64612 


.76323 


45 


16 


•60553 


•79583 


.61932 


•78514 


.63293 


•77421 


•64635 


•76304 


44 


17 


.60576 


•79565 


.61955 


.78496 


.63316 


•77402 


.64657 


.76286 


43 


18 


.60599 


•79547 


.61378 


.78478 


•63338 


•77384 


.64679 


.76267 


42 


IQ 


.60622 


•79530 


.62001 


.78460 


.63361 


.77366 


.64701 


.76248 


4i 


20 


.60645 


•79512 


.62024 


.78442 


.63383 


•77347 


■64723 


.76229 


40 


21 


.60668 


•79494 


.62046 


.78424 


.63406 


•77329 


.64746 


.76210 


39 


22 


.60691 


•79477 


.62069 


•78405 


.63428 


•773io 


.64768 


.76192 


38 


23 


.60714 


•79459 


.62092 


.78387 


•63451 


.77292 


.64790 


•76173 


37 


24 


.60738 


.79441 


.62115 


.78369 


.63473 


.77273 


.64812 


•76154 


36 


25 


.60761 


•79424 


.62138 


•78351 


.63496 


•77255 


.64834 


.76135 


35 


26 


.60784 


.79406 


.62160 


•78333 


•63518 


.77236 


.64856 


.76116 


34 


27 


.60807 


.79388 


.62183 


•78315 


.63540 


.77218 


.64878 


.76097 


33 


28 


.60830 


•79371 


.62206 


.78297 


•63563 


.77199 


.64901 


.76078 


32 


29 


.60853 


•79353 


.62229 


.78279 


•63585 


.77i8i 


.64923 


.76059 


31 


30 


.60876 


•79335 


.62251 


.78261 


.63608 


.77162 


.64945 


.76041 


30 


31 


.60899 


.793x8 


.62274 


•78243 


•63630 


.77144 


.64967 


.76022 


29 


32 


.60922 


.79300 


.62297 


.78225 


•63653 


.77125 


.64989 


.76003 


28 


33 


.60945 


.79282 


.62320 


.78206 


.63675 


.77107 


.65011 


•75984 


27 


34 


.60968 


.79264 


.62342 


.78188 


.63698 


.77088 


.65033 


.75965. 


26 


35 


.60991 


.79247 


•62365 


.78170 


.63720 


.77070 


•65055 


•75946 


25 


36 


.61015 


.79229 


.62388 


.78152 


•63742 


.77051 


.65077 


•75927 


24 


37 


.61038 


.79211 


.62411 


.78134 


•63765 


•77033 


.65100 


•75908 


23 


38 


.61061 


•79193 


•62433 


,78116 


.63787 


•77014 


.65122 


.75889 


22 


39 


.61084 


.79176 


.62456 


.78098 


.63810 


.76996 


.65144 


.75870 


21 


40 


.61107 


.79158 


.62479 


.78079 


.63832 


.76977 


.65166 


.75851 


20 


41 


.61130 


.79140 


.62502 


.78061 


.63854 


.76959 


.65188 


.75832 


19 


42 


•61 153 


.79122 


.62524 


.78043 


.63877 


.76940 


.65210 


.75813 


18 


43 


.61176 


•79105 


•62547 


.78025 


.63899 


.76921 


.65232 


•75794 


17 


44 


.61199 


•79087 


•62570 


.78007 


.63922 


•76903 


•65254 


•75775 


16 


45 


.61222 


.79069 


.62592 


.77988 


•63944 


.76884 


•65276 


•75756 


15 


46 


.61245 


•79051 


.62615 


•7797o 


.63966 


.76866 


.65298 


.75738 


14 


47 


.61268 


•79033 


.62638 


.77952 


.63989 


.76847 


•65320 


.75719 


13 


48 


.61291 


'79016 


.62660 


•77934 


.64011 


.76828 


•65342 


.75700 


12 


49 


.61314 


.78998 


.62683 


•779i6 


.64033 


.76810 


-65364 


.75680 


11 


5o 


•61337 


.78980 


.62706 


.77897 


.64056 


.76791 


.65386 


.75661 


10 


51 


•6t^6o 


.78962 


.62728 


.77879 


.64078 


.76772 


.65408 


.75642 


9 


52 


•61383 


.78944 


•62751 


.77861 


.64100 


•76754 


•65430 


•75623 


8 


53 


.61406 


.78926 


.62774 


.77843 


.64123 


.76735 


•65452 


•75604 


7 


54 


.61429 


.78908 


.62796 


•77824 


.64145 


.76717 


•65474 


.75585 


6 


55 


•6T451 


.78891 


.62819 


.77806 


.64167 


.76698 


.65496 


•75566 


5 


56 


•6i474 


.78873 


.62842 


.77788 


.64190 


.76679 


.65518 


•75547 


4 


57 


•6i497 


.78855 


.62864 


•77769 


.64212 


.76661 


.65540 


•75528 


3 


58 


.61520 


.78837 


.62887 


•77751 


.64234 


.76642 


.65562 


•75509 


2 


59 


•6i543 


.78819 


.62909 


•77733 


.64256 


.76623 


.65584 


•75490 


1 


60 


.61566 


.78801 


.62932 


.77715 


.64279 


.76604 


.65606 


.75471 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




52 


1 


51 





50 





49 








NATURAL SINES AND COSINES 



SOI 



4 


1° 


42° 


43° 


44° 




Sine 


Cosine 


Sine 


1 Cosine 


Sine 


Cosine 


Sine 


Cosine 


f 


.65606 


•75471 


•66913 


.74314 


.68200 


•73135 


.69466 


.71934 


60 


.65628 


•75452 


•66935 


•74295 


.68221 


.73116 


.69487 


•71914 


59 


.65650 


•75433 


.66956 


.74276 


.68242 


•73096 


.69508 


.71894 


58 


.65672 


•75414 


.66978 


.74256 


.68264 


.73076 


•69529 


•71873 


57 


.65694 


•75395 


.66999 


•74227 


.68285 


•73056 


.69549 


•71853 


56 


.65716 


•75375 


.67021 


.74217 


.68306 


•73036 


.69570 


.71833 


55 


.65738 


•75356 


.67043 


.74198 


.68327 


.73016 


.69591 


.71813 


54 


•65759 


•75337 


.67064 


.74178 


.68349 


.72996 


.69612 


.71792 


53 


.65781 


.75318 


.67086 


•7*159 


.68370 


.72:176 


•69633 


.71772 


52 


.65803 


•75299 


.67107 


•74139 


■68391 


•72957 


.69654 


•71752 


5i 


.65825 


.75280 


.67129 


'74120 


.68412 


.72937 


•69675 


•71732 


50 


.65847 


.75261 


.67151 


.74100 


.68434 


.72917 


.69696 


.71711 


49 


.65869 


.75241 


.67172 


.74080 


.68455 


•72897 


.69717 


•.71691 


48 


.65891 


.75222 


.67194 


.74061 


.68476 


.72377 


•69737 


.71671 


47 


•65913 


•75203 


.67215 


.74041 


.68497 


•72857 


.69758 


.71650 


46 


.65935 


•75184 


.67237 


./4022 


.68518 


•72837 


•69779 


.71630 


45 


•65956 


•75i65 


.67258 


./4002 


.68539 


.72817 


.69800 


.71610 


44 


.65978 


.75146 


.67280 


.73983 


.68561 


.72797 


.69821 


•71590 


43 


.66000 


.75126 


•67301 


•73963 


.68582 


.72777 


.69842 


•71569 


42 


.66022 


•75io7 


•67323 


•73944 


.68603 


•72757 


.69862 


•71549 


4i 


.66044 


.75088 


•67344 


•73924 


.68624 


•72737 


.69883 


.71529 


40 


.66066 


•75069 


.67366 


.73904 


.68645 


.72717 


.69904 


.71508 


39 


.66088 


•75050 


.67387 


.73885 


.68666 


.72697 


•69925 


.71488 


38 


.66109 


.75030 


.67409 


.73865 


.68688 


.72677 


.69946 


.71468 


37 


.66131 


.75011 


.67430 


.73846 


.68709 


.72657 


.69966 


•71447 


36 


.66153 


.74992 


•67452 


.73826 


.68730 


•72637 


.69987 


.71427 


35 


.66175 


•74973 


•67473 


.73806 


.68751 


.72617 


.70008 


.71407 


34 


.66197 


•74953 


•67495 


•73787 


.68772 


•72597 


.70029 


.71386 


33 


.66218 


•74934 


.67516 


•73767 


.68793 


•72577 


.70049 


.71366 


32 


.66240 


•74915 


.67538 


•73747 


.68814 


•72557 


.70070 


•71345 


3i 


.66262 


.74896 


•67559 


•73728 


.68835 


.72537 


.70091 


•71325 


30 


.66284 


.74876 


.67580 


.737o8 


.68857 


.72517 


.70112 


.71305 


29 


.66306 


.74857 


.67602 


.73688 


.68878 


•72497 


•70132 


.71284 


28 


.66327 


.74838 


.67623 


.73669 j 


.68899 


•72477 


•70153 


.71264 


27 


•66349 


.74818 


.67645 


•73649 


.68920 


•72457 


•70174 


•71243 


26 


•66371 


•74799 


.67666 


.73629 


.68941 


•72437 


•70195 


.71223 


25 


•66393 


.74780 


.67688 


.73610 


.68962 


.72417 


•70215 


.71203 


24 


.66414 


.7476o 


.67709 


.73590 


.68983 


•72397 


.70236 


.71182 


23 


.66436 


•74741 


•67730 


•73570 


.69004 


•72377 


.70257 


.71162 


22 


.66458 


.74722 


.67752 


•73551 


.69025 


•72357 


.70277 


.71141 


21 


.66480 


•74703 


•67773 


.73531 


.69046 


•72337 


.70298 


.71121 


20 


.66501 


.74683 


•67795 


•735II 


.69067 


•72317 


•70319 


.71100 


19 


.66523 


.74664 


.67816 


•73491 


.69088 


.72297 


•70339 


.71080 


18 


•66545 


.74644 


•67837 


•73472 


.69109 


.72277 


.70360 


•71059 


17 


.66566 


•74625 


.67859 


•73452 


.69130 


.72257 


.70381 


• 71039 


16 


.66588 


.74606 


.67880 


•73432 


.69151 


.72236 


.70401 


.71019 


15 


.66610 


.74586 


.67901 


•73413 


.69172 


.72216 


.70422 


.70998 


14 


.66632 


.74567 


.67923 


•73393 


.69193 


.72196 


•70443 


.70978 


13 


■66653 


.74548 


•67944 


•73373 


.69214 


.72176 


.70463 


•70957 


12 


•66675 


•74528 


•67965 


•73353 


•69235 


.72156 


.70484 


•70937 


11 


.66697 


•74509 


.67987 


•73333 


.69256 


.72136 


•70505 


.70916 


10 


.66718 


•74489 


.68008 


•73314 


.69277 


.72116 


•70525 


.70896 


9 


.66740 


•74470 


.68029 


•73294 


.69298 


•72095 


.70546 


•70875 


8 


.66762 


•74451 


.68051 


•73274 


.69319 


.72075 


.70567 


•70855 


7 


.66783 


•74431 


.68072 


•73254 


•69340 


•72055 


.70587 


.70834 


6 


.66805 


.74412 


.68093 


•73234 


.69361 


•72035 


.70608 


.70813 


5 


.66827 


•74392 


.68115 


•73215 


.69382 


.72015 


.70628 


.70793 


4 


.66848 


•74373 


.68136 


•73195 


.69403 


•71995 


.70649 


.70772 


3 


.66870 


•74353 


.68157 


•73175 


.69424 


•71974 


.70670 


.70752 


2 


.66891 


•74334 


.68179 


•73155 


•69445 


•71954 


.70690 


•70731 


1 


.66913 


•74314 


.68200 


•73135 


.69466 


•71034 


.70711 


.70711 





Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sink 1 


Cosine 


Sine 


1 


4£ 


1° 


47 


'O 


46 


1 


45 








502 



NATURAL SECANTS AND CO-SECANTS 











1° 


2° 


3° 




r 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


r 


O 




Infinite. 


1. 000 1 


57-299 


1 .0006 


28.654 


1. 0014 


19.107 


6c 


I 




3437-7Q 


1. 000 1 


56.359 


1 .0006 


28.417 


1. 0014 


19.002 


55 


2 




1718.90 


1 .0002 


55-450 


1 .0006 


28.184 


1.0014 


18.897 


5* 


3 




1145.90 


1 .0002 


54-570 


1.0006 


27-955 


1. 0014 


18.794 


57 


4 




859-44 


1 .0002 


53./18 


1 .0006 


27.730 


1. 0014 


18.692 


56 


5 




687.55 


1.0002 


52.891 


1.0007 


27.508 


1. 0014 


18.591 


55 


6 




572.96 


1 .0002 


52.090 


1.0007 


27.290 


1. 0015 


18.491 


SA 


7 




491. 11 


1.0002 


51-313 


1.0007 


27.075 


1.0015 


18.393 


53 


8 




429.72 


1.0002 


50.558 


1.0007 


26.864 


1.0015 


18.295 


52 


9 




381.97 


1.0002 


49.826 


1.0007 


26.655 


1.0015 


18.198 


5i 


IO 




343-77 


1 .0002 


49.114 


1.0007 


26.450 


1.0015 


18.103 


5c 


ii 




312.52 


1.0002 


48.422 


1.0007 


26.249 


1.0015 


18.008 


45 


12 


j 


286.48 


1.0002 


47-750 


1.0007 


26.050 


1.0016 


17.914 


48 


13 




264.44 


1.0002 


47.096 


1.0007 


25-854 


1.0016 


17.821 


47 


14 




245-55 


1.0002 


46.460 


1 .0008 


25.661 


1.0016 


17.730 


At 


15 




229.18 


1.0002 


45.840 


1 .0008 


25-471 


1. 0016 


17.639 


45 


16 




214.86 


1.0002 


45.237 


1 .0008 


25.284 


1. 0016 


17-549 


AA 


17 




202.22 


1.0002 


44.650 


1 .0008 


25.100 


1. 0016 


17.460 


A3 


18 




190.99 


1.0002 


44-077 


1 .0008 


24.918 


1. 001 7 


17-372 


42 


19 




180.73 


1 .0003 


43-520 


1 .0008 


24-739 


1. 001 7 


17.285 


41 


20 




171.89 


1 .0003 


42.976 


1.0008 


24.562 


1. 0017 


17.198 


4c 


21 




163.70 


1 .0003 


42.445 


1 .0008 


24-358 


1. 001 7 


17. 113 


35 


22 




156.26 


1 .0003 


41.928 


1.0008 


24.216 


1. 001 7 


17.028 


38 


23 




149.47 


1.0003 


41.423 


1 0009 


24.047 


1. 001 7 


16.944 


37 


24 


1 


143.24 


1.0003 


40.930 


1.0009 


23.880 


1.0018 


16.861 


36 


25 




I37.5I 


1 .0003 


40.448 


1.0009 


23.716 


1. 00 18 


16.779 


35 


26 




132.22 


1 .0003 


39-978 


1 .0009 


23-553 


1.0018 


16.698 


34 


27 




127.32 


1 .0003 


39-5i8 


1 .0009 


23-393 


1. 00 18 


16.617 


33 


28 




122.78 


1 .0003 


39.069 


1 1.0009 


23-235 


1. 0018 


16.538 


32 


29 




118.54 


1 .0003 


38.631 


1 .0009 


23.079 


1.0018 


16.459 


3i 


30 




H4-59 


1.0003 


38.201 


1.0009 


22.925 


1.0019 


16.380 


30 


31 




110.90 


1 .0003 


37.782 


1. 0010 


22.774 


1. 0019 


16.303 


29 


32 




IQ7-43 


1 .0003 


37-371 


1. 00 10 


22.624 


1.0019 


16.226 


28 


33 




104.17 


1 .0004 


36.969 


I.OOIO 


22.476 


1. 0019 


16.150 


27 


34 




IOI.II 


1 .0004 


36.576 


1. 00 10 


22.330 


1.0019 


16.075 


26 


35 




98.223 


1 .0004 


36.191 


I.OOIO 


22.186 


1.0019 


16.000 


25 


36 




95*495 


1 .0004 


35.8i4 


I.OOIO 


22.044 


1.0020 


15-926 


24 


37 




92.914 


1 .0004 


35-445 


I.OOIO 


2 1 .904 


1.0020 


15.853 


23 


38 


1. 000 1 


92.469 


1 .0004 


35-o84 


I.OOIO 


21.765 


1.0020 


I5.780 


22 


39 


1. 000 1 


88.149 


1 .0004 


34-729 


I. OOI I 


21.629 


1.0020 


I5.708 


21 


40 


1. 000 1 


85.946 


1 .0004 


34-382 


I. OOI I 


21.494 


1.0020 


I5.637 


20 


4i 


1. 000 1 


83.849 


1 .0004 


34.042 


I. OOI I 


21.360 


1. 002 1 


15.566 


19 


42 


1. 000 1 


81.853 


1 .0004 


33-7o8 


I. OOI I 


21.228 


1. 002 1 


15.496 


18 


43 


1. 000 1 


79-950 


1 .0004 


33-38i 


I. OOI I 


2 1 .098 


1. 002 1 


I5.427 


17 


44 


1. 000 1 


78.133 


1 .0004 


33.060 


I. OOI I 


20.970 


1. 002 1 


15.358 


16 


45 


1. 000 1 


76.396 


1.0005 


32.745 


1. 00 1 1 


20.843 


1. 002 1 


15.290 


15 


46 


1. 000 1 


74.736 


1 .0005 


32.437 


1. 0012 


20.717 


1.0022 


15.222 


14 


47 


1. 000 1 


73-146 


1 .0005 


32.134 


I. OOI2 


20.593 


1.0022 


15-155 


13 


48 


1. 000 1 


71.622 


1 .0005 


31-836 


I.OOI2 


20.471 


1.0022 


15-089 


12 


49 


1. 000 1 


71.160 


1.0005 


31-544 


I. OO I 2 


20.350 


1.0022 


I5-023 


11 


5o 


1. 000 1 


68.757 


1 .0005 


31-257 


I. OOI2 


20.230 


1.0022 


14.958 


10 


5i 


1. 000 1 


67.409 


1 .0005 


30.976 


I. OOI2 


20.112 


1.0023 


14.893 


9 


52 


1. 000 1 


66.113 


1 .0005 


30.699 


I.OOI2 


19-995 


1.0023 


14.829 


8 


53 


1. 000 1 


64.866 


1 .0005 


30.428 


I.OOI3 


19.880 


1.0023 


I4.765 


7 


54 


1. 000 1 


63.664 


1 .0005 


30.161 


I.OOI3 


19.766 


1.0023 


14.702 


6 


55 


1. 000 1 


62.507 


1 .0005 


29.899 


I.OOI3 


19-653 


1.0023 


14.640 


5 


56 


1. 000 1 


61.391 


1.0006 


29.641 


I.OOI3 


19-541 


1.0024 


14-578 


4 


57 


1. 000 1 


61.314 


1.0006 


29.388 


1. 001 3 


19-431 


1.0024 


I4.5I7 


3 


58 


1. 000 1 


59-274 


1.0006 


29.139 


1.0013 


19.322 


1.0024 


14.456 


2 


59 


1. 000 1 


58.270 


1 .0006 


28.894 


1. 0013 


19.214 


1.0024 


14-395 


1 


60 


1. 000 1 


57-299 


1 .0006 


28.654 


1. 0014 


19.107 


1.0024 


14-335 





/ 


Co-sec. 1 


Sec. 


Co-sec- 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 






8< 


)° 


Si 


1° 


8' 


7° 


8( 


3° 1 





NATURAL SECANTS AND CO-SECANTS 



S03 





40 




5° 


6 


>° 


7° 




/ 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


! Sec.' 


Co-sec 


Sec. 


Co-sec. 


/ 





1.0024 


14-335 


1 .0038 


11.474 


1.0055 


9.5668 


1.0075 


8.2055 


60 


I 


1.0025 


14.276 


1.0038 


11.436 


1.0055 


9.5404 


1 1.0075 


8.1861 


59 


2 


1.0025 


14.217 


1.0039 


n.398 


1.0056 


9-5141 


1.0076 


8.1668 


58 


3 


1.0025 


14-159 


1.0039 


11.360 


1.0056 


9.4880 


1.0076 


8.1476 


57 


4 


1.0025 


14.101 


1.0039 


n.323 


1.0056 


9.4620 


1.0076 


8.1285 


56 


5 


1.0025 


14.043 


1.0039 


11.286 


1.0057 


9.4362 


1.0077 


8.1094 


55 


6 


1.0026 


13-986 


1 .0040 


11.249 


1.0057 


9-4105 


1.0077 


8.0905 


54 


7 


1.0026 


I3-930 


1 .0040 


11-213 


1.0057 


9-3850 


1.0078 


8.0717 


53 


8 


1.0026 


13-874 


1 .0040 


11. 176 


1.0057 


9-3596 


1.0078 


8.0529 


52 


9 


1.0026 


13.818 


1.0040 


1 1. 140 


1.0058 


9-3343 


1.0078 


8.0342 


5i 


10 


1.0026 


13-763 


1. 004 1 


11. 104 


j 1.0058 


9.3092 


1.0079 


8.0156 


5o 


11 


1.0027 


13-708 


1. 004 1 


11.069 


f 1.0058 


9.2842 


1.0079 


7.9971 


49 


12 


1.0027 


I3.654 


1. 0041 


11-033 


1 1.0059 


9-2593 


1.0079 


7-9787 


48 


13 


1.0027 


13.600 


1. 004 1 


10.988 


1.0059 


9.2346 


1 .0080 


7.9604 


47 


14 


1.0027 


13-547 


1 .0042 


10.963 


! 1.0059 


9.2100 


1 .0080 


7.9421 


46 


15 


1.0027 


13-494 


1.0042 


10.929 


1 .0060 


9.i855 


1 .0080 


7.9240 


45 


16 


1.0028 


13-441 


1 .0042 


10.894 


1.0060 


9.1612 


1. 008 1 


7-9059 


44 


17 


1.0028 


13-389 


1.0043 


10.860 


1 .0060 


9.I370 


1. 008 1 


7.8879 


43 


18 


1.0028 


13-337 


1.0043 


10.826 


1. 006 1 


9.1129 


1.0082 


7.8700 


42 


IQ 


1.0028 


13.286 


1.0043 


10.792 


1. 006 1 


9.0890 


1 .0082 


7-8522 


4i 


20 


1.0029 


13-235 


1.0043 


10.758 


1. 006 1 


9.0651 


1.0082 


7-8344 


40 


21 


1.0029 


13-184 


1.0044 


10.725 


1 .0062 


9.0414 


1 .0083 


7.8168 


39 


22 


1.0029 


13-134 


1.0044 


10.692 


1 0062 


9.0179 


1 .0083 


7.7992 


38 


23 


1.0029 


13-084 


1 .0044 


10.659 


1 .0062 


8.9944 


1 .0084 


7.7817 


37 


24 


1.0029 


13-034 


1.0044 


10.626 


1 .0063 


8.9711 


1 .0084 


7.7642 


36 


25 


1.0030 


12.985 


1.0045 


10.593 


1 .0063 


8.9479 


1 .0084 


7.7469 


35 


26 


1.0030 


12.937 


1.0045 


10.561 


1 .0063 


8.9248 


1 .0085 


7.7296 


34 


27 


1.0030 


12.888 


1.0045 


10.529 


1.0064 


8.9018 


1.0085 


7.7124 


33 


28 


1 .0030 


12.840 


1 .0046 


10.497 


1 .0064 


8.8790 


1.0085 


7-6953 


32 


29 


1. 003 1 


12.793 


1 .0046 


10.465 


1 .0064 


8.8563 


1 .0086 


7.6783 


3i 


30 


1. 003 1 


12.745 


1 .0046 


10.433 


1.0065 


8.8337 


1 .0086 


7.6613 


30 


3i 


1. 003 1 


12.698 


1.0046 


10.402 


1 .0065 


8.8112 


1.0087 


7.6444 


29 


32 


1. 003 1 


12.652 


1.0047 


10.371 


1 .0065 


8.7888 


1.0087 


7.6276 


28 


33 


1.0032 


12.606 


1.0047 


10.340 


1 .0066 


8.7665 


1.0087 


7.6108 


27 


34 


1.0032 


12.560 


1.0047 


10.309 


1 .0066 


8.7444 


1.0088 


7-5942 


26 


35 


1.0032 


12.514 


1 .0048 


10.278 


1 .0066 


8.7223 


1.0088 


7-5776 


25 


35 


1.0032 


12.469 


1.0048 


10.248 


1.0067 


8.7004 


1 .0089 


7.5611 


24 


37 


1.0032 


12.424 


1.004S 


10.217 


1.0067 


8.6786 


1 .0089 


7-5446 


23 


38 


1-0033 


12-379 


1 .0048 


10.187 


1.0067 


8.6S69 


1 .0089 


7.5282 


22 


39 


1 -0033 


12.335 


1 .0049 


10.157 


1 .0068 


B-6 3 53 


1 .0090 


7-5ii9 


21 


40 


1.0033 


12.291 


1 .0049 


10.127 


1.0068 


8.6138 


1*0090 


7-4957 


20 


41 


1 -0033 


12.248 


1.0049 


10.098 


1.0068 


8.5924 


1 .0090 


7-4795 


19 


42 


1.0034 


12.204 


1.0050 


10.068 


1.0069 


8.5711 


1. 009 1 


7-4634 


18 


43 


1.0034 


12. 161 


1.0050 


10.039 


1 .0069 


8.5499 


1. 009 1 


7-4474 


17 


44 


1 .0034 


12. 118 


1.0050 


10.010 


' 1.0069 


8.5289 


1.0092 


7-4315 


16 


45 


1.0034 


12.076 


1.0050 


9.9812 


1.0070 


8.5079 


1.0092 


7-4I56 


15 


46 


1 -0035 


12.034 


1. 00 5 1 


99525 


1.0070 


8.4871 


1.0092 


7-3998 


14 


47 


1 -0035 


11.992 


1 .005 1 


9.9239 


1.0070 


8.4663 


1 .0093 


7-3840 


!3 


48 


1 -0035 


11.950 


1. 005 1 


9-8955 


1.0071 


8-4457 


1 -0093 


7-3683 


12 


49 


1-0035 


11.909 


1.0052 


9.8672 


1. 007 1 


8.4251 


1 .0094 


7-3527 


11 


5o 


1 .0036 


11.868 


1.0052 


9.8391 


1.0071 


8.4046 


1 .0094 


7-3372 


10 


51 


1.0036 


11.828 


1.0052 


9.8112 


1.0072 


8.3843 


1.0094 


7-3217 


9 


52 


1 .0036 


11.787 


1 -0053 


9-7834 


1.0072 


8.3640 


1.0095 


7-3063 


8 


53 


1.0036 


ci.747 


1 -0053 


9-7558 


1.0073 


8-3439 


1 .0095 


7.2909 


7 


54 


1.0037 


11.707 


1 -0053 


9.7283 


1.0073 


8.3238 


1 .0096 


7-2757 


6 


55 


1.0037 


11.668 


1 -0053 


9.7010 


1.0073 


8.3039 


1 .0096 


7.2604 


5 


56 


1.0037 


11.628 


1.0054 


9-6739 


1.0074 


8.2840 


1.0097 


7-2453 


4 


57 


1.0037 


n.589 


1.0054 


9.6469 


1.0074 


8.2642 


1.0097 


7.2302 


3 


58 


1.0038 


H-550 


1.0054 


9.6200 


1.0074 


8.2446 


1.0097 


7-2152 


2 


59 


1.0038 


11. 512 


1 -0055 


9-5933 


1.0075 


8.2250 


1 .0098 


7.2002 


1 


5o 


1 .0038 


11.474 


1.0055 


9.5668 


1.0075 


8.2055 


1 .0098 


7.1853 





/ 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


/ 




8. 


>° 


8 


1° 


8c 


\° 


8: 


1° 





5°4 



NATURAL SECANTS AND CO-SECANTS 





8° 


9° 


10° 


11° 




r 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


CO.SEC. 


Sec. 


Co-sec. 


/ 


O 


1.0098 


7-1853 


1.0125 


6.3924 


1.0154 


5.7588 


1.0187 


5.2408 


60 


I 


1 .0099 


7.1704 


1.0125 


6.3807 


1.0155 


5-7493 


1.0188 


5-2330 


59 


2 


1.0099 


7-1557 


1.0125 


6.3690 


1.0155 


5-7398 


1.0188 


5.2252 


58 


3 


1 .0099 


7.1409 


1.0126 


6-3574 


1.0156 


5.7304 


1.0189 


5-2174 


57 


4 


1. 0100 


7.1263 


1.0126 


6.3458 


1.0156 


5-72IO 


1. 0189 


5.2097 


56 


5 


I.OIOO 


7.1117 


1.0127 


6-3343 


1.0157 


5-7II7 


I.OIOO 


5-2019 


55 


6 


I.OIOI 


7.0972 


1.0127 


6.3228 


1.0157 


5-7023 


1.0191 


5.1942 


54 


7 


I.OIOI 


7.0827 


1.0128 


6.3113 


1.0158 


5-6930 


1.0191 


5.1865 


53 


8 


I.OI02 


7.0683 


1.0128 


6.2999 


1.0158 


5.6838 


1.0192 


5.1788 


52 


9 


I.OI02 


7-Q539 


1.0129 


6.2885 


1.0159 


5-6745 


1.0192 


5.1712 


5i 


IO 


I.OI02 


7-0396 


1.0129 


6.2772 


1.0159 


5.6653 


1.0193 


5.1636 


50 


ii 


I.OIO3 


7.0254 


1.0130 


6.2659 


1.0160 


5.6561 


1.0193 


5.1560 


49 


12 


I.OIO3 


7.01 12 


1.0130 


6.2546 


1.0160 


5.6470 


1. 0194 


5.1484 


48 


13 


I.OIO4 


6.9971 


1.0131 


6.2434 


1.0161 


5.6379 


1.0195 


5.1409 


47 


14 


I.OIO4 


6.9830 


1.0131 


6.2322 


1.0162 


5.6288 


1.0195 


5.1333 


46 


15 


I. OIO4 


6.9690 


1.0132 


6.2211 


1.0162 


5-6197 


1,0196 


5.1258 


45 


16 


I.OI05 


6.9550 


1.0132 


6.2100 


1. 163 


5-6107 


1. 0196 


5.1183 


44 


17 


I.OI05 


6.9411 


1.0133 


6.1990 


1.0163 


5-6017 


1.0197 


5.1109 


43 


18 


I.OIOO 


6.9273 


1.0133 


6.1880 


1.0164 


5.5928 


1.0198 


5.1034 


42 


19 


I.OI06 


6.9135 


1.0134 


6.1770 


1.0164 


5.5838 


1. 0198 


5.0960 


4i 


20 


I.OI07 


6.8998 


1. 0134 


6.1661 


1.0165 


5-5749 


1.0199 


5.0886 


40 


21 


I.OI07 


6.8861 


I-OI35 


6.1552 


1. 0165 


5.5660 


1.0199 


5.0812 


39 


22 


I.OI07 


6.8725 


I-OI35 


6.1443 


1. 0166 


5-5572 


1.0200 


5.0739 


38 


23 


I.OIO8 


6.8589 


1.0136 


6.1335 


1.0166 


5-5484 


1. 0201 


5.0666 


37 


24 


I. OI08 


6.8454 


1.0136 


6.1227 


1.0167 


5-5396 


1. 020 1 


5- 593 


36 


25 


I.OIO9 


6.8320 


1.0136 


6.1120 


1.0167 


5-53o8 


1.0202 


5.0520 


35 


26 


I. OIO9 


6.8185 


1.0137 


6.1013 


1. 0168 


5-5221 


1.0202 


5-0447 


34 


27 


I. OIIO 


6.8052 


1.0137 


6.0906 


1.0169 


5-5134 


1.0203 


50375 


33 


28 


I.OIIO 


6.7919 


1.0138 


6.0800 


1. 0169 


5-5047 


1.0204 


5.0302 


32 


29 


I.OIII 


6.7787 


1.0138 


6.0694 


1. 01 70 


5.4960 


1.0204 


5.0230 


3i 


30 


I.OIII 


6.7655 


1.0139 


6.0588 


1. 01 70 


5-4874 


1.0205 


5-0158 


30 


31 


I.OIII 


6.7523 


1.0139 


6.0483 


1.0171 


5.4788 


1.0205 


5-0087 


29 


32 


I.OII2 


6.7392 


1.0140 


6.0379 


1.0171 


5.4702 


1.0206 


5-0015 


28 


33 


I.OII2 


6.7262 


1. 0140 


6.0274 


1.0172 


5-4617 


1.0207 


4.9944 


27 


34 


I.OII3 


6.7132 


1.0141 


6.0170 


1.0172 


5-4532 


1.0207 


4-9873 


26 


35 


I.OII3 


6.7003 


1.0141 


6.0066 


1.0173 


5-4447 


1.0208 


4.9802 


25 


36 


I.OII4 


6.6874 


1.0142 


5-9963 


1.0174 


5-4362 


1.0208 


4-9732 


24 


37 


I.OII4 


6.6745 


1.0142 


5.9860 


1.0174 


5.4278 


1.0209 


4.9661 


23 


38 


I.OII5 


6.6617 


1.0143 


5-9758 


1.0175 


5-4194 


1. 02 10 


4-9591 


22 


39 


I.OII5 


6.6400 


1.0143 


5-9655 


1.0175 


5-4HO 


1. 02 10 


4.9521 


21 


40 


I.OII5 


6.6363 


1.0144 


5-9554 


1.0176 


5.4026 


1. 02 1 1 


4.9452 


20 


41 


I.OIl6 


6.6237 


1.0144 


5.9452 


1. 01 76 


5-3943 


1. 02 1 1 


4.9382 


19 


42 


I.OIl6 


6.6111 


1.0145 


5-9351 


1.0177 


5.3860 


1.02 12 


4.9313 


18 


43 


I.OII7 


6.5985 


1.0145 


5-9250 


1.0177 


5-3777 


1.0213 


4.9243 


17 


44 


I.OII7 


6.5860 


1.0146 


5-9150 


1. 01 78 


5-3695 


1.0213 


4-9175 


16 


45 


I.OIl8 


6.5736 


1. 0146 


5.9049 


1.0179 


5-36i2 


1.0214 


4.9106 


15 


46 


I.OIl8 


6.5612 


1.0147 


5.8050 


1.0179 


5-3530 


1. 02 1 5 


4-9037 


14 


47 


I.OII9 


6.5488 


1.0147 


5-8850 


1.0180 


5 3449 


1 .02 1 5 


4.8969 


13 


48 


I.OII9 


6.5365 


1. 0148 


5.875I 


1. 0180 


5-3367 


1.0210 


4.8901 


12 


49 


I.OII9 


6.5243 


1.0148 


5-8652 


1.0181 


5-3286 


1. 02 16 


4.8833 


11 


50 


I.OI20 


6.5121 


1. 0149 


5.8554 


1.0181 


5-3205 


1. 02 1 7 


4.8765 


10 


5i 


I.OI20 


6.4999 


1.0150 


5-8456 


1. 0182 


5-3124 


1.0218 


4.8697 


9 


52 


I.OI2I 


6.4878 


1.0150 


5.8358 


1.0182 


5-3044 


1.0218 


4.8630 


8 


53 


I.OI2I 


6-4757 


1.0151 


5.8261 


1.0183 


5-2963 


1.0219 


4.8563 


7 


54 


I.OI22 


6.4637 


I.OX5I 


5.8163 


1.0184 


5.2883 


1.0220 


4.8496 


6 


55 


I.OI22 


6.4517 


1.0152 


5-8067 


1.0184 


5-2803 


1.0220 


4.8429 


5 


56 


I.OI23 


6.4398 


1.0152 


5.7970 


1.0185 


5-2724 


1.0221 


4.8362 


4 


57 


I.OI23 


6.4279 


1.0153 


5-7874 


1.0185 


5.2645 


j.0221 


4.8296 


3 


58 


I.OI24 


6.4160 


I-OI53 


5.7778 


1. 0186 


5.2566 


T.0222 


4.8229 


2 


59 


I.OI24 


6.4042 


1.0154 


5.7683 


1. 0186 


5-2487 


1.0223 


4.8163 


1 


60 


I.OI25 


6.3924 


1.0154 


5.7588 


1.0187 


5.2408 


1.0223 


4.8097 





/ 


CO-SEC. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


/ 




81 





8( 


)° 


7t 


)° 


7* 


1° 





NATURAL SECANTS AND CO-SECANTS 



5°5 





12° 


13° 


14° 


/ 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


o 


1.0223 


4.8097 


1.0263 


4-4454 


1.0306 


4-1336 


I 


1.0224 


4.8032 


1.0264 


4.4398 


1.0307 


4.1287 


2 


1.0225 


4.7966 


1.0264 


4.4342 


1.0308 


4.1239 


3 


1.0225 


4.7901 


1.0265 


4.4287 


1.0308 


4.1191 


4 


1.0226 


4-7835 


1.0266 


4.4231 


1.0309 


4.1144 


5 


1.0226 


4.7770 


1.0266 


4.4176 


1.0310 


4.1096 


6 


1.0227 


4.7706 


1.0267 


4.4121 


1.0311 


4.1048 


7 


1.0228 


4.7641 


1.0268 


4.4065 


1-0311 


4.1001 


8 


1.0228 


4-7576 


1.0268 


4.401 1 


1. 03 1 2 


4-0953 


9 


1.0229 


4-7512 


1.0269 


43956 


1.0313 


4.0906 


IO 


1.0230 


4.7448 


1.0270 


4.3910 


1.0314 


4.0859 


ii 


1.0230 


4-7384 


1.0271 


4-3847 


1.0314 


4.0812 


12 


1.0231 


4.7320 


1.0271 


4-3792 


1-0315 


4.0765 


13 


1.0232 


4-7257 


1.0272 


4-3738 


1.0316 


4.0718 


14 


1.0232 


4.7193 


1.0273 


4.3684 


1-0317 


4.0672 


15 


1.0233 


4-7130 


1.0273 


4-3630 


1-0317 


4.0625 


16 


1.0234 


4.7067 


1.0274 


4-3576 


1.0318 


4-0579 


17 


1.0234 


4.7004 


1.0275 


4-3522 


1.0319 


4-0532 


18 


1.023s 


4.6942 


1.0276 


4.3469 


1.0320 


4.0486 


19 


1.0235 


4.6879 


1.0276 


4-3415 


1.0320 


4.0440 


20 


1.0236 


4.6817 


1.0277 


4-3362 


1.032 1 


4.0394 


21 


1.0237 


4-6754 


1.0278 


4.3309 


1.0322 


4.0348 


22 


1.0237 


4.6692 


1.0278 


4-3256 


1-0323 


4.0302 


23 


1.0238 


4.6631 


1.0279 


4-3203 


1.0323 


4.0256 


24 


1.0239 


4.6569 


1.0280 


4.3I50 


1.0324 


4.0211 


25 


1.0239 


4.6507 


1.0280 


4.3098 


1.0325 


4.0165 


26 


1.0240 


4.6446 


1.0281 


4-3045 


1.0326 


4.0120 


27 


1.0241 


4-6385 


1.0282 


4.2993 


1.0327 


4.0074 


28 


1.0241 


4.6324 


1.0283 


4.2941 


1.0327 


4.0029 


29 


1.0242 


4.6263 


1.0283 


4.2888 


1.0328 


3.9984 


30 


1.0243 


4.6202 


1.0284 


4.2836 


1.0329 


3-9939 


31 


1.0243 


4.6142 


1.0285 


4.2785 


1.0330 


3.9894 


32 


1.0244 


4.6081 


1.0285 


4-2733 


1.0330 


3-9850 


33 


1.0245 


4.6021 


1.0286 


4.2681 


1-0331 


3-9805 


34 


1.0245 


4.5961 


1.0287 


4.2630 


1.0332 


3.976o 


35 


1.0246 


4.5901 


1.0288 


4-2579 


1 -0333 


3.9716 


36 


1.0247 


4.5841 


1.0288 


4.2527 


1 -0334 


3.9672 


37 


1.0247 


4.5782 


1.0289 


4.2476 


1.0334 


3.9627 


38 


1.0248 


4.5722 


1.0200 


4.2425 ; 


1.0335 


3-9583 


39 


1.0249 


4-5663 


1. 0291 


4-2375 


1.0336 


3-9539 


40 


1.0249 


4-5604 


1.0291 


4.2324 


1.0337 


3-9495 


41 


1.0250 


4-5545 


1.0292 


4.2273 


1.0338 


3-9451 


42 


1-0251 


4-5486 


1.0293 


4.2223 


1-0338 


3.9408 


43 


1.0251 


4.5428 


1.0293 


4-2173 


1.0339 


3-9364 


44 


1.0252 


4-5369 


1.0294 


4.2122 


1.0340 


3.9320 


45 


1.0253 


4-53II 


1.0295 


4.2072 


1. 0341 


3-9277 


46 


1.0253 


4-5253 


1.0296 


4.2022 


1-0341 


39234 


47 


1.0254 


4-5195 


1.0296 


4.1972 , 


1.0342 


3-9199 


48 


1.0255 


4-5137 


1.0297 


4.1923 


1 -0343 


3-9147 


49 


1.0255 


4.5079 


1.0298 


4.1873 ; 


1.0344 


3.9104 


50 


1.0256 


4.5021 


1.0299 


4.1824 


1 -0345 


3.9061 


5i 


1.0257 


4.4964 


1.0299 


4.1774 


1 -0345 


3.9018 


52 


1.0257 


4.4907 


1.0300 


4.I725 


1.0346 


3.8976 


53 


1.0258 


4.4850 


1. 0301 


4.1676 


1 -0347 


3.8933 


54 


1.0259 


4-4793 


1.0302 


4.1627 


1.0348 


3.8990 


55 


1.0260 


4.4736 


1.0302 


4.I578 j 


1.0349 


3.8848 


56 


1.0260 


4.4679 


1-0303 


4.1529 


1.0349 


3-8805 


57 


1.0261 


4.4623 


1.0304 


4.1481 


1-0350 


3-8763 


58 


1.0262 


4.4566 


1-0305 


4.1432 


1.0351 


3.8721 


59 


1.0262 


4.4510 


1-0305 


4.1384 


1.0352 


3.8679 


60 


1.0263 


4-4454 


1 .0306 


4.I336 


1 -0353 


3.8637 


/ 


CO-SEC. 


Sec. 


Co-sec. 1 


Sec. 


Co-sec. 


Sec. 




71 


r° 


7( 


5° 


71 


>° 



15° 

Sec. Co-sec. 



I-0353 
I-0353 
I.0354 
I.0355 
1.0356 
I-0357 
1-0358 
1.0358 

1.0359 

1.0360 
1.0361 

1.0362 
1.0362 
1.0363 
1.0364 
1-0365 
1.0366 
1.0367 
1.0367 
1.0368 
1.0369 

1.0370 
1-0371 
1-0371 
1.0372 

1 -0373 
1 -03 74 
I-0375 
1.0376 
1.0376 
1.0377 
1.0378 

I-0379 
1.0380 
1. 038 1 
1.0382 
1.0382 
1.0383 
1.0384 
1.0385 
1.0386 

1.0387 
1.0387 
1.0388 
1.0389 
1.0390 

1-0391 
1.0392 

I -0393 
I-0393 
1.0394 

I.0395 
1.0396 
I.0397 
1.0398 
1.0399 
1.0399 

1 .0400 

1. 040 1 
1.0402 
1.0403 

CO-SEC. 



3-8637 
3-8595 
3-8553 
3.85I2 



3.8470 


56 


3.8428 


55 


3.8387 


54 


3.8346 


53 


3.8304 


52 


3.8263 


5i 


3.8222 


50 


3.8181 


49 


3.8140 


48 


3.8100 


47 


3.8059 


46 


3.8018 


45 


3.7978 


44 


3-7937 


43 


3-7897 


42 


3.7857 


4i 


3.7816 


40 


3-7776 


39 


3.7736 


38 


3.7697 


37 


3.7657 


36 


3.7617 


35 


3-7577 


34 


3.7538 


33 


3.7498 


32 


3-7459 


3i 


3.7420 


30 


3.738o 


29 


3.7341 


28 


3.7302 


27 


3-7263 


26 


3.7224 


25 


3-7186 


24 


3 7147 


23 


3.7108 


22 


3.7070 


21 


3-7031 


20 


3.6993 


19 


3.6955 


.18 


3-6917 


17 


3-6878 


t6 


3.6840 


15 


3.6802 


14 


3-6765 


13 


3.6727 


12 


3.6689 


11 


3-6651 


10 


3.6614 


9 


3.6576 


8 


3-6539 


7 


3.6502 


6 


3.6464 


5 


3.6427 


4 


3-6390 


3 


3.6353 


2 


3.6316 


1 


3.6279 





Sec. 


/ 








5°6 



NATURAL SECANTS AND CO-SECANTS 



1 


S° 


17° 


1 


8° 


19° 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


CO-SEC. 


1.0403 


3.6279 


1 -0457 


3.4203 


1-0515 


3.2361 


1.0576 


3-07I5 


1 .0404 


3-6243 


1.0458 


3.4170 


1.0516 


3-2332 


I-Q577 


3.0690 


1 .0405 


3.6206 


1.0459 


3-4138 


1-0517 


3.2303 


1.0578 


3.0664 


1 .0406 


3.6169 


1.0460 


3.4106 


1.0518 


3.2274 


I.0579 


3.0638 


1 .0406 


3-6133 


1. 046 1 


3.4073 


1.0519 


3-2245 


1.0580 


3.0612 


1.0407 


5.6096 


1. 0461 


3.4041 


1.0520 


3.2216 


1.0581 


3-0586 


1 .0408 


3.6060 


1.0462 


3-4009 


1.0521 


3.2188 


1.0582 


3-056I 


1 .0409 


3.6024 


1.0463 


3-3977 


1.0522 


3.2159 


1.0584 


3-0535 


1.0410 


3-5987 


1.0464 


3-3945 


1-0523 


3.2131 


1.0585 


3.0509 


1. 041 1 


3-5951 


1.0465 


3-3913 


1.0524 


3.2102 


1.0586 


3.0484 


1.0412 


3-5915 


1 .0466 


3-388i 


1.0525 


3.2074 


1.0587 


3-0458 


1-0413 


3-5879 


1.0467 


3-3849 


1.0526 


3.2045 


1.0588 


3-0433 


1-0413 


3-5843 


1.0468 


3-3817 


1.0527 


3.2017 


1.0589 


3.0407 


1. 0414 


3-5807 


1.0469 


3-3785 


1.0528 


3.1989 


1.0590 


3.0382 


1.0415 


3-5772 


1.0470 


3-3754 


1.0529 


3.1960 


1.0591 


3-Q357 


1. 0416 


3-5736 


1.0471 


3.3722 


1.0530 


3.1932 


1.0592 


3-0331 


1. 041 7 


3-5700 


1.0472 


3.3690 


1-0531 


3.1904 


1 -0593 


3.0306 


1.0418 


3-5665 


1 -0473 


3-3659 


1.0532 


3-i8r 


1.0594 


3.0281 


1.0419 


3-5629 


1.0474 


3-3627 


I-0533 


3.1848 


1 -Q595 


3.0256 


1.0420 


3-5594 


1 -0475 


3-3596 


I-0534 


3.1820 


1.0596 


3.0231 


1.0420 


3-5559 


1.0476 


3-3565 


I-0535 


3.1792 


1.0598 


3.0206 


1. 042 1 


3-5523 


1.0477 


3-3<34 


1.0536 


3-I764 


1.0599 


3.0181 


1.0422 


3-5488 


1.0478 


3-35Q2 


I-0537 


3-I736 


1 .0600 


3-0156 


1.0423 


3-5453 


1.0478 


3-3471 


1-0538 


3.1708 


1. 060 1 


3-0131 


1.0424 


3-54i8 


1.0479 


3 -344Q 


I-0539 


3.1681 


1.0602 


3.0106 


1.0425 


3S3^>3 


1 .0480 


3-3409 


1.0540 


3.1653 


1 .0603 


3.0081 


1.0426 


3-5348 


1. 048 1 


3.3378 


1-0541 


3-1625 


1 .0604 


3.0056 


1.0427 


3-5313 


1.0482 


3-3347 


1.0542 


3.I598 


1.0605 


3.0031 


1.0428 


3-5279 


1.0483 


3-33i6 


1 -0543 


3-I570 


1 .0606 


3.0007 


1.0428 


3-5244 


1.0484 


3.3286 


1.0544 


3-1543 


1.0607 


2.9982 


1.0429 


3-5209 


1.0485 


3-3255 


1 -Q545 


3-I5I5 


1 .0608 


2-9957 


1.0430 


3-5175 


1.0486 


3-3224 


1.0546 


3.1488 


1 .0609 


2-9933 


1. 043 1 


3-5140 


1.0487 


3-3194 


1 -Q547 


3-1461 


1.0611 


2 .9908 


1.0432 


3-5106 


1.0488 


3-3163 


1.0548 


3-1433 


1.0612 


2.9884 


1 -0433 


3-5072 


1 .0489 


3-3133 


1.0549 


3.1406 


1.0613 


2.9859 


1.0434 


3-5037 


1.0490 


3.3102 


1-0550 


3-1379 


1.0614 


2.9835 


1-0435 


3-5003 


1. 049 1 


3.3072 


1-0551 


3-1352 


1.0615 


2.9810 


1.0436 


3.4969 


1.0492 


3-3042 


1.0552 


3.I325 


1.0616 


2.9786 


1.0437 


3-4935 1 


1.0493 


3-30H 


1 -0553 


3.1298 


1.0617 


2.9762 


1.0438 


3.4901 j 


1.0494 


3.2981 


i.o554 


3-1271 


1. 0618 


2.9738 


1.0438 


3.4867 


1.0495 


3.2951 


1 -0555 


3.1244 


1.0619 


2-9713 


1.0439 


3-4833 


1 .0496 


3.2921 


1-0556 


3.1217 


1.0620 


2.9689 


1 .0440 


3-4799 


1.0497 


3.2891 


1.0557 


3-1190 


1.0622 


2.9665 


1. 0441 


3.4766 


1 .0498 


3.2861 


1-0558 


3-1163 


1.0623 


2. 9641 


1.0442 


3-4732 


1.0499 


3-2831 


I-0559 


3-H37 


1.0624 


2.9617 


1.0443 


3.4698 


1.0500 


3.2801 


1.0560 


3.1110 


1.0625 


2-9593 


1 .0444 


3.4665 


1. 050 1 


3.2772 


1.0561 


3-1083 


1.0626 


2.9569 


1.0445 


3-4632 


1.0502 


3.2742 


1.0562 


3-1057 


1.0627 


2-9545 


1 .0446 


3-4598 


1-0503 


3.2712 


1-0563 


3.1030 


1.0628 


2.9521 


1.0447 


3-4565 


1.0504 


3-2683 


1.0565 


3.1004 


1.0629 


2.9497 


1 .0448 


3-4532 


1-0505 


3-2653 


1.0566 


3-0977 


1.0630 


2.9474 


1.0448 


3.4498 


1.0506 


3.2624 


1-0567 


3-0951 


1.0632 


2.9450 


1.0449 


3-4465 


1-0507 


3-2594 


1.0568 


3-0925 


1.0633 


2.9426 


1.0450 


3-4432 


1.0508 


3-2565 


1.0569 


3.0898 


1.0634 


2.9402 


1-0451 


3-4399 


1.0509 


3.2535 


1.0570 


3.0872 


1-0635 


2.9379 


1.0452 


3-4366 


1. 05 10 


3.2506 


1-0571 


3.0846 


1.0636 


2-9355 


1 -Q453 


3-4334 


1-0511 


3-2477 


1.0572 


3.0820 


1.0637 


2.9332 


1.0454 


3-430I 


1.0512 


3.2448 


I-0573 


3-Q793 


1.0638 


2.9308 


1 -0455 


3.4268 


1-0513 


3.2419 


1 -0574 


3.0767 


1.0639 


2.9285 


1.0456 


3-4236 


1-0514 


3.2390 


I-0575 


3-074I 


1. 0641 


2.9261 


1 -045 7 


3-4203 


1-0515 


3.2361 


1-0576 


3-07I5 


1.0642 


2.9238 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


CO-SEC. 


Sec. 


Tc 


1° 


72 





71 





7C 


>° 



NATURAL SECANTS AND CO-SECANTS 



5°7 





2( 


)° 


21° 


22° 


23° 


/ 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 





1.0642 


2.9238 


1.0711 


2.7904 


1.0785 


2.6695 


1.0864 


2.5593 


I 


1.0643 


2.9215 


1-0713 


2.7883 


1.0787 


2.6675 


1.0865 


2-5575 


2 


1 .0644 


2.9191 


1.0714 


2.7862 


1.0788 


2.6656 


1.0866 


2.5558 


3 


1.0645 


2.9168 


1.0715 


2.7841 


1.0789 


2.6637 


1.0868 


2.5540 


4 


1.0646 


2-9145 


1.0716 


2.7820 


1.0790 


2.6618 


1.0869 


2.5523 


5 


1.0647 


2.9122 


1-0717 


2-7799 


1.0792 


2.6599 


1.0870 


2.5506 





1.0648 


2.9098 


1.0719 


2.7778 


1.0793 


2.6580 


1.0872 


2.5488 


7 


1.0650 


2.9075 


1.0720 


2-7757 


1.0794 


2.6561 


1.0873 


2.5471 


8 


1. 065 1 


2.9052 


1.0721 


2.7736 


1 -0795 


2.6542 


1.0874 


2.5453 


9 


1.0652 


2.9029 


1.0722 


2.7715 


1.0797 


2.6523 


1.0876 


2.5436 





1-0653 


2.9006 


1.0723 


2.7694 


1.0798 


2.6504 


1.0877 


2.5419 


1 


1.0654 


2.8983 


1.0725 


2.7674 


1.0799 


2.6485 


1.0878 


2.5402 


2 


1.0655 


2.8960 


1.0726 


2.7653 


1. 080 1 


2.6466 


1.0880 


2.5384 


3 


1.0656 


2.8937 


1.0727 


2.7632 


1.0802 


2.6447 


1. 088 1 


2-5367 


4 


1.0658 


2.8915 


1.0728 


2.7611 


1 .0803 


2.6428 


1.0882 


2.5350 


5 


1.0659 


2.8892 


1.0729 


2.7591 


1.0804 


2.6410 


1.0884 


2-5333 


6 


1 .0660 


2.8869 


1.0731 


2.7570 


1.0806 


2.6391 


1.0885 


2.5316 


7 


1. 066 1 


2.8846 


1.0732 


2.7550 


| 1.0807 


2.6372 


1.0886 


2.5299 


8 


1.0662 


2.8824 


I-Q733 


2.7529 


1.0808 


2.6353 


1.0888 


2.5281 





1.0663 


2.8801 


I-Q734 


2.7509 


1.0810 


2-6335 


1.0889 


2.5264 





1.0664 


2.8778 


1.0736 


2.7488 


1. 081 1 


2.6316 


1. 0891 


2.5247 


1 


1.0666 


2.8756 


1-0737 


2.7468 


1.0812 


2.6297 


1.0892 


2.5230 


2 


1.0667 


2.8733 


1.0738 


2-7447 


1.0813 


2.6279 


1.0893 


2.5213 


3 


1.0668 


2.8711 


I-0739 


2.7427 


1.0815 


2.6260 


1.0895 


2.5196 


4 


1.0669 


2.8688 


1.0740 


2.7406 


1.0816 


2.6242 


1.0896 


2.5179 


5 


1.0670 


2.8666 


1.0742 


2.7386 


1. 081 7 


2.6223 


1.0897 


2.5163 


6 


1. 067 1 


2.8644 


1 -0743 


2.7366 


1.0819 


2.6205 


1.0899 


2.5146 


7 


1.0673 


2.8621 


1.0744 


2.7346 


1.0820 


2.6186 


1 .0900 


2.5129 


8 


1.0674 


2.8599 


1 -0745 


2.7325 


1. 082 1 


2.6168 


1.0902 


2.5112 


9 


1.0675 


2.8577 


1.0747 


2.7305 


1.0823 


2.6150 


1.0903 


2.5095 





1.0676 


2.8554 


1.0748 


2.7285 


1.0824 


2.6131 


1.0904 


2.5078 


1 


1.0677 


2.8532 


1.0749 


2.7265 


1.0825 


2.6113 


1.0906 


2.5062 


2 


1.0678 


2.8510 


1-0750 


2.7245 


1.0826 


2.6095 


1.0907 


2.5045 


3 


1.0679 


2.8488 


1-0751 


2.7225 


1.0828 


2.6076 


1.0908 


2.5028 


4 


1. 0681 


2.8466 


I-0753 


2.7205 


1.0829 


2.6058 


1.0910 


2.5011 


5 


1.0682 


2.8444 


I-0754 


2./I85 


1.0830 


2 .6040 


1.0911 


2.4995 


6 


1.0683 


2.8422 


10755 


2.7165 


1.0832 


2.6022 


1-0913 


2.4978 


7 


1.0684 


2 .8400 


1.0756 


2.7145 


1.0833 


2 .6003 


1.0914 


2.4961 


8 


1.0685 


2.8378 


1.0758 


2.7125 


1.0834 


2.5985 


1.0915 


2-4945 


9 


1.0686 


2.8356 


I-Q759 


2.7105 


1.0836 


2.5967 


1. 091 7 


2.4928 





1.0688 


2.8334 


1.0760 


2.7085 


1.0837 


2.5949 


1.0918 


2.4912 


1 


1.0689 


2.8312 


1.0761 


2.7065 


1.0838 


2.5931 


1.0920 


2.4895 


2 


1.0600 


2.8290 


1.0763 


2.7045 


1 .0840 


2.5913 


1. 092 1 


2.4879 


3 


1. 069 1 


2.8269 


1.0764 


2.7026 


1. 0841 


2.5895 


1.0922 


2.4862 


4 


1.0692 


2.8247 


1.0765 


2.7006 


1.0842 


2.5877 


1.0924 


2.4846 


5 


1 .0694 


2.8225 


1.0766 


2.6986 


1.0844 


2.5859 


1.0925 


2.4829 


6 


1.0695 


2.8204 


1.0768 


2.6967 


1.0845 


2.5841 


1.0927 


2.4813 


7 


1.0696 


2.8182 


1.0769 


2.6947 


1.0846 


2.5823 


1.0928 


2-4797 


3 


1.0697 


2.8160 


1.0770 


2.6927 


1.0847 


2.5805 


1.0929 


2.4780 


P 


1.0698 


2.8139 


1.0771 


2.6908 


1 .0849 


2.5787 


1-0931 


2.4764 





1.0699 


2.8117 


I-0773 


2.6888 


1.0850 


2.5770 


1.0932 


2.4748 


1 


1.0701 


2.8096 


1.0774 


2.6869 


1. 085 1 


2.5752 


1.0934 


2.4731 


2 


1.0702 


2.8074 


I-0775 


2.6849 


1.0853 


2-5734 


1 -0935 


2.4715 


3 


1.0703 


2.8053 


1.0776 


2.6830 


1.0854 


2.5716 


1.0936 


2.4699 


4 


1.0704 


2.8032 


1.0778 


2.6810 


1.0855 


2.5699 


1.0938 


2.4683 


5 


1.0705 


2.8010 


1.0779 


2.6791 


1.0857 


2.5681 


1.0939 


2.4666 


6 


1.0707 


2.7989 


1.0780 


2.6772 


1.0858 


2.5663 


1. 0941 


2.4650 


7 


1.0708 


2.7968 


1.0781 


2.6752 


1.0859 


2.5646 


1.0942 


2.4634 


s 


1.0709 


2.7947 


1.0783 


2.6733 


1. 086 1 


2.5628 


1 .0943 


2.4618 


9 


1.0710 


2.7925 


1.0784 


2.6714 


1.0862 


2.5610 


1.0945 


2.4602 





1.0711 


2.7904 


1.0785 


2.6695 


1.0864 


2-5593 


1.0946 


2.4586 
Sec. 


/ 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 




61 


)° 


61 


3° 


6' 


r° 


64 


3° 



5 o8 



NATURAL SECANTS AND CO-SECANTS 



24° 


2 


5° 


26° 


27° 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 
1.1126 


Co-sec. 


Sec. 


Co-sec. 


i .0946 


2.4586 


1. 1034 


2.3662 


2.2812 


1. 1223 


2.2027 


1.0948 


2.4570 


1.1035 


2.3647 


1.1127 


2.2798 


1. 1225 


2.2014 


1.0949 


2-4554 


1.1037 


2.3632 


1.1129 


2.2784 


1. 1226 


2.2002 


1-0951 


2.4538 


1. 1038 


2.3618 


1.1131 


2.2771 


1. 1228 


2.1989 


1.0952 


2.4522 


1. 1040 


2.3603 


1.1132 


2.2757 


1. 1230 


2.1977 


1 -0953 


2.4506 


1.1041 


2.3588 


1.1134 


2.2744 


1.1231 


2.1964 


1 -0955 


2.4490 


1.1043 


2-3574 


I.U35 


2.2730 


1.1233 


2.1952 


1.0956 


2.4474 


1. 1044 


2.3559 


1.1137 


2.2717 


1. 1235 


2.1939 


1.0958 


2.4458 


1. 1046 


2-3544 


1.1139 


2.2703 


1. 1237 


2.1927 


1.0959 


2.4442 


1. 1047 


2.3530 


1.1 140 


2.2690 


1. 1-38 


2.1914 


1.0961 


2.4426 


1.1049 


2-3515 


1.1142 


2.2676 


1. 1 240 


2.1902 


1.0962 


2.4411 


1. 1050 


2.3501 


1.1143 


2.2663 


1. 1242 


2.1889 


1.0963 


2-4395 


1. 1052 


2.3486 


1.1145 


2.2650 


1. 1243 


2.1877 


1.0965 


2-4379 


1. 1053 


2.3472 


1.1147 


2.2636 


1. 1245 


2.1865 


1.0966 


2.4363 


1. 1055 


2-3457 


1.1148 


2 2623 


1. 1247 


2.1852 


1.0968 


2-4347 


1. 1056 


2-3443 


1.1150 


2.2610 


1. 1248 


2.1840 


1.0969 


2.4332 


1. 1058 


2.3428 


1.1151 


2.2596 


1. 1250 


2.1828 


1. 097 1 


2.4316 


1. 1059 


2.3414 


I.H53 


2.2583 


1. 1252 


2.1815 


1.0972 


2.4300 


1.1061 


2-3399 


1.1*55 


2.2570 


1.1253 


2.1803 


1.0973 


2.4285 


1. 1062 


2.3385 


1-1156 


2.2556 


1. 1255 


2.1791 


1.0975 


2.4269 


1. 1064 


2.3371 


1.1158 


2-2543 


1. 1257 


2.1778 


1.0976 


2.4254 


1. 1065 


2.3356 


1.1159 


2.2530 


1. 1258 


2.1766 


1.0978 


2.4238 


1. 1067 


2.3342 


1.1161 


2.2517 


1. 1260 


2.1754 


1.0979 


2.4222 


1. 1068 


2.3328 


1.1163 


2.2503 


1. 1262 


2.1742 


1. 098 1 


2.4207 


1. 1070 


2.3313 


1.1164 


2.2490 


1. 1264 


2.1730 


1.0982 


2.4191 


1. 1072 


2.3299 


1.1166 


2.2477 


1. 1265 


2.1717 


1.0984 


2.4176 


1. 1073 


2.3285 


1.1167 


2.2464 


1. 1267 


2.1705 


1.0985 


2.4160 


1. 1075 


2.3271 


1.1169 


2.2451 


1. 1269 


2.1693 


1.0986 


2.4145 


1. 1076 


2.3256 


1.1171 


2.2438 


1. 1270 


2.1681 


1.0988 


2.4130 


1. 1078 


2.3242 


1.1172 


2.2425 


1. 1272 


2.1669 


1.0989 


2.4114 


1. 1079 


2.3228 


1.1174 


2.2411 


1. 1274 


2.1657 


1. 099 1 


2.4099 


1.1081 


2.3214 


1.1176 


2.2398 


1. 1275 


2.1645 


1.0992 


2.4083 


1. 1082 


2.3200 


1.1177 


2.2385 


1. 1277 


2.1633 


1.0994 


2.4068 


1. 1084 


2.3186 


1.1179 


2.2372 


1. 1279 


2.1620 


1.0995 


2.4053 


1. 1085 


2.3172 


1.1180 


2.2359 


1.1281 


2.1608 


1.0997 


2.4037 


1. 1087 


2.3158 


1.1182 


2.2346 


1. 1282 


2.1596 


1.0998 


2.4022 


1. 1088 


2.3143 


1.1184 


2-2333 


1. 1284 


2.1584 


1. 1000 


2.4007 


1. 1090 


2.3129 


1.1185 


2.2320 


1. 1286 


2.1572 


I.IOOI 


2.3992 


1. 1092 


2-3II5 


1.1187 


2.2307 


1. 1287 


2.1560 


1. 1003 


2.3976 


1. 1093 


2.3101 


1.1189 


2.2294 


1. 1289 


2.1548 


1. 1004 


2.3961 


1. 1095 


2.3087 


1.1190 


2.2282 


1.1291 


2.1536 


1. 1005 


2.3946 


1. 1096 


2.3073 


1.1192 


2.2269 


1. 1293 


2.1525 


1. 1007 


2.3931 


1. 1098 


2.3059 


1.1193 


2.2256 


1. 1294 


2.1513 


1. 1008 


2.3916 


1. 1099 


2.3046 


1.1195 


2.2243 


1. 1296 


2.1501 


I.IOIO 


2.3901 


I.IIOI 


2.3032 


1.1197 


2.2230 


1. 1298 


2.1489 


1. ton 


2.3886 ; 


I.II02 


2.3018 


1.1 198 


2.2217 


1. 1299 


2.1477 


1.1013 


2.3871 


I.IIO4 


2.3004 


1. 1 200 


2.2204 


1.1301 


2.1465 


1.1014 


2.3856 ! 


I.IIOO 


2.2990 


1. 1202 


2.2192 


1-1303 


2.1453 


1.1016 


2.3841 


I.II07 


2.2976 


1. 1203 


2.2179 


1. 1305 


2.1441 


1.1017 


2.3826 


I.IIO9 


2.2962 


1. 1205 


2.2166 


1. 1306 


2.1430 


1.1019 


2.3811 


i. mo 


2.2949 


1. 1207 


2.2153 


1. 1308 


2.1418 


1. 1020 


2.3796 


1. Ilia 


2.2935 


1. 1208 


2.2141 


1.1310 


2.1406 


1. 1022 


2.3781 


1.1113 


2.2921 


1.1210 


2.2128 


1.1312 


2.1394 


1. 1023 


2.3766 


1. HIS 


2.2907 


1.1212 


2.2115 


1-1313 


2.1382 


1. 1025 


2.3751 


1.1116 


2.2894 


1.1213 


2.2103 


1-1315 


2.1371 


1. 1026 


2.3736 


1.1118 


2.2880 


1.1215 


2.2090 


1.1317 


2.1359 


1. 1028 


2.3721 


1.1120 


2.2866 


1.1217 


2.2077 


1.1319 


2.1347 


1. 1029 


2.3706 


1.1121 


2.2853 


1.1218 


2.2065 


1. 1320 


2-1335 


1.1031 


2.3691 


1.1123 


2.2839 


1. 1220 


2.2052 


1. 1322 


2.1324 


1. 1032 


2.3677 j 


1.1 124 


2.2825 


1. 1222 


2.2039 


1-1324 


2.1312 


1. 1034 


2.3662 


1.1126 


2.2812 


1. 1223 


2.2027 


1. 1326 


2.1300 
Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


CO-SEC. 1 


6£ 


>° 1 


64 


1° 


6S 


1° 


62 






NATURAL SECANTS AND CO-SECANTS 



509 



28° 


29° 


30° 


3] 


L° 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 
1. 1666 


Co-sec. 


1. 1326 


2.1300 


I.J433 


2.0627 


I.I547 


2 .0000 


1. 9416 


1. 1327 


2.1289 


1.1435 


2.0616 


I-I549 


1.9990 


1. 1668 


1.9407 


1.1329 


2.1277 


I-I437 


2.0605 


I.I55I 


1 .9980 


1. 1670 


1-9397 


1-1331 


2.1266 


I- 1439 


2.0594 


1. 1553 


1.9970 


1. 1672 


1.9388 


1.1333 


2.1254 


1.1441 


2.05S3 


I-I555 


1.9960 


1. 1674 


1.9378 


I.I334 


2.1242 


I-I443 


2.0573 


I-I557 


1.9950 


1. 1676 


1.9369 


1. 1336 


2.1231 


I-I445 


2.0562 


1. 1559 


1.9940 


1. 1678 


1.9360 


1.1338 


2.1219 


1. 1446 


2.0551 


1.1561 


1.9930 


1.1681 


I-9350 


1. 1 340 


2.1208 


1. 1448 


2.0540 


1. 1562 


1.9920 


1.1683 


I-934I 


1.1341 


2.1196 


1. 1450 


2.0530 


1-1564 


1. 9910 


1.1685 


1-9332 


I-I343 


2.1185 


I.I452 


2.0519 


1. 1566 


1 .9900 


1. 1687 


1.9322 


1. 1345 


2.1173 


I.I454 


2.0508 


1.1568 


1.9890 


1. 1689 


I.93I3 


I.I347 


2.1162 


1. 1456 


2 .0498 


1. 1570 


1.9880 


1.1691 


1.9304 


I-I349 


2.1150 


I.I458 


2.0487 


I-I572 


1.9870 


1-1693 


1-9295 


I-I350 


2.1139 


I-I459 


2.0476 


I-I574 


1.9860 


1.1695 


1.9285 


I-I352 


2.1127 


1.1461 


2.0466 


I-I576 


1.9850 


1. 1697 


1.9276 


I-I354 


2.1116 


1. 1463 


2.0455 


1.1578 


1 .9840 


1. 1699 


1.9267 


1. 1356 


2.1104 


1. 1465 


2.0444 


1. 1580 


1.9830 


1.1701 


1.9258 


I-I357 


2.1093 


1. 1467 


2.0434 


1. 1582 


1.9820 


1-1703 


1.9248 


1 .1359 


2.1082 


1. 1469 


2.0423 


1.1584 


1. 98 1 1 


1-1705 


1.9239 


1-1361 


2.1070 


1.1471 


2.0413 


1.1586 


1. 980 1 


1. 1707 


1.9230 


1. 1363 


2.1059 


I-I473 


2.0402 


1.1588 


1.9791 


1. 1709 


1.9221 


1.1365 


2.1048 


1. 1474 


2.0392 


1. 1590 


1.9781 


1.1712 


1. 92 1 2 


1. 1366 


2.1036 


1. 1476 


2.0381 


1. 1592 


1.9771 


1.1714 


1.9203 


1. 1 368 


2.1025 


1.1478 


2.0370 


I-I594 


1.9761 


1.1716 


I-9I93 


i-i37o 


2.1014 


1. 1480 


2.0360 


1. 1596 


1-9752 


1.1718 


1.9184 


1. 1372 


2.1002 


1. 1482 


2.0349 


1.1598 


1.9742 


1. 1720 


I-9I75 


I-I373 


2.0991 


1. 1484 


2-0339 


1. 1600 


1.9732 


1. 1722 


1.9166 


1. 1375 


2.0980 


1. i486 


2.0329 


1. 1602 


1.9722 


1. 1724 


I-9I57 


I-I377 


2.0969 


1. 1488 


2.0318 


1. 1604 


i-97i3 


1. 1726 


1.9148 


I- 1379 


2.0957 


1. 1489 


2.0308 


1. 1606 


1.9703 


1. 1728 


I-9I39 


1,1381 


2.0946 


1.1491 


2.0297 


1. 1608 


1.9693 


1. 1730 


1.9130 


1. 1382 


2-0935 


J. 1493 


2.0287 


1.1610 


1.9683 


1. 1732 


1.9121 


1. 1384 


2.0924 


I-I495 


2.0276 


1.1612 


1.9674 


I-I734 


1.9112 


1.1386 


2.0912 


1. 1497 


2.0266 


1.1614 


1.9664 


I-I737 


1.9102 


1. 1 388 


2.0901 


1. 1499 


2.0256 


1.1616 


1.9654 


I-I739 


1.9093 


1. 1 390 


2.0890 


1.1501 


2.0245 


1.1618 


1.9645 


1.1741 


1.9084 


I-I3QI 


2.0879 


I-I503 


2.0235 


1. 1620 


1-9635 


I-I743 


1.9075 


I.I393 


2.0868 


1-1505 


2.0224 


1. 1622 


1.9625 


I-I745 


1 .9066 


1 -1395 


2.0857 


1-1507 


2.0214 


1. 1624 


1.9616 


I-I747 


I.9057 


I- 1397 


2.0846 


1. 1508 


2.0204 


1. 1626 


1.9606 


1. 1749 


1 .9048 


I-I399 


2.0835 


1-1510 


2.0T94 


1.1628 


1.9596 


I-I75I 


1.9039 


1.1401 


2.0824 


1.1512 


2.0183 


1. 1630 


1.9587 


I- 1753 


1.9030 


1. 1402 


2.0812 


I-I5I4 


2.0173 


1. 1632 


1-9577 


1. 1756 


1. 902 1 


I. 1404 


2.0801 


1.1516 


2.0163 


1. 1634 


1.9568 


1. 1758 


1. 9013 


1. 1406 


2.0790 


1.1518 


2.0152 


1. 1636 


1.9558 


1. 1760 


1 .9004 


1. 1408 


2.0779 


1. 1520 


2.0142 


.1.1638 


1.9549 


1. 1762 


1.8995 


1.1410 


2.0768 


1. 1522 


2.0132 


1. 1640 


1-9539 


1. 1764 


1.8986 


I.1411 


2.0757 


1. 1524 


2.0122 


1. 1642 


1 -9530 


1. 1766 


1.8977 


1.1413 


2.0746 


1. 1526 


a.oni 


1. 1644 


1.9520 


1. 1768 


1.8968 


1.1415 


2.0735 


1. 1528 


2.0101 


1. 1646 


1.9S10 


1. 1770 


1.8959 


I.1417 


2.0725 


I-I530 


2.0091 


1. 1648 


1,9501 


1. 1772 


1.8950 


1.1419 


2.0714 


I-I53I 


2.0081 


1. 1650 


1. 9491 


1. 1775 


1. 8941 


1.1421 


2.0703 


I-I533 


2.0071 


1. 1652 


1.9482 


1. 1777 


1.8932 


1. 1422 


2.0692 


1.1535 


2.0061 


1. 1654 


1-9473 


1. 1779 


1.8924 


1. 1424 


2.0681 


I-I537 


2.0050 


1.1656 


1.9463 


1.1781 


1.8915 


1. 1426 


2.0670 


I-I539 


2.0040 


1. 1658 


1-9454 


1.1783 


1.8906 


1. 1428 


2.0659 


1.1541 


2.0030 


1. 1660 


1.9444 


1.1785 


1.8897 


1.1430 


2.0648 


I-I543 


2.0020 


1. 1662 


1-9435 


1.1787 


1.8888 


1. 1432 


2.0637 


1 -1545 


2.0010 


1. 1664 


1.9425 


1. 1790 


1.8879 


1. 1433 


2.0627 


T-I547 


2.0000 


1. 1666 


1. 9416 


1. 1792 


1.8871 


CO-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


6 


L° 


61 


3° 


5< 


)° 


5! 


3° 



5i° 



NATURAL SECANTS AND CO-SECANTS 



! 32° 


33° 


34° 


35° 






•Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. C( 


5-SEC. 


f 


i. 1792 


1.8871 


1. 1924 


I.8361 


1.2062 


1.7883 


1.2208 1 


7434 


60 


1. 1794 - 


1.8862 


1. 1926 


1.8352 


1.2064 


1.7875 


1. 2210 1 


7427 


59 


1. 1796 


1.8853 


1. 1928 


I.8344 


1.2067 


1.7867 


1. 2213 1 


7420 


58 


1. 1798 


1.8844 


1.1930 


I.8336 


1.2069 


1.7860 


1. 2215 1 


•7413 


57 


1. 1800 


1.8836 


I-I033 


I.8328 


1.2072 


1.7852. 


1. 2218 1 


•7405 


56 


1. 1802 


1.8827 


I-I935 


I.8320 


1.2074 


1.7844 


1.2220 1 


■7398 


55 


1. 1805 


1.8818 


I.I937 


I.83H 


1.2076 


1-7837 


1.2223 1 


739i 


54 


1.7807 


1.8809 


1 -1939 


I.8303 


1.2079 


1.7829 


1.2225 1 


7384 


53 


1. 1809 


1. 880 1 


1. 1942 


I.8295 


1. 2081 


1. 7821 


1.2228 1 


7377 


52 


1.1811 


1.8792 


1. 1944 


I.8287 


1.2083 


1.7814 


1.2230 1 


7369 


5i 


1.1813 


1.8783 


1. 1946 


I.8279 


1.2086 


1.7806 


1.2233 1 


7362 


50 


1.1815 


1.8785 


1. 1948 


I.8271 


1.2088 


1.7798 


1.2255 1 


7355 


49 


1.1818 


1.8766 


I-T95I 


I.8263 


1. 2091 


1.7791 


1.2238 1 


7348 


48 


1. 1820 


1.8757 


I-I953 


I.8255 


1.2093 


1.7783 


1.2240 1 


734i 


47 


1. 1822 


1.8749 


I-I955 


I.8246 


1.2095 


1.7776 


1.2243 1 


7334 


46 


1. 1824 


1.8740 


1. 1958 


I.8238 


1.2098 


1.7768 


1.2245 1 


7327 


45 


1. 1826 


1-8731 


1. i960 


I.8230 


1. 2100 


1.7760 


1.2248 1 


7319 


44 


1. 1828 


1.8723 


1. 1962 


I.8222 


1. 2 103 


1-7753 


1.2250 1 


7312 


43 


1.1831 


1.8714 


1. 1964 


I.8214 


1.2105 


1-7745 


1.2253 1 


7305 


42 


1-1833 


1.8706 


1. 1967 


I.8206 


1.2107 


1.7738 


1.2255 1 


7298 


4i 


1.183s 


1.8697 


1. 1969 


I.8198 


1.2110 


I-773Q 


1.2258 1 


7291 


40 


1.1837 


1.8688 


1.1971 


I.8190 


1.2112 


1-7723 


1.2260 1 


7284 


39 


1. 1839 


1.8680 


1. 1974 


I.8182 


1.2115 


I-77I5 


1.2263 1 


7277 


38 


1.1841 


1.8671 


1. 1976 


I.8174 


1.2117 


1.7708 


1.2265 1 


7270 


37 


1. 1844 


1.8663 


1. 1978 


I.8166 


1.2119 


1.7700 


1.2268 1 


7263 


36 


1. 1846 


1.8654 


1. 1980 


I.8158 


1. 2122 


1.7693 


1.2270 1 


7256 


35 


1.1848 


1.8646 


1. 1983 


I.8150 


1.2124 


1.7685 


1.2273 1 


7249 


34 


1.1850 


1.8637 


1. 1985 


I.8142 


1. 2127 


1.7678 


1.2276 1 


7242 


33 


1.1852 


1.8629 


1. 1987 


I.8134 


1. 2129 


1.7670 


1.2278 1 


7234 


32 


1.185s 


1.8620 


1. 1990 


I.8126 


1.2132 


1.7663 


1. 2281 1 


7227 


3i 


1.1857 


1. 861 1 


1. 1992 


I.8118 


1.2134 


I.7655 


1.2283 1 


7220 


30 


1.1859 


1.8603 


1. 1994 


I.8IIO 


1.2136 


1.7648 


1.2286 1 


7213 


29 


1.1861 


1.859s 


1. 1997 


I.8102 


1.2159 


1.7640 


1.2288 1 


7206 


28 


1.1863 


1.8586 


1. 1999 


I.8094 


1.2141 


1-7633 


1. 2291 1 


7199 


27 


1. 1866 


1.8578 


1. 200 1 


I.8086 


1.2144 


1.7625 


1.2293 1 


7192 


26 


1. 1868 


1.8569 


1.2004 


I.8078 


1. 2146 


1.7618 


1.2296 1 


7185 


25 


1. 1870 


1.8561 


1.2006 


I.8070 


1.2149 


1. 7610 


1.2298 1 


7178 


24 


1. 1872 


1.8552 


1.2008 


I.8062 


1.2151 


1.7603 


1.2301 1 


7171 


23 


1. 1874 


1.8544 


1.2010 


I.8054 


i.? 153 


1-7596 


1.2304 1 


7164 


22 


1.1877 


1.8535 


1. 2013 


I.8047 


1.2156 


1.7588 


1.2306 1 


7157 


21 


1. 1879 


1.8527 


1.2015 


I.8039 


1.2158 


1.7581 


1.2309 1 


7i5i 


20 


1.1881 


1.8519 


1. 2017 


I.8031 


1.2161 


1-7573 


1.2311 1 


7144 


19 


1.1883 


1.8510 


1.2020 


I.8023 


1.2163 


1.7566 


1.2314 1 


7137 


18 


1. 1886 


1.8502 


1.2022 


I.8015 


1. 2166 


1-7559 


1.2316 1 


7130 


17 


1. 1888 


1.8493 


1.2024 


I.8007 


1.2168 


I.755I 


1.2319 1 


7123 


16 


1. 1890 


1.8485 


1.2027 


I.7999 


1.2171 


1-7544 


1.2322 1 


7116 


15 


1. 1892 


1.8477 


1.2029 


I.7992 


1.2173 


1-7537 


1.2324 1 


7109 


14 


1. 1894 


1.8468 


1. 2031 


I.7984 


I-2I75 


1.7529 


1.2327 1 


7102 


13 


1. 1897 


1 .8460 


1.2034 


1.7976 


1. 2178 


1.7522 


1.2329 1 


7095 


12 


1. 1899 


1.8452 


1.2036 


I.7968 


1. 2 180 


I-75I4 


1.2332 1 


7088 


11 


1.1901 


.1.8443 


1.2039 


I.7960 


1.2183 


I.7507 


1.2335 1 


7081 


10 


1. 1903 


1-8435 


1. 2041 


1-7953 


1.2185 


1.7500 


1.2337 1 


7075 


9 


1. 1906 


1.8427 


1.2043 


1-7945 


1.2188 


1-7493 


1.2340 1 


7068 


8 


1. 1908 


1.8418 


1.2046 


1-7937 


1. 2190 


I-7485 


1.2342 1 


7061 


7 


1.1910 


1. 8410 


1.2048 


1.7929 


1.2193 


1.7478 


1-2345 1 


7054 


6 


1.1912 


1.8402 


1.2050 


1.7921 


1. 2 1 95 


1.7471 


1.2348 1 


7047 


5 


1.1915 


1.8394 


1.2053 


1.7914 


1. 2198 


I-7463 


1.2350 1 


7040 


4 


1.1917 


1.8385 


1.2055 


1.7906 


1.2200 


I.7456 


1-2353 1 


7033 


3 


1.1919 


1-8377 


1.2057 


1.7898 


1.2203 


1.7449 


1.2355 1 


7027 


2 


1.1921 


1.8369 


1.2060 


1.7891 


1.2205 


1.7442 


1.2358 1 


7020 


1 


1. 1.922 


1.8361 


1.2062 


1.7883 


1.2208 


1-7434 


1. 2361 1 


7013 





Co-sec. 


Sec. 


CO-SEC. 


Sec. 


CO-SEC. 


Sec. 


CO-SEC. 


Sec. 


f 


5 


7° 


1 5 


5° 


5, 


5° 


54° 







NATURAL SECANTS AND CO-SECANTS 



5" 



36 





37 


( 


38 





39 





Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


1.2361 


1-7013 


1. 2521 


1.6616 


1.2690 


1.6243 


1.2867 


1.^890 


1.2363 


1.7006 


1.2524 


1. 6610 


1.2693 


1.6237 


1. 2871 


1.5884 


1.2366 


1.6999 


1.2527 


1.6603 


1.2696 


1.6231 


1.2874 


1-5879 


1.2368 


1.6993 


1.2530 


1-6597 


1.2699 


1.6224 


1.2877 


1-5873 


1.2371 


1.6986 


1.2532 


1.6591 


1.2702 


1.6218 


1.2880 


1.5867 


1-2374 


1.6979 


1-2535 


1.6584 


1.2705 


1.6212 


1.2883 


1.5862 


1.2376 


1.6972 


1.2538 


1.6578 


1.2707 


1.6206 


1.2886 


1.5856 


1-2379 


1.6965 


1-2541 


1.6572 


1. 2710 


1.6200 


1.2889 


1.5850 


1.2382 


1.6959 


1-2543 


1-6565 


1-2713 


1.6T94 


1.2892 


1-5845 


1.2384 


1.6952 


1.2546 


1-6559 


1. 2716 


1.6188 


1.2895 


1-5839 


1.2387 


1.6945 


1.2549 


1.6552 


1.2719 


1.6182 


1.2898 


1.5833 


1.2389 


1.6938 


1.2552 


1.6546 


1.2722 


1.6176 


1. 2901 


1.5828 


1.2392 


1.6932 


1-2554 


1.6540 


1.2725 


1. 61 70 


1.2904 


1.5822 


1-2395 


1.6925 


1-2557 


1-6533 


1.2728 


1.6164 


1.2907 


1.5816 


1-2397 


1.6918 


1.2560 


1.6527 


1.2731 


1.6159 


1. 2910 


1.5811 


1.2400 


1. 691 2 


1.2563 


1.6521 


1-2734 


i.6i53 


1.2913 


1.5805 


1.2403 


1.6905 


1.2565 


1.6514 


1-2737 


1.6147 


1. 2916 


1-5799 


1.2405 


1.6898 


1.2568 


1.6508 


1-2739 


1.6141 


1. 2919 


1-5794 


1.2408 


1. 6891 


1-2571 


1.6502 


1.2742 


i.6i35 


1.2922 


1.5788 


1.2411 


1.6885 


1-2574 


1 .6496 


1-2745 


1.6129 


1.2926 


1.5783 


1.2413 


1.6878 


1.2577 


1 .6489 


1.2748 


1.6123 


1.2929 


1-5777 


1. 2416 


1. 687 1 


1.2579 


1 .6483 


1.2751 


1.6117 


1.2932 


I-577I 


1.2419 


1.6865 


1.2582 


1.6477 


1-2754 


1.6111 


1.2935 


1.5766 


1. 242 1 


1.6858 


1.2585 


1.6470 


1.2757 


1.6105 


1.2938 


1.5760 


1.2424 


1. 685 1 


1.2588 


1 .6464 


1.2760 


1.6099 


1. 2941 


1-5755 


1.2427 


1.6845 


1.2591 


1.6458 


1.2763 


1.6093 


1.2944 


1-5749 


1.2429 


1.6838 


1.2593 


1-6452 


1.2766 


1.6087 


1.2947 


1-5743 


1.2432 


1. 683 1 


1.2596 


1 .6445 


1.2769 


1. 6081 


1.2950 


1-5738 


1.2435 


1.6825 


1.2599 


1.6439 


1.2772 


1.6077 


1-2953 


1.5732 


1-2437 


1. 6818 


1.2602 


1-6433 


1.2775 


1.6070 


1.2956 


1.5727 


1.2440 


1.6812 


1.2605 


1.6427 


1.2778 


1.6064 


1.2960 


1.5721 


1-2443 


1.6805 


1.2607 


1.6420 


1. 2781 


1.6058 


1.2963 


i-57i6 


1.2445 


1.6798 


1. 2610 


1. 6414 


1.2784 


1.6052 


1.2966 


1.5710 


1.2448 


1.6792 


1.2613 


1 .6408 


1.2787 


1 .6046 


1.2969 


1-5705 


1.2451 


1.6785 


1. 2616 


1.6402 


1.2790 


1 .6040 


1.2972 


1.5699 


1.2453 


1.6779 


1. 2619 


1.6396 


1.2793 


1.6034 


1.2975 


1.5694 


1.2456 


1.6772 


1.2622 


1.6389 


1-2795 


1.6029 


1.2978 


1.5688 


1.2459 


1.6766 


1.2624 


1.6383 


1.2798 


1.6023 


1. 2981 


1.5683 


1. 2461 


1-6759 


1.2627 


1.6377 


1. 2801 


1. 601 7 


1.2985 


1.5677 


1.2464 


1.6752 


1.2630 


1-6371 


1.2804 


1. 601 1 


1.2988 


1.5672 


1.2467 


1.6746 


1.2633 


1.6365 


1.2807 


1.6005 


1. 2991 


1.5666 


1.2470 


1.6739 


1.2636 


1.6359 


1. 2810 


1 .6000 


1.2994 


1.5661 


1.2472 


1.6733 


1.2639 


1.6352 


1.2813 


1-5994 


1.2997 


1.5655 


1-2475 


1.6726 


1. 2641 


1 .6346 


1.2816 


1.5988 


1.3000 


1.5650 


1.2478 


1.6720 


1.2644 


1.6340 


1.2819 


1.5982 


1.3003 


1.5644 


1.2480 


1-6713 


1.2647 


1-6334 


1.2822 


1-5976 


1 .3006 


1-5639 


1.2483 


1.6707 


1.2650 


1.6328 


1.2825 


I-597I 


1,3010 


1.5633 


1.2486 


1.6700 


1-2653 


1.6322 


1.2828 


I-5965 


1.3013 


1.5628 


1.2488 


1.6694 


1.2656 


1.6316 


1.2831 


1-5959 


1. 3016 


1.5622 


1.2490 


1.66S7 


1.2659 


1.6309 


1.2834 


1-5953 


1.3019 


1-5617 


1.2494 


1. 6681 


1. 2661 


1.6303 


; 1.2837 


1-5947 


1.3022 


1.5611 


1.2497 


1.6674 


1.2664 


1.6297 


1.2840 


1.5942 


1-3025 


1.5606 


1.2499 


1.6668 


1.2667 


1.6291 


1.2843 


1-5936 


1.3029 


1.5600 


1.2502 


1. 6661 


1.2670 


1.6285 


1.2846 


I-593Q 


1-3032 


1-5595 


1.2505 


1.6655 


1.2673 


1.6279 


1.2849 


1.5924 


1-3035 


I-5590 


1.2508 


1.6648 


1.2676 


1.6273 


1.2852 


I-59I9 


1.3038 


1.5584 


1.2510 


i .6642 


1.2679 


1.6267 


1.2855 


I-59I3 


1. 3041 


1-5579 


1-2513 


1.6636 


1.2681 


1.6261 


1.2858 


I.5907 


1 .3044 


1-5573 


1.2516 


1.6629 


1.2684 


1.6255 


1.2861 


1.5901 


1.3048 


1.5568 


1.2519 


1.6623 


1.2687 


1.6249 


1.2864 


1.5896 


1-3051 


I-5563 


1. 2521 


1.6616 


1.2690 


1.6243 


1.2867 


1.5890 


1-3054 


1-5557 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


5 


3° 


5 


2° 


5 


1° 


5 


0° 



512 



NATURAL SECANTS AND CO-SECANTS 



4C 


1° 


4] 


L° 


42° 


43° 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


1.3054 


1-5557 


1.3250 


1-5242 


1.3456 


1-4945 


1.3673 


1.4663 


1-3057 


1-5552 


1-3253 


1-5237 


1.3460 


1.4940 


1-3677 


1.4658 


1.3060 


L5546 


1.3257 


1-5232 


1.3463 


1-4935 


1.3681 


1.4654 


1.3064 


I-554I 


1.3260 


1.5227 


1-3467 


1.4930 


1.3684 


1.4649 


1.3067 


I.5536 


1.3263 


1.5222 


1.3470 


1.4925 


1.3688 


1.4644 


1.3070 


I.5530 


1.3267 


1-5217 


1-3474 


1. 492 1 


1.3692 


1 .4640 


1-3073 


1-5525 


1.3270 


1. 5212 


1-3477 


1.4916 


1-3695 


1.4635 


1.3076 


I-5520 


1-3274 


1.5207 


1.3481 


1. 49 1 1 


1.3699 


1.4631 


1.3080 


I-55I4 


1.3277 


1.5202 


I-3485 


1.4906 


1-3703 


1.4626 


1.3083 


1.5509 


1.3280 


1.5197 


1.3488 


1. 490 1 


1-3707 


1.4622 


1.3086 


I-5503 


1.3284 


1.5192 


1.3492 


1.4897 


1.3710 


1. 461 7 


1.3089 


1.5498 


1.3287 


1.5187 


1-3495 


1.4892 


i-37i4 


1.4613 


1.3092 


1-5493 


1.3290 


1.5182 


1-3499 


1.4887 


i-37i8 


1.4608 


1.3096 


I-5487 


1.3294 


1-5177 


I-3502 


1.4882 


1.3722 


1 .4604 


1.3099 


1.5482 


1.3297 


1.5171 


1.3506 


1.4877 


1-3725 


1-4599 


1. 3102 


1-5477 


1.3301 


1.5166 


I-3509 


1.4873 


1-3729 


1-4595 


1-3105 


I.S47I 


1.3304 


1.5161 


I-35I3 


1.4868 


1-3733 


1.4590 


1.3109 


1.5466 


1.3307 


1.5156 


I-35I7 


1.4863 


1-3737 


1.4586 


1.3112 


1.5461 


I-33H 


1.5151 


1.3520 


1.4858 


1 -3740 


1.4581 


i.3"5 


1-5456 


I-33I4 


1.5146 


1-3524 


1.4854 


1-3744 


1-4577 


i.3"8 


1-5450 


I.33I8 


1.5141 


1-3527 


1.4849 


1.3748 


1-4572 


1.3121 


1-5445 


I-332I 


1.5136 


I-353I 


1.4844 


1-3752 


1.4568 


1.3125 


1.5440 


I.3324 


1.5131 


1-3534 


1.4839 


1-3756 


1-4563 


1.3128 


1.5434 


1.3328 


1.5126 


1-353^ 


1.4835 


1-3759 


1-4559 


1.3131 


1.5429 


I-333I 


1.5121 


1-3542 


1.4830 


1.3763 


1-4554 


1-3134 


1.5424 


1-3335 


1.5116 


1-3545 


1.4825 


1.3767 


I-4550 


1.3138 


I-54I9 


I.3338 


1.5111 


1-3549 


1. 482 1 


I.377I 


1-4545 


1.3141 


I.54I3 


1-3342 


1.5106 


1-3552 


1.4816 


1-3774 


1 -4541 


1-3144 


1.5408 


1-3345 


1.5101 


1.3556 


1. 481 1 


1.3778 


1-4536 


1.3148 


1.5403 


I-3348 


1.5096 


1.3560 


1.4806 


1.3782 


1-4532 


1.3151 


I.5398 


1-3352 


1.5092 


1.3563 


1.4802 


1.3786 


1-4527 


1.3154 


1.5392 


1-3355 


1.5087 


1.3567 


1-4797 


1.3790 


1-4523 


1.3157 


1.5387 


1-3359 


1.5082 


I-357I 


1.4792 


1-3794 


1.4518 


1.3161 


1.5382 


1.3362 


1.5077 


1-3574 


1.4788 


1-3797 


1 4514 


1.3164 


1-5377 


1.3366 


1.5072 


1-3578 


1.4783 


1. 3801 


1. 4510 


1.3167 


I.537I 


1.3369 


1.5067 


i.358i 


1.4778 


1.3805 


I-4505 


1.3170 


1.5366 


1.3372 


1.5062 


I-3585 


1-4774 


1.3809 


1.4501 


i-3i74 


i.536i 


1-3376 


1-5057 


1,3589 


1.4769 


1-3813 


1.4496 


1.3177 


1-5356 


1-3379 


1.5052 


1-3592 


1.4764 


1.3816 


1.4492 


1.3180 


I-535I 


I-3383 


1.5047 


1-3596 


1.4760 


1.3820 


1.4487 


1.3184 


1-5345 


1.3386 


1.5042 


1.3600 


1-4755 


1.3824 


1.4483 


1.3187 


I-5340 


■ I-3390 


1-5037 


1.3603 


1-4750 


1.3828 


1.4479 


1.3190 


1-5335 


1-3393 


1.5032 


1.3607 


1.4746 


1.3832 


1.4474 


1-3193 


1 -533Q 


1-3397 


1.5027 


1.3611 


1. 4741 


1.3836 


1.4470 


1-3197 


1.5325 


1 .3400 


1*5022 


1.3614 


1.4736 


1.3839 


1.4465 


1.3200 


I-53I9 


1.3404 


1.5018 


1. 36 1 8 


1-4732 


1.3843 


1. 446 1 


1.3203 


I-53I4 


I-3407 


1-5013 


1.3622 


1.4727 


1.3847 


1-4457 


1.3207 


1-5309 


1. 341 1 


1.5008 


1.3625 


1-4723 


1.3851 


1.4452 


1. 3210 


I-5304 


I-34I4 


1-5003 


1.3629 


1.4718 


1.3855 


1.4448 


1-3213 


1.5299 


1.3418 


1.4998 


1-3633 


I-47I3 


1.3859 


1-4443 


1-3217 


1.5294 


1. 342 1 


1-4993 


1.3636 


1.4709 


1.3863 


1-4439 


1.3220 


I.5289 


1.342 5 


1.4988 


1.3640 


1.4704 


1.3867 


1-4435 


1.3223 


1.5283 


1.3428 


1.4983 


1.3644 


1 .4699 


1.3870 


1.4430 


1.3227 


1.5278 


1-3432 


1.4979 


1-3647 


1.4695 


1.3874 


1.4426 


1.3230 


1-5273 


1-3435 


1.4974 


1-3651 


1.4690 


1.3878 


1.4422 


1.3233 


1.5268 


1-3439 


1 .4969 


1-3655 


1.4686 


1.3882 


I-44I7 


1.3237 


1.5263 


1.3442 


1.4964 


1.3658 


1. 4681 


1.3886 


I-44I3 


1.3240 


1.5258 


1.3446 


1-4959 


1.3662 


1.4676 


1.3890 


1 .4408 


1-3243 


1-5253 


1-3449 


1-4954 


1.3666 


1.4672 


1.3894 


1.4404 


1-3247 


1.5248 


1.3453 


1.4949 


1.3669 


1.4667 


1.3898 


1.4400 


1.3250 


1.5242 


I.3456 


1-4945 


1.3673 


1.4663 


1.3902 


1-4395 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


CO-SEC. 


Sec. 


4< 


}° 


4, 


B° 


4' 


7 q 


4( 


3° 



NATURAL SECANTS AND CO-SECANTS 



513 





440 






440 






440 


i 


Sec. 


Co-sec. 


60 


f 
21 


Sec. 


Co-sec. 


39 


41 


Sec 
1 .4065 


Co-sec. 





1.3902 


i-4395 


1.3984 


1-4305 


1. 4221 


I 


1-3905 


I-439I 


59 


22 


1.3988 


1. 430 1 


38 


42 


1.4069 


1.4217 


2 


1.3909 


1-4387 


58 


23 


1.3992 


1.4297 


37 


43' 


1-4073 


1. 4212 


3 


i-39i3 


1.4382 


57 


24 


1.3996 


1.4292 


36 


44 


1 4077 


1.4208 


4 


i-39i7 


1-4378 


56 


25 


1.4000 


1.4288 


35 


45 


1. 408 1 


1.4204 


5 


1.3921 


1-4374 


55 


26 


1.4004 


1.4284 


34 


46 


1.4085 


1.4200 


6 


1-3925 


I.4370 


54 


27 


1 .4008 


1.4280 


33 


47 


1 .4089 


1.4196 


7 


1.3929 


I-4365 


53 


28 


1. 4012 


1.4276 


32 


48 


1.4093 


1.4192 


8 


1-3933 


I-436i 


52 


29 


1. 4016 


1.4271 


31 


49 


1.4097 


1.4188 


9 


1-3937 


1-4357 


51 


30 


1.4020 


1.4267 


30 


50 


1.4101 


1-4183 


10 


1 -3941 


1-4352 


50 


31 


1.4024 


1.4263 


29 


51 


1.4105 


1.4179 


11 


1-3945 


1.4348 


49 


32 


1.4028 


1.4259 


28 


52 


1. 4109 


1-4175 


12 


1-3949 


1-4344 


48 


33 


1.4032 


1.4254 


27 


53 


1.4113 


1-4171 


13 


1-3953 


1-4339 


47 


34 


1.4036 


1.4250 


26 


54 


1.4117 


1.4167 


14 


1-3957 


1-4335 


46 


35 


1.4040 


1.4246 


25 


55 


1. 4122 


1.4163 


15 


1.3960 


I-433I 


45 


36 


1.4044 


T.4242 


24 


56 


1.4126 


1-4159 


16 


1.3964 


1-4327 


44 


37 


1.4048 


1.4238 


23 


57 


1-4130 


1-4154 


17 


1.3968 


1.4322 


43 


38 


1.4052 


1-4233 


22 


58 


1-4134 


1.4150 


18 


1.3972 


1.4318 


42 


39 


1.4056 


1.4229 


21 


59 


1,4138 


1. 4146 


19 


1.3976 


I-43I4 


41 


40 


1 .4060 


1.4225 


20 


60 


1.4142 


1. 4142 


20 


1 .3980 


1.4310 


40 


/ 






/ 


i ' 






/ 


CO-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec 




4, 


5° 






4 


5" 






4 


5° 



to 
18 
n 
16 
15 

13 

T2 
II 

IO 

9 
8 
7 
6 
5 
4 
3 
2 

1 
o 



Si4 



LOGARITHMS OF NUMBERS* 
Table 6i 



IOO 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

432 


000000 


0434 


0868 


1301 


1734 


2166 


2598 


3029 


346i 


3891 


IOI 


4321 


475i 


5181 


5609 


6038 


6466 


6894 


7321 


7748 


8174 


428 


I02 


8600 


9026 


9451 


9876 


*0300 


*0724 


*ii47 


*i 57 o 


*i993 


*24i5 


424 


I03 


012837 


3259 


3680 


4100 


452i 


4940 


536o 


5779 


6197 


6616 


420 


IO4 


7033 


745i 


7868 


8284 


8700 


9116 


9532 


9947 


*036i 


*o775 416 


I05 


021 189 


1603 


2016 


2428 


2841 


3252 


3664 


4075 


4486 


4896 


412 


I06 


5306 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


I07 


9384 


9789 


*oi95 


*o6oo 


*ioo4 


*i4o8 


*l8l2 


*22l6 


*26i9 


*302I 


404 


I08 


033424 


3826 


4227 


4628 


5029 


5430 


5830 


6230 


6629 


7028 


400 


IO9 


7426 


7S25 


8223 


8620 


9017 


'9414 


9811 


*0207 


*o6o2 


*0998 


397 


N. 


Diff. 
434 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


43 


87 


130 


174 


217 


260 


304 


347 


391 


434 




433 


43 


87 


130 


173 


217 


260 


303 


346 


390 


433 




432 


43 


86 


130 


173 


216 


259 


302 


346 


389 


432 




43i 


43 


86 


129 


172 


216 


259 


302 


345 


388 


43i 




430 


43 


86 


129 


172 


215 


258 


301 


344 


387 


430 




429 


43 


86 


129 


172 


215 


257 


300 


343 


386 


429 




428 


43 


86 


128 


171 


214 


257 


300 


342 


385 


428 




427 


43 


85 


128 


171 


214 


256 


299 


342 


384 


427 




426 


43 


85 


128 


170 


213 


256 


298 


34i 


383 


426 




425 


43 


85 


128 


170 


213 


255 


298 


340 


383 


425 




424 


42 


85 


127 


170 


212 


254 


297 


339 


382 


424 




423 


42 


85 


127 


169 


212 


254 


296 


338 


381 


423 




422 


42 


84 


127 


169 


211 


253 


295 


338 


380 


422 




421 


42 


84 


126 


168 


211 


253 


295 


337 


379 


421 




420 


42 


84 


126 


168 


210 


252 


294 


336 


378 


420 


W 


419 


42 


84 


126 


168 


210 


251 


293 


335 


377 


4 ig 


H 
< 


418 


42 


84 


125 


167 


209 


251 


293 


334 


376 


418 


417 


42 


83 


125 


167 


209 


250 


292 


334 


375 


4i7 


416 


42 


83 


125 


166 


208 


250 


291 


333 


374 


416 




4i5 


42 


83 


125 


166 


208 


249 


291 


332 


374 


4i5 


_) 


414 


4i 


83 


124 


166 


207 


248 


290 


33i 


373 


414 


< 


413 


4i 


83 


124 


165 


207 


248 


289 


330 


372 


413 


z 


412 


4i 


82 


124 


165 


206 


247 


288 


330 


37i 


412 


O 


411 


4i 


82 


123 


164 


206 


247 


288 


329 


37o 


411 


H 


410 


4i 


82 


123 


164 


205 


246 


287 


328 


369 


410 


ti 


409 


4i 


82 


123 


164 


205 


245 


286 


327 


368 


409 


O 


408 


4i 


82 


122 


163 


204 


245 


286 


326 


367 


408 


O 


407 


41 


81 


122 


163 


204 


244 


285 


326 


366 


407 


406 


4i 


81 


122 


162 


203 


244 


284 


325 


365 


406 


405 


4i 


81 


122 


162 


203 


243 


284 


324 


365 


405 




404 


40 


81 


121 


162 


202 


242 


283 


323 


364 


404 




403 


40 


81 


121 


161 


202 


242 


282 


322 


363 


4°3 




402 


40 


80 


121 


161 


201 


241 


281 


322 


362 


402 




401 


40 


80 


120 


160 


201 


241 


281 


321 


361 


401 




400 


40 


80 


120 


160 


200 


240 


280 


320 


360 


400 




399 


40 


80 


120 


160 


200 


239 


279 


319 


359 


399 




398 


40 


80 


119 


159 


199 


239 


279 


3i8 


358 


398 




397 


40 


79 


119 


159 


199 


238 


278 


318 


357 


397 




396 


40 


79 


119 


158 


198 


238 


277 


3i7 


356 


396 




395 


40 


79 


119 


158 


198 


237 


277 


316 


356 


395 




394 


39 


79 


118 


158 


197 


236 


276 


3i5 


355 


394 




393 


39 


79 


118 


157 


197 


236 


275 


3i4 


354 


393 




392 


39 


78 


118 


i57 


196 


235 


274 


314 


353 


392 




39i 


39 


78 


117 


156 


196 


235 


274 


313 


352 


39i 




390 


39 


78 


117 


156 


195 


234 


273 


312 


35i 


390 




389 


39 


78 


117 


156 


195 


233 


272 


311 


35o 


389 




388 


39 


78 


116 


155 


194 


233 


272 


310 


349 


388 


L 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



*From Allen's "Field and Office Tables." Copyright, 1903, 1914. by 
C. F. Allen. 



LOGARITHMS OF NUMBERS 



SIS 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


no 


041393 


1787 


2182 


2576 


2969 


3362 


3755 


4148 


4540 


4932 


393 


in 


5323 


5714 


6105 


6495 


6885 


7275 


■7664 


8053 


8442 


8830 


390 


112 


9218 


9606 


9993 


^0380 


*0766 


*H53 


*I538 


*i924 


^'2309 


*2694 


386 


113 


053078 


3463 


3846 


4230 


4613 


4996 


5378 


5760 


6142 


6524 


383 


114 


6905 


7286 


7666 


8046 


8426 


8805 


9185 


9563 


9942 


*0320 


379 


115 


060698 


1075 


1452 


1829 


2206 


2582 


2958 


3333 


3709 


4083 


376 


116 


4458 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


7815 


373 


117 


8186 


8557 


8928 


9298 


9668 


*oo38 


*0407 


^0776 


*ii45 


*I5*4 


37o 


118 


071882 


2250 


2617 


2985 


3352 


37i8 


4085 


4451 


4816 


5182 


366 


ng 


5547 


59'i2 


6276 


6640 


7004 


7368 


7731 


8094 


8457 


8819 


363 


120 


079181 


9543 


9904 


*o266 


#0626 


^0987 


*i 34 7 


*i707 


*2o67 


#2426 


360 


121 


082785 


3*44 


3503 


3861 


4219 


4576 


4934 


5291 


5647 


6004 


357 


122 


6360 


6716 


7071 


7426 


7781 


8136 


8490 


8845 


9198 


9552 


355 


123 


9905 


*0258 


*o6n 


♦0963 


*i3i5 


*i667 


*20l8 


*237o 


*272I 


#3071 


352 


124 


093422 


3772 


4122 


447i 


4820 


5169 


5518 


5866 


6215 


6562 


349 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


387 


39 


77 


116 


155 


194 


232 


271 


310 


348 


387 




386 


39 


77 


116 


154 


193 


232 


270 


309 


347 


386 




385 


39 


77 


116 


154 


193 


231 


270 


308 


347 


3 £ 5 




384 


38 


77 


115 


154 


192 


230 


269 


307 


346 


384 




383 


38 


77 


115 


153 


192 


230 


268 


306 


345 


383 




382 


38 


76 


115 


153 


191 


229 


267 


306 


344 


382 




381 


38 


76 


114 


152 


191 


229 


267 


305 


343 


381 




380 


38 


76 


114 


152 


190 


228 


266 


304 


342 


380 




379 


38 


76 


114 


152 


190 


227 


265 


303 


34i 


379 




378 


38 


76 


113 


151 


189 


227 


265 


302 


340 


378 




377 


38 


75 


"3 


151 


189 


226 


264 


302 


339 


377 




376 


38 


75 


113 


150 


188 


226 


263 


301 


338 


376 




375 


38 


75 


113 


150 


188 


225 


263 


300 


338 


375 


CO 

< 

0. 


374 


37 


75 


112 


150 


187 


224 


262 


299 


337 


374 


373 


37 


75 


112 


149 


187 


224 


261 


298 


336 


373 


372 


37 


74 


112 


149 


186 


223 


260 


298 


335 


372 


37i 


37 


74 


in 


148 


186 


223 


260 


297 


334 


37i 




37o 


37 


74 


in 


148 


185 


222 


259 


296 


333 


37o 


< 

z 




36g 


37 


74 


in 


148 


185 


221 


258 


295 


332 


369 


368 


37 


74 


no 


147 


184 


221 


258 


294 


33i 


368 


367 


37 


73 


no 


147 


184 


220 


257 


294 


330 


367 


366 


37 


73 


no 


146 


183 


220 


256 


293 


329 


366 


H 


365 


37 


73 


no 


146 


183 


219 


256 


292 


329 


365 


ft 


364 


36 


73 


109 


146 


182 


218 


255 


291 


328 


364 


O 

0. 



a, 


363 


36 


73 


109 


145 


182 


218 


254 


290 


327 


363 


362 


36 


72 


109 


145 


181 


217 


253 


290 


326 


362 


361 


36 


72 


108 


144 


181 


217 


253 


289 


325 


361 


360 


36 


72 


108 


144 


180 


2l6 


252 


288 


324 


360 




359 


36 


72 


108 


144 


180 


215 


251 


287 


323 


359 




358 


36 


72 


107 


143 


179 


215 


251 


286 


322 


358 




357 


36 


7i 


107 


143 


179 


214 


250 


286 


321 


357 




356 


3 5 


7i 


107 


142 


178 


214 


249 


285 


320 


356 




355 


36 


7i 


107 


142 


178 


213 


249 


284 


320 


355 




354 


35 


7i 


106 


142 


177 


212 


248 


283 


319 


354 




353 


35 


7i 


106 


141 


177 


212 


247 


282 


3i8 


353 




352 


35 


70 


106 


141 


176 


211 


246 


282 


317 


352 




35i 


35 


70 


105 


140 


176 


211 


246 


281 


316 


351 




350 


35 


70 


105 


140 


175 


210 


245 


280 


315 


350 




349 


35 


70 


105 


140 


175 


209 


244 


279 


314 


349 




348 


35 


70 


104 


139 


174 


209 


244 


278 


313 


348 




347 


35 


69 


104 


139 


174 


208 


243 


278 


312 


347 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



5i6 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

346 


125 


096910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


*0026 


126 


10037 1 


0715 


1059 


1403 


1747 


2091 


2434 


2777 


3119 


3462 


343 


127 


3804 


4146 


4487 


4828 


5169 


5510 


5851 


6191 


6531 


6871 


34i 


128 


7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


♦0253 


338 


129 


1 1 0590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609 


335 


130 


1 13943 


4277 


461 1 


4944 


5278 


561 1 


5943 


6276 


6608 


6940 


333 


131 


7271 


7603 


7934 


8265 


8595 


8926 


9256 


9586 


9915 


*0245 


330 


*I32 


120574 


0903 


1231 


1560 


1888 


2216 


2544 


2871 


3198 


3525 


328 


133 


3852 


4178 


4504 


4830 


5156 


5481 


5806 


6131 


6456 


6781 


325 


134 


7105 


7429 


7753 


8076 


8399 


8722 


9°45 


9368 


9690 


*OOI2 


323 


135 


130334 


0655 


0977 


1298 


1619 


1939 


2260 


2580 


2900 


3219 


321 


136 


3539 


3858 


4177 


4496 


4814 


5133 


5451 


5769 


6086 


6403 


3i8 


137 


6721 


7037 


7354 
*o5o8 


7671 


7987 


8303 


8618 


8934 


9249 


9564 


316 


138 


9879 


*oi94 


*0822 


*H36 


*I450 


*I763 


^2076 


*2 3 8 9 


*2702 


314 


139 


1430 1 5 


3327 


3639 


3951 


4263 


4574 


4885 


5196 


5507 


58l8 


3ii 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




347 


35 


69 


104 


139 


174 


208 


243 


278 


312 


347 




346 


35 


69 


104 


138 


173 


208 


242 


277 


311 


346 




345 


35 


69 


104 


138 


173 


207 


242 


276 


311 


345 




344 


34 


69 


103 


138 


172 


206 


241 


275 


310 


344 




343 


34 


69 


T03 


137 


172 


206 


240 


274 


309 


343 




342 


34 


68 


103 


137 


171 


205 


239 


274 


308 


342 




34i 


34 


68 


102 


136 


171 


205 


239 


273 


307 


341 




340 


34 


68 


102 


136 


170 


204 


238 


272 


306 


340 




339 


34 


68 


102 


136 


170 


203 


237 


271 


305 


339 




338 


34 


68 


IOI 


135 


169 


203 


237 


270 


304 


338 




337 


34 


67 


IOI 


135 


169 


202 


236 


270 


303 


337 




336 


34 


67 


IOI 


134 


168 


202 


235 


269 


302 


336 


W 


335 


34 


67 


IOI 


134 


168 


201 


235 


268 


302 


335 


H 


334 


33 


67 


IOO 


134 


167 


200 


234 


267 


301 


334 


N 


333 


33 


67 


IOO 


133 


167 


200 


233 


266 


300 


333 


< 


332 


33 


66 


IOO 


133 


166 


199 


232 


266 


299 


332 


a< 


33i 


33 


66 


99 


132 


166 


199 


232 


265 


298 


33i 


< 


330 


33 


66 


99 


132 


165 


198 


231 


264 


297 


330 


329 


33 


66 


99 


132 


165 


197 


230 


263 


296 


3 2 9 


2 


328 


33 


66 


98 


131 


164 


197 


230 


262 


295 


328 


O 


327 


33 


65 


98 


131 


164 


196 


229 


262 


294 


327 


H 
O 


326 


33 


65 


98- 


130 


163 


196 


228 


261 


293 


326 


325 


33 


65 


98 


130 


163 


195 


228 


260 


293 


325 


324 


32 


65 


97 


130 


162 


194 


227 


259 


292 


324 


£ 


323 


32 


65 


. 97 


129 


162 


194 


226 


258 


291 


323 





322 


32 


64 


97 


129 


161 


193 


225 


258 


290 


322 


ptf 


321 


32 


64 


96 


128 


161 


193 


225 


257 


289 


321 


& 


320 


32 


64 


96 


128 


160 


192 


224 


256 


288 


320 




319 


32 


64 


96 


128 


160 


191 


223 


255 


287 


3i9 




318 


32 


64 


95 


127 


159 


191 


223 


254 


286 


3i8 




3i7 


32 


63 


95 


127 


159 


190 


222 


254 


285 


3i7 




316 


32 


63 


95 


126 


158 


190 


221 


253 


284 


316 




3i5 


32 


63 


95 


126 


158 


189 


221 


252 


284 


315 




3i4 


3i 


63 


94 


126 


157 


188 


220 


251 


283 


3M 




3i3 


3i 


63 


94 


125 


157 


188 


219 


250 


282 


313 




312 


3i 


62 


94 


125 


156 


187 


218 


250 


281 


312 




311 


3i 


62 


93 


124 


156 


187 


218 


249 


280 


3" 




310 


3i 


62 


93 


124 


155 


186 


217 


248 


279 


310 




309 


3i 


62 


93 


124 


155 


185 


216 


247 


278 


309 




308 


3i 


62 


92 


123 


154 


185 


216 


246 


277 


308 




307 


3i 


61 


92 


123 


154 


184 


215 


246 


276 


307 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



517 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


140 


146128 


6438 


6748 


7058 


7367 


7676 


7985 


8294 


8603 


891 1 


309 


141 


9219 


9527 


9835 


*0I43 


*0449 


*Q756 


*io63 


*i37o 


*i676 


*i982 


307 


142 


1522SS 


2594 


2900 


3205 


35io 


3815 


4120 


4424 


4728 


5°32 


305 


M3 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


7759 


8061 


303 


144 


S362 


8664 


8965 


9266 


9567 


9868 


*oi68 


^0469 


*o769 


*io68 


301 


M5 


161 368 


1667 


1967 


2266 


2564 


2863 


3161 


3460 


375S 


4055 


299 


146 


4353 


4650 


4947 


5244 


5541 


5S38 


6i34 


6430 


6726 


7022 


297 


I4 £ 


7317 


7613 


7908 


8203 


8497 


8792 


9086 


9380 


9674 


9968 


295 


148 


170262 


0555 


0848 


1141 


1434 


1726 


2019 


2311 


2603 


2895 


293 


149 


31S6 


3478 


3769 


4060 


4351 


4641 


4932 


5222 


5512 


5802 291 


150 


176091 


6381 


6670 


6959 


7248 


7536 


.7825 


8113 


8401 


8689 


289 


151 


8977 


9264 


9552 


9839 


*OI26 


*04i3 


^0699 


*0986 


*1272 


*I558 


287 


152 


181844 


2129 


2415 


2700 


2985 


3270 


3555 


3839 


4123 


4407 


285 


153 


4691 


4975 


5259 


5542 


5825 


6108 


6391 


6674 


6956 


7239 


283 


154 


7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


*oo5i 


281 


155 


190332 


0612 


0892 


1171 


145 1 


1730 


2010 


22S9 


2567 


2846 


279 


156 


3125 


3403 


3681 


3959 


4237 


4514 


4792 


5069 


5346 


5623 


278 


157 


5900 


6176 


6453 


6729 


7005 


7281 


7556 


7S32 


8107 


.8382 


276 


158 


8657 


8932 


9206 


948i 


9755 


*0029 


#0303 


*Q577 


*0850 


*II24 


274 


159 


201397 


1670 


1943 


2216 


24S8 


2761 


3033 


3305 


3577 


3848 


272 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




306 


3i 


61 


92 


122 


153 


184 


214 


245 


275 


306 




305 


3i 


61 


92 


122 


153 


183 


214 


244 


275 


305 




304 


30 


61 


. 9i 


122 


152 


182 


213 


243 


274 


304 




303 


30 


61 


91 


121 


152 


182 


212 


242 


273 


303 




302 


30 


60 


91 


121 


151 


181 


211 


242 


272 


302 




301 


30 


60 


90 


120 


151 


181 


211 


241 


271 


301 




300 


30 


60 


90 


120 


150 


180 


210 


240 


270 


300 




299 


30 


60 


90 


120 


150 


179 


209 


239 


269 


299 




298 


30 


60 


89 


119 


149 


179 


209 


238 


268 


298 




297 


30 


59 


89 


119 


149 


178 


208 


238 


267 


297 




296 


30 


59 


89 


11S 


148 


178 


207 


237 


266 


.296 


CO 


295 


30 


59 


89 


118 


148 


177 


207 


236 


266 


295 


294 


29 


59 


88 


118 


147 


176 


206 


235 


265 


294 


< 


293 


29 


59 


88 


117 


147 


176 


205 


234 


264 


293 


ft 


292 


29 


58 


88 


117 


146 


175 


204 


234 


263 


292 


< 


291 


29 


58 


87 


116 


146 


175 


204 


233 


262 


291 


290 


29 


58 


87 


116 


145 


i74 


203 


232 


261 


290 


z 


28g 


29 


58 


87 


116 


145 


173 


202 


231 


260 


28g 





288 


29 


58 


86 


115 


144 


173 


202 


230 


259 


288 


H 


287 


29 


57 


86 


115 


144 


172 


201 


230 


258 


287 


X 


286 


29 


57 


86 


114 


143 


172 


200 


229 


257 


286 





285 


29 


57 


86 


114 


143 


171 


200 


228 


257 


285 


a* 


284 


28 


57 


85 


114 


142 


170 


199 


227 


256 


284 





283 


28 


57 


85 


113 


142 


170 


198 


226 


255 


283 


tt 
& 


282 


28 


56 


85 


113 


141 


169 


197 


226 


254 


282 


281 


28 


56 


84 


112 


141 


169 


197 


225 


253 


281 




280 


28 


56 


84 


112 


140 


168 


196 


224 


252 


280 




279 
278 


28 


56 


84 


112 


140 


167 


195 


223 


251 


279 




28 


56 


83 


in 


139 


167 


195 


222 


250 


278 




277 


28 


55 


83 


in 


139 


166 


194 


222 


249 


277 




276 


28 


55 


83 


no 


138 


166 


193 


221 


248 


276 




275 


28 


55 


83 


no 


138 


165 


193 


220 


248 


275 




274 


27 


55 


82 


no 


137 


164 


192 


219 


247 


274 




273 


27 


55 


82 


109 


137 


164 


191 


218 


246 


273 




272 


27 


54 


82 


109 


136 


163 


190 


218 


245 


272 





271 


27 


54 


81 


108 


136 


163 


190 


217 


244 


271 
Diff. 


Diff.. 


I 


2 


3 


4 


5 


6 


7 


8 


9 



5i 



LOGARITHMS OF NUMBERS 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


1 60 


204120 


439i 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


161 


6S26 


7096 


7365 


7634 


7904 


8i73 


8441 


8710 


8979 


9247 


269 


162 


9515 


9783 


^0051 


*03 1 9 


*0586 


*o853 


*II2I 


*I388 


*i654 


*I92I 


267 


163 


212188 


2454 


2720 


2986 


3252 


35i8 


3783 


4049 


4314 


4579 


266 


164 


4844 


5109 


5373 


5638 


5902 


6166 


643O 


6694 


6957 


7221 


264 


165 


217484 


7747 


8010 


8273 


8536 


8798 


9060 


9323 


9585 


9846 


262 


166 


220108 


0370 


0631 


0S92 


"53 


1414 


1675 


1936 


2196 


2456 


261 


167 


2716 


2976 


3236 


3496 


3755 


4015 


4274 


4533 


4792 


5051 


259 


168 


5309 


5568 


5826 


60S4 


6342 


6600 


6858 


7"5 


7372 


7630 


258 


169 


7887 


8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


*oi 9 3 


256 


170 


230449 


0704 


0960 


1215 


1470 


1724 


1979 


2234 


2488 


2742 


255 


171 


2996 


3250 


3504 


3757 


401 1 


4264 


4517 


4770 


5023 


5276 


253 


172 


5528 


578i 


6033 


6285 


6537 


6789 


704I 


7292 


7544 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


9550 


9800 


*oo5o 


*03oo 


250 


174 


240549 


0799 


1048 


1297 


1546 


1795 


2044 


2293 


2541 


2790 


249 


175 


243038 


32S6 


3534 


3782 


4030 


4277 


4525 


4772 


5019 


5266 


248 


176 


5513 


5759 


6006 


6252 


6499 


6745 


699I 


7237 


7482 


7728 


246 


177 


7973 


8219 


8464 


8709 


8954 


919S 


9443 


9687 


9932 


*oi76 


245 


178 


250420 


0664 


0908 


1151 


1395 


1638 


1881 


2125 


2368 


2610 


243 


179 


2853 


3096 


3338 


358o 


3822 


4064 


4306 


4548 


4790 


5031 


242 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




272 


27 


54 


82 


109 


136 


163 


190 


218 


245 


272 




271 


27 


54 


81 


108 


136 


163 


190 


217 


244 


271 




270 


27 


54 


81 


108 


135 


162 


189 


216 


243 


270 




269 


27 


54 


81 


108 


135 


161 


188 


215 


242 


26g 




268 


27 


54 


80 


107 


134 


161 


188 


214 


241 


268 




267 


27 


53 


80 


107 


134 


160 


187 


214 


240 


267 




266 


- 27 


53 


80 


106 


133 


160 


186 


213 


239 


266 




265 


27 


53 


80 


106 


133 


159 


186 


212 


239 


265 




264 


26 


53 


79 


106 


132 


158 


185 


211 


238 


264 


ro 


263 


26 


53 


79 


105 


132 


158 


184 


210 


237 


263 


H 


262 


26 


52 


79 


105 


131 


157 


183 


210 


236 


262 


ti 


261 


26 


52 


78 


104 


131 


157 


183 


209 


235 


261 


< 

a, 

< 
Z 

O 


260 


26 


52 


78 


104 


130 


156 


182 


208 


234 


260 


259 


26 


52 


78 


104 


130 


155 


181 


207 


233 


259 


258 


26 


52 


77 


103 


129 


155 


181 


206 


232 


258 


257 


26 


5i 


77 


103 


129 


154 


180 


206 


231 


257 


256 


26 


5i 


77 


102 


128 


154 


179 


205 


230 


256 


255 


26 


5i 


77 


102 


128 


153 


179 


204 


230 


255 


H 


254 


25 


5i 


76 


102 


127 


152 


178 


203 


229 


254 


& 


253 


25 


5i 


76 


IOI 


127 


152 


177 


202 


228 


253 


O 
(X 
O 


252 


25 


50 


76 


IOI 


126 


151 


176 


202 


227 


252 


251 


25 


50 


75 


100 


126 


151 


176 


201 


226 


251 


tf 


250 


25 


50 


75 


IOO 


125 


150 


175 


200 


225 


250 


& 


249 


25 


50 


75 


IOO 


125 


149 


174 


199 


224 


249 




248 


25 


50 


74 


99 


124 


149 


174 


198 


223 


248 




247 


25 


49 


74 


99 


124 


148 


173 


198 


222 


247 




246 


25 


49 


74 


9? 


123 


148 


172 


197 


221 


246 




245 


25 


49 


74 


9 ^ 


123 


147 


172 


196 


221 


245 




244 


24 


49 


73 


98 


122 


146 


171 


i95 


220 


244 




243 


24 


49 


73 


97 


122 


146 


170 


194 


219 


243 




242 


24 


48 


73 


97 


121 


145 


169 


194 


218 


242 




241 


24 


48 


72 


96 


121 


145 


169 


193 


217 


241 




240 


24 


48 


72 


96 


120 


144 


168 


192 


216 


240 


, 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Dill. 









LOGARITHMS 


OF 


NUMBERS 




519 


- 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


i8o 


255273 


5514 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


7439 


241 


181 


7679 


7918 


S158 


8398 


8637 


SS77 


9116 


9355 


9594 


9833 


239 


182 


260071 


0310 


0548 


0787 


1025 


1263 


1501 


1739 


1976 


2214 


238 


183 


2451 


26S8 


2925 


3162 


3399 


3636 


3873 


4109 


4346 


4582 


237 


184 


4818 


5054 


5290 


5525 


576i 


5996 


6232 


6467 


6702 


6937 


235 


185 


267172 


7406 


7641 


7875 


8110 


8344 


8578 


8812 


9046 


9279 


234 


186 


9513 


9746 


9980 


*02I3 


^446 


*o679 


*09I2 


*ii44 


*i377 


*i6o9 


233 


187 


271842 


2074 


2306 


2538 


2770 


3001 


3233 


3464 


3696 


3927 


232 


188 


4158 


4389 


4620 


4850 


5081 


53i 1 


5542 


5772 


6002 


6232 


230 


189 


6462 


6692 


6921 


7151 


7380 


7609 


7838 


8067 


8296 


8525 


229 , 


190 


278754 


S982 


9211 


9439 


9667 


9895 


*OI23 


*Q35i 


*o 57 8 


*o8o6 


228 


191 


281033 


1261 


1488 


1715 


1942 


2169 


2396 


2622 


2849 


3075 


227 


ig2 


3301 


3527 


3753 


3979 


4205 


4431 


4656 


4882 


5107 


5332 


226 


193 


5557 


5782 


6007 


6232 


6456 


66S1 


6905 


7130 


7354 


7578 


225 


194 


7802 


8026 


8249 


8473 


8696 


8920 


9 T 43 


9366 


9589 


9812 


223 


195 


290035 


0257 


04S0 


0702 


0925 


1147 


1369 


i59i 


1813 


2034 


222 


196 


2256 


2478 


2699 


2920 


3Hi 


3363 


3584 


3804 


4025 


4246 


221 


197 


4466 


4687 


4907 


5127 


5347 


5567 


5787 


6007 


6226 


6446 


220 


198 


6665 


6S84 


7104 


7323 


7542 


7761 


7979 


8198 


8416 


8635 


219 


199 


8853 


9071 


9289 


9507 


9725 


9943 


*oi6i 


^378 


^595 


*o8i 3 


218 


200 


301030 


1247 


1464 


1681 


1898 


2114 


2331 


2547 


2764 


2980 


217 


201 


3196 


34i2 


3628 


3844 


4059 


4275 


4491 


4706 


4921 


5136 


216 


202 


535i 


5566 


578i 


599 6 


6211 


6425 


6639 


6854 


7068 


7282 


215 


203 


7496 


7710 


7924 


8i37 


8351 


8564 


8778 


8991 


9204 


9417 


213 


204 


9630 


9843 


*oo56 


*0268 


*048i 


*o693 


*o9o6 


*iii8 


*i33° 


*I542 1 212 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




239 
238 


24 


48 


72 


96 


120 


143 


167 


191 


215 


239 




24 


48 


71 


95 


119 


i43 


167 


190 


214 


238 




237 


24 


47 


71 


95 


119 


142 


166 


190 


213 


237 




236 


24 


47 


71 


94 


118 


142 


165 


189 


212 


236 




235 


24 


47 


71 


94 


118 


141 


165 


188 


212 


235 




234 


23 


47 


70 


94 


117 


140 


164 


187 


211 


234 




233 


23 


47 


70 


93 


117 


140 


163 


186 


210 


233 


(W 


232 


23 


46 


70 


93 


116 


139 


162 


186 


209 


232 


< 


231 


23 


46 


69 


92 


116 


139 


162 


185 


208 


231 


230 


23 


46 


69 


92 


115 


138 


161 


184 


207 


230 


a< 


229 


23 


46 


69 


92 


115 


i37 


160 


183 


206 


229 


_j 


228 


23 


46 


68 


9i 


114 


137 


160 


182 


205 


228 


< 


227 


23 


45 


68 


9i 


114 


136 


159 


182 


204 


227 


z 


226 


23 


45 


68 


90 


113 


136 


158 


181 


203 


226 





225 


23 


45 


68 


90 


113 


135 


158 


180 


203 


225 


*-* 


224 


22 


45 


67 


90 


112 


134 


157 


179 


202 


224 


223 


22 


45 


67 


89 


112 


i34 


156 


178 


201 


223 


O 


222 


22 


44 


67 


89 


in 


133 


155 


178 


200 


222 


cu 


221 


22 


44 


66 


88 


in 


133 


155 


177 


199 


221 




0. 


220 


22 


44 


66 


8S 


no 


132 


154 


176 


198 


220 


219 


22 


44 


66 


88 


no 


131 


153 


175 


197 


2ig 




218 


22 


44 


65 


87- 


109 


131 


153 


174 


196 


218 




217 


22 


43 


65 


87 


109 


130 


152 


174 


i95 


217 




216 


22 


43 


65 


86 


108 


130 


151 


173 


194 


216 




215 


22 


43 


65 


86 


108 


129 


151 


172 


194 


215 




214 


21 


43 


64 


86 


107 


128 


150 


171 


193 


214 


j 


213 


21 


43 


64 


85 


107 


128 


149 


170 


192 


213 


„ 


212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 


Diff. 


I 


2 


3 


4 


5 


6 


1 7 


8 


9 | Diff - 



S20 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 




Diff. 


205 


311754 


1966 


2177 


2389 


2600 


2812 


3023 


3234 


3445 


3656 


211 


206 


3S67 


4078 


4289 


4499 


4710 


4920 


5130 


534o 


555i 


5760 


210 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


209 


208 


8063 


8272 


8481 


8689 


8898 


9106 


9314 


9522 


9730 


9938 


208 


2og 


320146 


0354 


0562 


0769 


0977 


1 184 


1391 


1598 


1805 


2012 


207 


210 


322219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


206 


211 


4282 


4488 


4694 


4899 


5105 


5310 


5516 


5721 


5926 


6131 


205 


212 


6336 


6541 


6745 


6950 


7i55 


7359 


7563 


7767 


7972 


8176 


204 


213 


8380 


8583 


8787 


8991 


9194 


9398 


9601 


9805 


*ooo8 


*02II 


203 


214 


330414 


0617 


0819 


1022 


1225 


1427 


1630 


1832 


2034 


2236 


202 


215 


332438 


2640 


2842 


3044 


3246 


3447 


3649 


3850 


4051 


4253 


202 


216 


4454 


4655 


4856 


5057 


5257 


5458 


5658 


5859 


6059 


6260 


201 


217 


6460 


6660 


6860 


7060 


7260 


7459 


7659 


7858 


8058 


8257 


200 


218 


8456 


8656 


8855 


9054 


9253 


9451 


9650 


9849 


*oo47 


*0246 


199 


219 


340444 


0642 


0841 


1039 


1237 


1435 


1632 


1830 


2028 


2225 


198 


220 


342423 


2620 


2817 


3014 


3212 


3409 


3606 


3802 


3999 


4196 


197 


221 


4392 


4589 


4785 


4981 


5178 


5374 


5570 


5766 


5962 


6i57 


196 


222' 


6353 


6549 


6744 


6939 


7i35 


7330 


7525 


7720 


7915 


8110 


195 


223 


8305 


8500 


8694 


8889 


9083 


9278 


9472 


9666 


9860 


*oo54 


194 


224 


350248 


0442 


0636 


0829 


1023 


1216 


1410 


1603 


1796 


1989 


193 


225 


352183 


2375 


2568 


2761 


2954 


3147 


3339 


3532 


3724 


3916 


193 


226 


4108 


43oi 


4493 


4685 


4876 


5068 


5260 


5452 


5643 


5834 


192 


227 


6026 


6217 


6408 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 


8125 


8316 


8506 


8696 


8886 


9076 


9266 


9456 


9646 


190 


229 


9835 


*0025 


*02I5 


*0404 


^593 


*0783 


*0972 


*n6i 


*I35° 


**539 


189 


230 


361728 


1917 


2105 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


231 


3612 


3800 


3988 


4176 


4363 


455i 


4739 


4926 


5ii3 


5301 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


6796 


S 83 


7169 


187 


233 


7356 


7542 


7729 


7915 


8101 


8287 


8473 


8659 


8845 


9030 


186 


234 


9216 


9401 


9587 


9772 


9958 


*oi43 


*0328 


*05i3 


*o698 


*o883 


185 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 




211 


21 


42 


63 


84 


106 


127 


148 


169 


190 


211 




210 


21 


42 


63 


84 


105 


126 


147 


168 


189 


210 




209 


21 


42 


63 


84 


105 


125 


146 


167 


188 


209 




208 


21 


42 


62 


83 


104 


125 


146 


166 


187 


208 


207 


21 


4i 


62 


83 


104 


124 


145 


166 


186 


207 


tt 


206 


21 


4i 


62 


82 


103 


124 


144 


165 


185 


206 


< 


205 


21 


4i 


62 


82 


103 


123 


144 


164 


185 


205 


Pa 


204 


20 


4i 


61 


82 


102 


122 


143 


163 


184 


204 


j 


203 


20 


4i 


61 


81 


102 


122 


142 


162 


183 


203 


< 


202 


20 


40 


61 


81 


101 


121 


141 


162 


182 


202 


O 


201 


20 


40 


60 


80 


ior 


121 


141 


161 


181 


201 


200 


20 


40 


60 


80 


100 


120 


140 


160 


180 


200 


1—1 
H 


199 


20 


40 


60 


80 


100 


119 


139 


159 


179 


199 


P* 


198 


20 


40 


59 


79 


99 


119 


139 


158 


178 


198 


O 


197 


20 


39 


59 


79 


99 


118 


138 


158 


177 


197 


04 


ig6 


20 


39 


59 


78 


98 


118 


137 


157 


176 


196 


O 


195 


20 


39 


59 


78 


98 


117 


137 


156 


176 


195 


194 


19 


39 


58 


78 


*97 


116 


136 


155 


i75 


194 


193 


19 


39 


58 


77 


97 


116 


135 


154 


i74 


193 




ig2 


19 


38 


58 


77 


96 


115 


134 


154 


i73 


192 




191 


19 


38 


57 


76 


96 


115 


134 


153 


172 


191 




190 


19 


38 


57 


76 


95 


114 


133 


152 


171 


190 




lB % 


19 


38 


57 


76 


95 


113 


132 


151 


170 


189 




188 


19 


38 


56 


75 


94 


113 


132 


150 


169 


188 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



521 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


235 


371068 


1253 


1437 


1622 


1806 


1991 


2175 


2360 


2544 


2728 


184 


236 


2912 


3096 


3280 


3464 


3647 


3831 


4015 


4198 


4382 


4565 


184 


237 


4748 


4932 


5"5 


5298 


5481 


5664 


5846 


6029 


6212 


6394 


183 


238 


6577 


6759 


6942 


7124 


7306 


7488 


7670 


7852 


8034 


8216 


1S2 


239 


8398 


8580 


8761 


8943 


9124 


9306 


9487 


9668 


9849 


*0030 


181 


240 


3802 1 1 


0392 


0573 


0754 


0934 


i"5 


1296 


1476 


1656 


1837 


181 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


3815 


3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


5606 


5785 


5964 


6142 


6321 


6499 


6677 


6856 


7034 


7212 


178 


244 


739o 


7568 


7746 


7923 


8101 


8279 


8456 


8634 


881 1 


8989 


178 


245 


389166 


9343 


952o 


9698 


9875 


*oo5i 


*0228 


*04Q5 


*0 5 S2 


*0759 


177 


246 


39°935 


1112 


1288 


1464 


1641 


1817 


1993 


2169 


2345 


2521 


176 


247 


2697 


2873 


3048 


3224 


3400 


3575 


3751 


3926 


4101 


4277 


176 


248 


4452 


4627 


4802 


4977 


5152 


5326 


5501 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7766 


174 


250 


397940 


8114 


8287 


8461 


8634 


8808 


8981 


9154 


* 932 ? 


9501 


173 


251 


9674 


9847 


*0020 


*OI92 


^365 


*o 53 8 


*oyii 


*o883 


*io56 


*I228 


173 


252 


401401 


1573 


1745 


1917 


20S9 


2261 


2433 


2605 


2777 


2949 


172 


253 


3121 


3292 


3464 


3635 


3807 


3978 


4149 


4320 


4492 


4663 


171 


254 


4834 


5005 


5176 


5346 


5517 


5688 


5858 


6029 


6199 


637O 


171 


255 


406540 


6710 


688l 


7051 


7221 


7391 


756i 


7731 


7901 


8070 


170 


236 


8240 


8410 


8579 


8749 


8918 


9087 


9257 


9426 


9595 


9764 


169 


257 


9933 *oio2 


*027I 


*0440 


*o6o9 


*0777 


*0946 


*ni4 


"•'1283 


*i45i 


169 


258 


41 1620 


1788 


1956 


2124 


2293 


2461 


2629 


2796 


2964 


3132 


168 


259 


33oo 


3467 


3635 


3803 


3970 


4137 


4305 


4472 


4039 


4806 


167 


260 


414973 


5140 


5307 


5474 


5641 


5808 


5974 


6141 


6308 


6474 


167 


261 


6641 


6807 


6973 


7139 


7306 


7472 


7638 


7804 


797o 


8i35 


166 


262 


8301 


8467 


8633 


8798 


8964 


9129 


9295 


9460 


9625 


9791 


165 


263 


9956 


*OI2I 


*0286 


*045i 


*o6i6 


*o78i 


*0945 


*IIIO 


*i275 


*I439 


165 


264 


421604 


1768 


1933 


2097 


2261 


2426 


2590 


2754 


2918 


3082 


164 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


187 


19 


37 


56 


75 


94 


112 


131 


150 


168 


187 




186 


19 


37 


56 


74 


93 


112 


130 


149 


167 


186 




x ! 5 


19 


37 


56 


74 


93 


in 


130 


148 


167 


185 




184 


18 


37 


55 


74 


92 


no 


129 


147 


166 


184 




183 


18 


37 


55 


73 


92 


no 


128 


146 


165 


183 


CO 


182 


18 


36 


55 


73 


9i 


109 


127 


146 


164 


182 


H 


181 


18 


36 


54 


72 


9i 


109 


127 


145 


163 


181 


tt 


180 


18 


36 


54 


72 


90 


108 


126 


144 


162 . 


180 


< 


179 


18 


36 


54 


72 


90 


107 


125 


143 


161 


179 




178 


18 


36 


53 


7i 


89 


107 


125 


142 


160 


178 


h3 


177 


18 


35 


53 


7i 


89 


106 


124 


142 


159 


177 


< 


176 


18 


35 


53 


70 


88 


106 


123 


141 


158 


176 


Z 


175 


18 


35 


53 


70 


88 


105 


123 


140 


158 


175 


O 


174 


17 


35 


52 


70 


87 


104 


122 


139 


157 


174 


H 


173 


17 


35 


52 


69 


87 


104 


121 


138 


156 


173 


X 


172 


17 


34 


52 


69 


86 


103 


120 


138 


155 


172 


O 


171 


17 


34 


5i 


68 


86 


103 


120 


i37 


154 


171 


O 


170 


17 


34 


5i 


68 


85 


102 


119 


136 


153 


170 


K 


i6g 


17 


34 


5i 


68 


85 


101 


118 


i35 


152 


i6g 


0. 


168 


17 


34 


50 


67 


84 


101 


118 


134 


151 


168 




167 


17 


33 


50 


67 


84 


100 


117 


i34 


150 


167 




166 


17 


33 


50 


66 


83 


100 


116 


133 


149 


166 




165 


17 


33 


50 


66 


83 


99 


116 


132 


149 


165 




164 
Diff. 


16 

I 


33 


49 


66 


82 


98 


115 


131 


14S 


164 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























522 



LOGARITHMS OF NUMBERS 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


— 1 
Diflf. 


265 


423246 


34io 


3574 


3737 


3901 


4065 


4228- 


4392 


4555 


4718 


164 


266 


4882 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6186 


6349 


163 


267 


651 1 


6674 


6836 


6999 


7161 


7324 


7486 


7648 


781 1 


7973 


162 


268 


8135 


8297 


8459 


8621 


8783 


8944 


9106 


9268 


9429 


,959i 


162 


269 


9752 


9914 


*oo75 


*0236 


*o 39 8 


*0559 


*0720 


*o88i 


*I042 


*I203 


161 


270 


431364 


1525 


1685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


2969 


3130 


3290 


3450 


3610 


377o 


3930 


4090 


4249 


4409 


160 


272 


4569 


4729 


4888 


5048 


5207 


5367 


5526 


5685 


5844 


6004 


159 


273 


6163 


6322 


6481 


6640 


6799 


6957 


7116 


7275 


7433 


7592 


159 


274 


775i 


7909 


8067 


8226 


8384 


8542 


8701 


8859 


9017 


9175 


158 


275 


439333 


9491 


9648 


9806 


9964 


*OI22 


*o279 


^437 


*0594 


*o752 


158 


276 


440909 


1066 


1224 


1381 


1538 


1695 


1852 


2009 


2166 


2323 


157 


277 


2480 


2637 


2793 


2950 


3106 


3263 


3419 


3576 


3732 


3889 


157 


278 


4045 


4201 


4357 


4513 


4669 


4825 


4981 


5137 


5293 


5449 


156 


279 


5604 


5760 


5915 


6071 


6226 


6382 


6537 


6692 


6848 


7003 


155 


280 


447158 


7313 


7468 


7623 


7778 


7933 


8088 


8242 


8397 


8552 


155 


281 


8706 


8861 


9015 


9170 


9324 


9478 


9633 


9787 


9941 


*oo95 


154 


282 


450249 


0403 


0557 


0711 


0865 


1018 


1 172 


1326 


1479 


1633 


154 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


2859 


3012 


3165 


153 


284 


33i8 


347i 


3624 


3777 


3930 


4082 


4235 


4387 


454o 


4692 


153 


285 


454845 


4997 


5150 


5302 


5454 


5606 


5758 


59io 


6062 


6214 


152 


286 


6366 


6518 


6670 


6821 


6973 


7125 


7276 


7428 


7579 


7731 


152 


287 


7882 


8033 


8184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


151 


288 


9392 


9543 


9694 


9845 


9995 


*oi46 


^0296 


*0447 


*c>597 


*0748 


151 


289 


460898 


1048 


1 198 


1348 


1499 


1649 


1799 


1948 


2098 


2248 


150 


290 


462398 


2548 


2697 


2847 


2997 


3146 


3296 


3445 


3594 


3744 


150 


291 


3893 


4042 


4191 


434o 


4490 


4639 


4788 


4936 


5085 


5234 


149 


292 


5383 


5532 


5680 


5829 


5977 


6126 


6274 


6423 


6571 


6719 


149 


293 


6868 


7016 


7164 


7312 


7460 


7608 


7756 


7904 


8052 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9085 


9233 


9380 


9527 


9675 


148 


295 


469822 


9969 


*on6 


*o26>3 


*04io 


*o557 


*o704 


*o85i 


^0998 


*ii45 


147 


296 


471292 


1438 


1585 


1732 


1878 


2025 


2171 


2318 


2464 


2610 


146 


297 


2756 


2903 


3049 


3195 


3341 


3487 


3633 


3779 


3925 


4071 


146 


298 


4216 


4362 


4508 


4653 


4799 


4944 


5090 


5235 


538i 


5526 


146 


299 


5671 


5816 


5962 


6107 


6252 


6397 


6542 


6687 


6832 


6976 


145 


N. 


Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 
164 




164 


16 


33 


49 


66 


82 


98 


115 


131 


148 




163 


16 


33 


49 


65 


82 


98 


114 


130 


147 


163 




162 


16 


32 


49 


65 


81 


97 


113 


130 


146 


162 




161 


16 


32 


48 


64 


81 


97 


113 


129 


145 


161 




160 


16 


32 


48 


64 


80 


96 


112 


128 


144 


160 


159 


16 


32 


48 


64 


80 


95 


in 


127 


143 


159 


< 


158 


16 


32 


47 


^ 


79 


95 


in 


126 


142 


158 


& 


157 


16 


3i 


47 


63 


79 


94 


no 


126 


141 


157 


J 


156 


16 


3i 


47 


62 


78 


94 


109 


125 


140 


156 


< 


155 


16 


3i 


47 


62 


78 


93 


109 


124 


140 


155 


z 


154 


15 


3i 


46 


62 


77 


92 


108 


123 


139 


154 


O 


153 


15 


3i 


46 


61 


77 


92 


107 


122 


138 


153 


1— 1 

H 

04 


152 


J 5 I 


30 


46 


61 


76 


91 


106 


122 


137 


152 


151 


15 


30 


45 


60 


76 


91 


106 


121 


136 


151 


O 


150 


15 


30 


45 


60 


75 


90 


105 


120 


135 


150 


O 

P-i 


149 


15 


30 


45 


60 


75 


§ 9 


104 


119 


134 


149 


148 


15 


30 


44 


59 


74 


89 


104 


118 


133 


148 


147 


15 


29 


44 


59 


74 


88 


103 


118 


132 


147 




146 


15 


29 


44 


5 § 


73 


88 


102 


117 


131 


146 




145 


15 


29 


44 


58 


73 


87 


I02 


116 


131 


M5 




144 


14 


29 


43 


58 


72 


86 


IOI 


115 


130 


144 




143 


14 


29 


43 


57 


72 


86 


IOO 


114 


129 


143 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 



LOGARITHMS OF NUMBERS 



523 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


300 


477121 


7266 


741 1 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


145 


301 


8566 


8711 


8855 


8999 


9M3 


9287 


943i 


9575 


9719 


9863 


144 


302 


480007 


0151 


0294 


0438 


0582 


0725 


0869 


1012 


1 156 


1299 


144 


303 


1443 


1586 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


2731 


143 


304 


2874 


3016 


3159 


3302 


3445 


3587 


3730 


3872 


4015 


4i57 


143 


305 


484300 


4442 


4585 


4727 


4869 


501 1 


5153 


5295 


5437 


5579 


142 


306 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


142 


307 


7138 


7280 


7421 


7503 


7704 


7845 


7986 


8127 


8269 


8410 


141 


308 


8551 


8692 


8833 


8974 


,9H4 


9255 


9396 


9537 


9677 


9818 


141 


309 


9958 


*oo99 


*0239 


*038o 


*0520 


*o66i 


*o8oi 


*094i 


*io8i 


*I222 


140 


310 


491362 


1502 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


3ii 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


312 


4155 


4294 


4433 


4572 


4711 


4850 


4989 


5128 


5267 


5406 


139 


313 


5544 


5683 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


679I 


139 


3M 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


315 


4983 1 1 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


.9550 


138 


316 


9687 


9824 


9962 


*oo99 


*o236 


*©374 


*05 1 1 


*o648 


*0785 


^0922 


137 


317 


50i 59 


1 196 


1333 


1470 


1607 


1744 


1880 


2017 


2154 


229I 


137 


3i8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


35i8 


3655 


136 


319 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


505150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


637O 


136 


321 


6505 


6640 


6776 


691 1 


7046 


7181 


7316 


745i 


7586 


7721 


135 


322 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


323 


9203 


9337 


9471 


9606 


9740 


9874 


*ooo9 


*oi43 


*o277 


*04ii 


134 


324 


510545 


0679 


0813 


0947 


1081 


1215 


1349 


1482 


1616 


I750 


134 


325 


511883 


2017 


2151 


2284 


2418 


2551 


2684 


2818 


2951 


3084 


133 


326 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4415 


133 


327 


4548 


4681 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


328 


5874 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


132 


329 


7196 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330 


518514 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


331 


9828 


9959 


*oo9o 


*022I 


*0353 


*o484 


*o6i5 


*0745 


*o876 


*ioo7 


131 


332 


5 2II 38 


1269 


1400 


I530 


1661 


1792 


1922 


2053 


2183 


2314 


131 


333 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


334 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 


4785 


4915 


130 


335 


525045 


5174 


5304 


5434 


5563 


5693 


5822 


595i 


6081 


6210 


129 


336 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7243 


7372 


75oi 


129 


337 


7630 


7759 


7888 


8016 


8i45 


8274 


8402 


8531 


8660 


8788 


129 


338 


8917 


9045 


9*74 


9302 


9430 


9559 


9687 


9815 


9943 


*0072 


128 


339 


530200 


0328 


0456 


0584 


0712 


0840 


0968 


1096 


1223 


1351 


128 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




142 


14 


28 


43 


57 


71 


85 


99 


114 


128 


142 


tn 


141 


14 


28 


42 


56 


71 


85 


99 


113 


127 


141 


< 


140 


14 


28 


42 


56 


70 


84 


98 


112 


126 


140 


139 


14 


28 


42 


56 


70 


83 


97 


in 


125 


139 


fc 


138 


14 


28 


4i 


55 


69 


83 


97 


no 


124 


138 


< 
O 


137 


14 


27 


4i 


55 


69 


82 


96 


no 


123 


137 


136 


14 


27 


4i 


54 


68 


82 


95 


109 


122 


136 


135 


14 


27 


4i 


54 


68 


81 


95 


108 


122 


135 


134 


13 


27 


40 


54 


67 


80 


94 


107 


121 


134 


133 


13 


27 


40 


53 


67 


80 


93 


106 


I20 


133 


O 
0. 


132 


13 


26 


40 


53 


66 


79 


92 


106 


119 


132 


131 


13 


26 


39 


52 


66 


79 


92 


105 


Il8 


131 


130 


13 


26 


39 


52 


65 


78 


9i 


104 


117 


130 





129 


13 


26 


39 


52 


65 


77 


9° 


103 


Il6 


129 


ft 

1 * 


128 


13 


26 


38 


5i 


64 


77 


90 


102 


115 


128 


127 


13 


25 


38 


5i 


64 


76 


89 


102 


114 


127 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



524 



LOGARITHMS OF NUMBERS 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


34° 


531479 


1607 


1734 


1862 


1990 


2117 


2245 


2372 


2500 


2627 


128 


341 


2754 


2882 


3009 


3136 


3264 


3391 


3518 


3645 


3772 


3899 


127 


342 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


5041 


5167 


127 


343 


5294 


5421 


5547 


5674 


5800 


5927 


6053 


6i8-> 


6306 


6432 


126 


344 


6558 


6685 


681 1 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


345 


537819 


7945 


8071 


8197 


8322 


8448 


8574 


8699 


8825 


8951 


126 


346 


9076 


9202 


9327 


9452 


9578 


9703 


9829 


99J4 


*oo79 


*0204 


125 


347 


540329 


0455 


0580 


0705 


0830 


0955 


1080 


1205 


1330 


1454 


125 


348 


1579 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


349 


2825 


2950 


3074 


3199 


3323 


3447 


357i 


3696 


3820 


3944 


124 


350 


544068 


4192 


43i6 


4440 


4564 


4688 


4812 


4936 


5060 


5183 


124 


35i 


5307 


543i 


5555 


5678 


5802 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6666 


6789 


6913 


7036 


7159 


7282 
8512 


7405 


7529 


7652 


123 


353 


7775 


7898 


8021 


8144 


8267 


8389 


8635 


8758 


8881 


123 


354 


9003 


9126 


9249 


937i 


9494 


9616 


9739 


9861 


9984 


*oio6 


123 


355 


550228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


1328 


122 


356 


145° 


1572 


1694 


1816 


1938 


2060 


2181 


2303 


2425 


2547 


122 


357 


2668 


2790 


291 1 


3033 


3155 


3276 


3398 


3519 


3640 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


473i 


4852 


4973 


121 


359 


5094 


5215 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


556303 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7387 


I20 


361 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8349 


8469 


8589 


I20 


362 


8709 


8829 


8948 


9068 


9188 


93o8 


9428 


9548 


9667 


9787 


I20 


363 


9907 


*0026 


*oi46 


*0265 


*o 3 8 5 


*0504 


*o624 


*o743 


*o863 


♦0982 


II 9 


364 


561 101 


1221 


1340 


1459 


1578 


1698 


1817 


1936 


2055 


2174 


119 


365 


562293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


II 9 


366 


348i 


360O 


37i8 


3837 


3955 


4074 


4192 


43i 1 


4429 


4548 


* n 2 


367 


4666 


4784 


4903 


5021 


5139 


5257 


5376 


5494 


5612 


5730 


118 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


n8 


36g 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


n8 


37o 


568202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


37i 


9374 


949I 


960S 


9725 


9842 


9959 


*oo76 


*oi93 


^309 


*0426 


117 


372 


570543 


0660 


0776 


0893 


IOIO 


1 126 


1243 


1359 


1476 


1592 


117 


373 


1709 


1825 


1942 


2058 


2174 


2291 


2407 


2523 


2639 


2755 


n6 


374 


2872 


2988 


3 J o4 


3220 


3336 


3452 


3568 


3684 


3800 


3915 


116 


375 


574031 


4H7 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5188 


5303 


5419 


5534 


5 6 50 


5765 


5880 


5990 


6111 


6226 


115 


377 


6341 


6457 


6572 


66S7 


6802 


6917 


7032 


7147 


. 7262 


7377 


115 


378 


7492 


7607 


7722 


7836 


7951 


8066 


81S1 


8295 


8410 


8525 


115 


379 


8639 


8754 


8868 


8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




128 


13 


26 


38 


51 


64 


77 


90 


102 


115 


128 




127 


13 


25 


38 


51 


64 


76 


89 


102 


114 


127 


00 


126 


13 


25 


38 


50 


63 


76 


88 


IOI 


113 


126 


125 


13 


25 


38 


50 


63 


75 


88 


100 


113 


125 


< 


124 


12 


25 


37 


50 


62 


74 


87 


99 


112 


124 


Ah 


123 


12 


25 


37 


49 


62 


74 


86 


98 


in 


123 




122 


12 


24 


37 


49 


61 


73 


85 


98 


no 


122 


(U 


121 


12 


24 


36 


48 


61 


73 


85 


97 


109 


121 


O 


120 


12 


24 


36 


48 


60 


72 


84 


96 


108 


120 


Oh 


iiq 


12 


24 


36 


48 


60 


7i 


83 


95 


107 


119 




118 


12 


24 


35 


47 


59 


7i 


83 


94 


106 


118 




117 


12 


23 


35 


47 


59 


70 


82 


94 


105 


117 




116 


12 


23 


35 


46 


58 


7o 


81 


93 


104 


116 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



525 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

! 


380 


579784 


9S9S 


*OOI2 


*OI26 


*024I 


*°355 


*0469 


*o 5 8 3 


*o697 


*o8n 


114 


381 


580925 


1039 


1153 


1267 


1381 


1495 


1608 


1722 


1836 


1950 


114 


382 


2063 


2177 


229I 


2404 


2518 


2631 


2745 


2858 


2972 


3085 


114 


383 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 


113 


384 


4331 


4444. 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


113 


385 


585461 


5574 


5686 


5799 


5912 


6024 


6i37 


6250 


6362 


6475 


113 


386 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


7486 


7599 


112 


387 


771 1 


7823 


7935 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


388 


8832 


8944 


9056 


9167 


9279 


939i 


9503 


9615 


9726 


9838 


112 


389 


9950 


*oo6i 


*oi73 


*o284 


*0396 


*0507 


*o6i9 


*0730 


*o842 


*0953 


112 


390 


59i° 6 5 


1176 


1287 


1399 


1510 


162 1 


1732 


1843 


1955 


2066 


in 


391 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


2954 


3064 


3^75 


in 


392 


3286 


3397 


35o8 


3618 


3729 


3840 


3950 


4061 


4171 


4282 


in 


393 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 


no 


394 


5496 


5606 


5717 


5827 


5937 


6047 


6i57 


6267 


6377 


6487 


no 


395 


596597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


7586 


no 


396 


7695 


7805 


79H 


8024 


8i34 


8243 


8353 


8462 


8572 


8681 


no 


397 


8791 


8900 


9009 


9119 


9228 


9337 


9446 


. 955 £ 


9665 


9774 


109 


398 


9883 


9992 


*OIOI 


*02IO 


^319 


♦0428 


*0537 


*o646 


*0755 


*o864 


109 


399 


600973 


1082 


1 191 


I299 


1408 


1517 


1625 


1734 


1843 


I95i 


109 


400 


602060 


2169 


2277 


2386 


2494 


2603 


2711 


2819 


2928 


3036 


108 


401 


3144 


3253 


336i 


3469 


3577 


36S6 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


49S2 


5089 


5197 


108 


403 


5305 


5413 


5521 


5628 


5736 


5844 


5951 


6059 


6166 


6274 


108 


404 


6381 


6489 


6596 


6704 


6811 


6919 


7026 


7133 


7241 


7348 


107 


405 


607455 


7562 


7669 


7777 


7884 


7991 


8098 


8205 


8312 


8419 


107 


406 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


938i 


9488 


107 


407 


9594 


9701 


9808 


9914 


*002I 


*OI28 


*o234 


*o 3 4i 


*0447 


*0554 


107 


408 


610660 


0767 


0873 


0979 


IO86 


1192 


1298 


1405 


1511 


1617 


106 


409 


1723 


1829 


1936 


2042 


2148 


2254 


2360 


2466 


2572 


2678 


106 


410 


612784 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 


106 


411 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


4581 


4686 


4792 


106 


412 


4897 


5003 


5108 


5213 


5319 


5424 


5529 


5634 


5740 


5845 


105 


413 


5950 


6055 


6160 


6265 


637O 


6476 


6581 


6686 


6790 


6895 


105 


414 


7000 


7105 


7210 


7315 


7420 


7525 


7629 


7734 


7839 


7943 


105 


415 


618048 


8i53 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


416 


9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


*0032 


104 


A1 l 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


1072 


104 


418 


1176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2IIO 


104 


4 ig 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 


104 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




"5 


12 


23 


35 


46 


58 


69 


81 


92 


104 


"5 




114 


n 


23 


34 


46 


57 


68 


80 


91 


103 


114 


W 


"3 


n 


23 


34 


45 


5 J 


68 


79 


90 


102 


"3 


H 
< 


112 


n 


22 


34 


45 


56 


67 


78 


90 


IOI 


112 


in 


n 


22 


33 


44 


56 


67 


78 


89 


IOO 


in 


no 


n 


22 


33 


44 


55 


66 


77 


88 


99 


no 


O 

Oh 


log 


n 


22 


33 


44 


55 


65 


76 


87 


98 


109 


108 


n 


22 


32 


43 


54 


65 


76 


86 


97 


108 


107 


n 


21 


32 


43 


54 


64 


75 


86 


96 


107 


106 


11 


21 


32 


42 


53 


64 


74 


85 


95 


106 




105 


n 


21 


32 


42 


53 


63 


74 


84 


95 


105 




104 


10 


21 


3i 


42 


52 


62 


73 


83 


94 


104 




103 


10 


21 


3i 


4i 


52 


62 


72 


82 


93 


103 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



526 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 


5 


fc 


7 


8 


9 


Diff. 

103 


420 


623249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5004 


5i°7 


5210 


103 


422 


5312 


5415 


5518 


5621 


5724 


5827 


5929 


6032 


6135 


6238 


103 


423 


6340 


6443 


6546 


6648 


6751 


6853 


6956 


7058 


7161 


7263 


103 


424 


7366 


7468 


7571 


7673 


7775 


7878 


7980 


8082 


8185 


8287 


102 


4 2 5 


628389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


426 


9410 


9512 


9613 


9715 


9817 


9919 


*002I 


*OI23 


*6224 


#0326 


102 


427 


630428 


0530 


0631 


0733 


0835 


0936 


IO38 


1139 


1241 


1342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


2255 


2356 


IOI 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3x65 


3266 


3367 


IOI 


430 


633468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


IOI 


43i 


4477 


4578 


4679 


4779 


4880 


4981 


5081 


5182 


5283 


5383 


IOI 


432 


5484 


5584 


5685 


5785 


5^86 


5986 


6087 


6187 


6287 


6388 


IOO 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


739° 


IOO 


434 


7490 


7590 


7690 


7790 


7890 


7990 


809O 


8190 


8290 


8389 


IOO 


435 


638489 


8589 


8689 


8789 


8888 


8988 


9088 


9188 


9287 


9387 


IOO 


436 


9486 


9586 


9686 


9785 


9885 


9984 


*oo84 


*oi83 


*028 3 


$0382 


99 


437 


640481 


0581 


0680 


0779 


0879 


0978 


1077 


1177 


1276 


1375 


99 


438 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


643453 


3551 


3650 


3749 


3847 


3946 


4044 


4H3 


4242 


434o 


98 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 


98 


442 


5422 


552i 


5619 


5717 


5815 


5913 


6011 


6110 


6208 


6306 


98 


443 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


444 


7383 


748i 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 


98 


445 


648360 


8458 


8555 


8653 


8750 


8848 


8945 


9043 


9140 


9237 


97 


446 


9335 


9432 


9530 


9627 


9724 


9821 


9919 


*ooi6 


*oii3 


*02I0 


97 


447 


650308 


0405 


0502 


0599 


0696 


0793 


0890 


0987 


1084 


Il8l 


97 


448 


1278 


1375 


1472 


1569 


1666 


1762 


1859 


1956 


2053 


2150 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3Il6 


97 


450 


653213 


3309 


3405 


3502 


3598 


3695 


379i 


3888 


3984 


4080 


96 


45i 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 


96 


452 


5138 


5235 


5331 


5427 


5523 5619 


5715 


5810 


5906 


6002 


96 


453 


6098 


6194 


6290 


6386 


64S2 


6577 


6673 


6769 


6864 


6960 


96 


454 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 


96 


455 


6580 1 1 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


887O 


95 


456 


8965 


9060 


* 9I5 £ 


9250 


9346 


9441 


9536 


9631 


9726 


982I 


95 


457 


9916 


*OOII 


*oio6 


*020I 


*0296 


^391 


#0486 


*058i 


*o676 


*077i 


95 


458 


660865 


0960 


1055 


II5O 


1245 


1339 


1434 


1529 


1623 


1718 


95 


459 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 


95 


460 


662758 


2852 


2947 


3041 


3135 


3230 


3324 


34i8 


3512 


3607 


94 


461 


3701 


3795 


3889 


3983 


4078 


4172 


4266 


4360 


4454 


4548 


94 


462 


4642 


4736 4830 


4924 


5018 


5112 


5206 


5299 


5393 


5487 


94 


463 


558i 


5675 


5769 


5862 


5956 


6050 


6143 


6237 


6331 


6424 


94 


464 


6518 


6612 


6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 


94 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




104 


10 


21 


31 


42 


52 


62 


73 


83 


94 


104 


CO 

H 


103 


10 


21 


31 


41 


52 


62 


72 


82 


93 


103 


102 


10 


20 


31 


41 


51 


61 


7i 


82 


92 


102 


< 


101 


10 


20 


30 


40 


51 


61 


7i 


81 


9i 


IOI 


& 


100 


10 


20 


30 


40 


50 


60 


70 


80 


90 


IOO 


cu 


99 


10 


20 


30 


40 


50 


59 


69 


79 


89 


gg 





q8 


10 


20 


29 


39 


49 


59 


69 


78 


88 


98 


tf 


97 


10 


19 


29 


39 


49 


58 


68 


78 


87 


97 


04 


96 


10 


19 


29 


38 


48 


58 


67 


77 


86 


96 




95 


10 


19 


29 


38 


48 


57 


67 


76 


86 


95 




Diff. 


X 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

1 



LOGARITHMS OF NUMBERS 



527 



In. 

! 465 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


667453 


7546 


7640 


7733 


7826 


7920 


8013 


8106 


8199 


8293 


93 


466 


S3S6 


8479 


8572 


8665 


8759 


8852 


8945 


9038 


9131 


9224 


93 


467 


9317 


9410 


9503 


9596 


9689 


9782 


9875 


9967 


*oo6o 


*oi53 


93 


468 


670246 


0339 


0431 


0524 


0617 


0710 


0802 


0895 


0988 


10S0 


93 


469 


1 173 


1265 


1358 


145 1 


1543 


1636 


1728 


182 1 


1913 


2005 


93 


470 


672098 


2190 


2283 


2375 


2467 


2560 


2652 


2744 


2836 


2929 


92 


471 


3021 


3ii3 


3205 


3297 


3390 3482 


3574 


3666 


3758 


3850 


92 


472 


3942 


4°34 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 


92 


473 


4861 


4953 


5045 


5137 


5228 


5320 


54i2 


5503 


5595 


5687 


92 


n74 


5778 


5870 


5962 


6053 


6145 


6236 


6328 


6419 


6511 


6602 


92 


475 


676694 


6785 


6876 


6968 


7059 


7151 


7242 


7333 


7424 


75i6 


91 


476 


7607 


7698 


7789 


7881 


7972 


8063 


8154 


8245 


8336 


8427 


9i 


477 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


9i 


478 


9428 


9519 


9610 


9700 


9791 


9882 


9973 


*oo63 


*oi54 


*0245 


9i 


479 


680336 


0426 


0517 


0607 


0698 


0789 


0879 


0970 


1060 


1151 


9i 


480 


681241 


1332 


1422 


1513 


1603 


1693 


1784 


1874 


1964 


2055 


90 


481 


2145 


2235 


2326 


2416 


2506 


2596 


2686 


2777 


2867 


2957 


90 


482 


3047 


3137 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 


1 483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 


484 


4845 


4935 


5025 


5ii4 


5204 


5294 


5383 


5473 


5563 


5652 


90 


485 


685742 


5831 


5921 


6010 


6100 


6189 


6279 


6368 


6458 


6547 


89 


486 


6636 


6726 


6815 


6904 


6994 


7083 


7172 


7261 


7351 


7440 


89 


487 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


8i53 


8242 


8331 


89 


488 


8420 


8509 


8598 


8687 


8776 


8865 


8953 


9042 


9131 


9220 


89 


489 


9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 


*ooi9 


*oio7 


89 


490 


690196 


0285 


0373 


0462 


0550 


0639 


0728 


0816 


0905 


0993 


89 


491 


1081 


1170 1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 


88 


492 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 


2671 


2759 


88 


493 


2847 


2935 


3023 


3111 


3i99 


3287 


3375 


3463 


355i 


3639 


88 


494 


c 3727 


3815 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 


88 


495 


694605 


4693 


47Sl 


4868 


4956 


5044 


5131 


5219 


5307 


5394 


88 


496 


5482 


5569 


5657 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 


497 


6356 


6444 


6531 


6618 


6706 


6793 


6880 


6968 


7055 


7142 


87 


498 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 


7926 


8014 


87 


499 


8101 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


500 


698970 


9057 


9144 


9231 


93i7 


9404 


9491 


9578 


9664 


9751 


87 


501 


9838 


9924 


*OOII 


*oo98 


*oi84 


*027I 


*o 35 8 


*0444 


*o53i 


*o6i7 


ll 


502 


700704 0790 


0877 


0963 


1050 


1136 


1222 


1309 


1395 


1482 


86 


503 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


504 


2431 


2517 


2603 


2689 


' 2775 


2861 


2947 


3033 


3ii9 


3205 


86 


505 


703291 


3377 


3463 


3549 


3635 


3721 


3807 


3893 


3979 


4065 


86 


506 


415 1 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


86 


507 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


508 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 


6632 


85 


509 


6718 


6803 


6888 


6974 


7059 


7144. 


7229 


7315 


7400 


7485 


85 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


94 


9 


19 


28 


38 


47 


5 $ 


66 


75 


85 


94 


CO 


93 


9 


19 


28 


37 


47 


56 


65 


74 


84 


93 


tf 


92 


9 


18 


28 


37 


46 


55 


64 


74 


83 


92 


< 


9i 


9 


18 


27 


36 


46 


55 


64 


73 


82 


9i 


ft 


90 


9 


18 


27 


36 


45 


54 


63 


72 


81 


90 


cC 


89 


9 


18 


27 


36 


45 


53 


62 


7i 


80 


89 





88 


9 


18 


26 


35 


44 


53 


62 


70 


79 


88 


tt 


87 


9 


17 


26 


35 


44 


52 


61 


70 


78 


87 


d. 


86 ( 


9 


17 


26 


34 


43 


52 


60 


69 


77 


86 




85 


9 


17 


26 


34 


43 


5i 


60 


68 


77 


85 




Diff. 


I 


2 


3 


4 5 


6 


7 


8 


9 


Diff. 



528 



LOGARITHMS OF NUMBERS 



' N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


5io 


707570 


7655 


7740 


7826 


791 1 


7996 


8081 


8166 


8251 


8336 


85 


5" 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9 OI 5 


9100 


9185 


85 


512 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 


*oo33 


85 


513 


710117 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0879 


85 


514 


0963 


1048 


1132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 


84 


5i5 


71 1807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


84 


5i6 


2650 


2734 


2818 


2902 


2986 


3070 


3154 


3238 


3323 


3407 


84 


517 


349 1 


3575 


3659 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


5i8 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


84 


519 


5167 


5251 


5335 


5418 


5502 


5586 


5669 


5753 


5836 


5920 


84 


520 


716003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 


83 


521 


6838 


6921 


7004 


70S8 


.7171 


7254 


7338 


7421 


7504 


7587 


83 


522 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


523 


8502 


8585 


8668 


8751 


8834 


8917 


9000 


9083 


9165 


9248 


83 


524 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


991 1 


9994 


*oo77 


83 


525 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0903 


83 


526 


0986 


1068 


1151 


1233 


1316 


1398 


148 1 


1563 


1646 


1728 


82 


527 


1811 


1893 


1975 


2058 


2140 


2222 


2305 


2387 


2469 


2552 


82 


528 


2634 


2716 


2798 


28SI 


2963 


3045 


3127 


3209 


3291 


3374 


82 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


53o 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


493i 


5013 


82 


53i 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 


82 


532 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 


82 


533 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


746o 


81 


534 


7541 


7623 


7704 


7785 


^866 


7948 


8029 


8110 


8191 


8273 


81 


535 


728354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


81 


536 


9165 


9246 


9327 


9408 


94-89 


9570 


9651 


9732 


9813 


9893 


81 


537 


9974 


*oo55 


*oi36 


*02IJ 


^0298 


*o 37 8 


*0459 


*0540 


*062I 


*070 2 


81 


53C 


730782 


0863 


0944 


1024 


1 105 


1 186 


1266 


1347 


1428 


1508 


8i 


539 


1589 


1669 


1750 


1830 


1911 


1991 


2072 


2152 


2233 


2313 


81 


54o 


732394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3ii7 


80 


54i 


3197 


3278 


3358 


3438 


35i8 


3598 


3679 


3759 


3839 


3919 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


456o 


4640 


4720 


80 


543 


4800 


4880 


4960 


5040 


5120 


5200 


5279 


5359 


5439 


5519 


80 


544 


5599 


5679 


5759 


5838 


59i8 


5998 


6078 


6i57 


6237 


6317 


80 


545 


736397 


6476 


6556 


6635 


6715 


6795 


6874 


6954 


7034 


7ii3 


80 


546 


7193 


7272 


7352 


7431 


75" 


759o 


7670 


7749 


7829 


7908 


79 


547 


7987 


8067 


8146 


8225 


8305 


8384 


8463 


8543 


8622 


8701 


79 


1 548 


8781 


8860 


8939 


9018 


9097 


9177 


9256 


. 933 5 


9414 


9493 


79 


549 


9572 


9651 


9731 


9810 


9889 


9968 


*oo47 


*OI26 


*0205 


*0284 


79 


55c- 


740363 


0442 


0521 


0600 


0678 


0757 


0836 


0915 


0994 


1073 


79 


55i 


1152 


1230 


1309 


1388 


1467 


1546 


1624 


1703 


1782 


i860 


79 


552 


1939 


2018 


2096 


2175 


2254 


2332 


241 1 


2489 


2568 


2647 


79 


553 


2725 


2804 


2882 


2961 


3039 


3118 


3196 


3275 


3353 


3431 


78 


554 


3510 


3588 


3667 


3745 


3^23 


3902 


3980 


4058 


4136 


4215 


78 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


w 

[h 


86 


9 


17 


26 


. 34 


43 


52 


60 


69 


77 


86 


X 


85 


9 


17 


26 


34 


43 


51 


60 


68 


77 


85 


< 


84 


8 


17 


25 


34 


42 


50 


59 


67 


76 


84 


fc 


83 


8 


17 


25 


33 


42 


50 


58 


66 


75 


83 


. 


82 


8 


16 


25 


33 


4i 


49 


57 


66 


74 


82 


cu 


81 


8 


16 


24 


32 


4i 


49 


57 


65 


73 


81 




04 


80 


8 


16 


24 


32 


40 


48 


56 


64 


72 


80 


cw 


79 


8 


16 


24 


32 


40 


47 


55 


63 


7i 


79 


1 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



529 



N. 
555 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


744293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


78 


556 


5075 


5153 


5231 


5309 


5387 


5465 


5543 


5621 


5699 


5777 


78 


557 


5S55 


5933 


601 1 


60S9 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7955 


8033 


8110 


78 


560 


748188 


8266 


8343 


8421 


8498 


8576 


8653 


873i 


8808 


8885 


77 


561 


8963 


9040 


9118 


9 J 95 


9272 


9350 


9427 


9504 


9582 


9659 


77 


562 


9736 


9S14 


9891 


9968 


*oo45 


*OI23 


*0200 


*0277 


*0354 


*043i 


77 


5 6 3 


750508 


0586 


0663 


0740 


0817 


0894 


O97I 


1048 


1125 


1202 


77 


564 


1279 


1356 


1433 


1510 


1587 


1664 


1741 


1818 


1895 


1972 


77 


565 


752048 


2125 


2202 


2279 


2356 


2433 


2509 


2586 


2663 


2740 


77 


566 


2S16 


2893 


2970 


3047 


3123 


3200 


3277 


3353 


3430 


35o6 


77 


567 


35S3 


3660 


3736 


3S13 


3889 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


4501 


4578 


4654 


4730 


4807 


4883 


4960 


5036 


76 


569 


5112 


5i89 


5265 


5341 


5417 


5494 


5570 


5646 


5722 


5799 


76 


57o 


755875 


5951 


6027 


6103 


6180 


6256 


6332 


6408 


6484 


6560 


76 


57i 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7548 


7624 


7700 


7775 


7851 


7927 


8003 


8079 


76 


573 


8i55 


8230 


8306 


8382 


8458 


8533 


8609 


8685 


8761 


8836 


76 


574 


8912 


89S8 


9063 


9*39 


9214 


9290 


9366 


9441 


9517 


9592 


76 


575 


759668 


9743 


9819 


9894 


9970 


*oo45 


*OI2I 


*oi96 


*0272 


*Q347 


75 


576 


760422 


0498 


0573 


0649 


0724 


0799 


0875 


0950 


IO25 


IIOI 


75 


577 


1176 


1251 


1326 


1402 


1477 


1552 


1627 


1702 


1778 


1853 


75 


578 


1928 


2003 


2078 


2153 


2228 


2303 


2378 


2453 


2529 


2604 


75 


579 


2679 


2754 


2S29 


2904 


2978 


3053 


3128 


3203 


3278 


3353 


75 


580 


763428- 


3503 


3578 


3653 


3727 


3802 


3877 


3952 


4027 


4101 


75 


581 


4176 


4251 


4326 


4400 


4475 


455o 


4624 


4699 


4774 


4848 


75 


582 


4923 


4998 


5072 


5H7 


5221 


5296 


5370 


5445 


552o 


5594 


75 


583 


5669 


5743 


5818 


5892 


5966 


6041 


6lI5 


6190 


6264 


6338 


74 


584 


6413 


6487 


6562 


6636 


6710 


6785 


6859 


6933 


7007 


70S2 


74 


585 


767156 


7230 


73°4 


7379 


7453 


7527 


760I 


7675 


7749 


7823 


74 


586 


7898 


7972 


8046 


8120 


8i94 


8268 


8342 


8416 


8490 


8564 


74 


587 


8638 


8712 


87S6 


8860 


8934 


9008 


9082 


9^6 


9230 


9303 


74 


588 


9377 


945i 


9525 


9599 


9673 


9746 


9820 


9894 


996S 


*0O42 


74 


589 


7701 15 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 


0778 


74 


590 


770852 


0926 


0999 


1073 


1 146 


1220 


I293 


1367 


1440 


1514 


74 


59i 


1587 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 


73 


592 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2S35 


2908 


2981 


73 


593 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4298 


4371 


4444 


73 


595 


774517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


5100 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


5610 


56S3 


5756 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


641 1 


6483 


6556 


6629 


73 


598 


6701 


6774 


6S46 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7S62 


7934 


8006 


8079 


72 


N. 


Biff. 1 1 2 3 4 5 


6 


7 


8 


9 


Diff. 


CO 


78 1 8 


16 23 


31 


39 


47 


55 


62 


70 


78 


tt 


77 8 


15 23 


3i 


39 


46 


54 


62 


69 


77 


< 


76 


8 


15 23 


30 


38 


46 


53 


61 


68 


76 


cu 


75 


8 


15 


23 


30 


38 


45 


53 


60 


68 


75 





74 


7 


15 


22 | 30 


37 


44 


52 


59 


67 


74 


73 


7 


15 


22 j 29 


37 


44 


5i 


58 


66 


73 


72 


7 


14 


22 I 29 


36 


43 


50 


58 


65 


72 
Diff, 




Diff. 


I 


2 3 4 5 


6 


7 


8 


9 



53o 



LOGARITHMS OF NUMBERS 



N. 

600 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


778i5i 


8224 


8296 


8368 


8441 


8513 


8585 


8658 


8730 


8802 


72 


601 


8874 


8947 


9019 


9091 


9163 


9236 


9308 


9380 


9452 


9524 


72 


602 


959 6 


9669 


9741 


9813 


9885 


9957 


*0029 


*OIOI 


*oi73 


*o245 


72 


603 


780317 


0389 


0461 


0533 


0605 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1 109 


Il8l 


1253 


1324 


1396 


1468 


1540 


1612 


1684 


72 


605 


781755 


1827 


1899 


197 1 


2042 


2114 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3ii7 


72 


607 


3189 


3260 


3332 


3403 


3475 


3546 


3618 


3689 


376i 


3832 


71 


608 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


4403 


4475 


4546 


71 


609 


4617 


4689 


4760 


4831 


4902 


4974 


5045 


5116 


5187 


5259 


71 


610 


785330 


54oi 


5472 


5543 


5615 


5686 


5757 


5828 


5899 


597o 


71 


611 


6041 


6112 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


612 


6751 


6822 


6893 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


71 


613 


7460 


753i 


7602 


7673 


7744 


78i5 


7885 


7956 


8027 


8098 


71 


614 


8168 


8239 


8310 


8381 


8451 


8522 


8593 


8663 


8734 


8804 


71 


6*5 


788875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


95io 


71 


616 


958i 


9651 


9722 


9792 


9S63 


9933 


*ooo4 


*oo74 


*oi44 


*02I5 


70 


617 


790285 


0356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 


0988 


1059 


1129 


1 199 


1269 


1340 


1410 


1480 


I550 


1620 


70 


6ig 


169 1 


1761 


1831 


1901 


1971 


2041 


2111 


2181 


2252 


2322 


70 


620 


792392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


3162 


3231 


33oi 


3371 


344i 


35i 1 


358i 


3651 


3721 


70 


622 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


5115 


70 


624 


5185 


5254 


5324 


5393 


5463 


5532 


5602 


5672 


5741 


581 1 


70 


625 


79588o 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 


69 


626 


6574 


6644 


6713 


67S2 


6852 


6921 


6990 


7060 


7129 


7198 


69 


627 


7268 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 


7890 


69 


628 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 


69 


629 


8651 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


630 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 


69 


631 


800029 


0098 


0167 


0236 


0305 


0373 


0442 


051 1 


0580 


0648 


69 


632 


0717 


0786 


0854 


0923 


0992 


106 1 


1129 


1 198 


1266 


1335 


69 


633 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 


69 


634 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 


68 


635 


802774 


2842 


2910 


2979 


3047 


3116 


3184 


3252 


3321 


3389 


68 


636 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


407 i 


68 


637 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 


68 


638 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


639 


5501 


5569 


5637 


5705 


5773 


5S41 


5908 


5976 


6044 


6112 


68 


640 


806180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 


68 


641 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8i43 


68 


643 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8953 


9021 


9088 


9 J 56 


9223 


9290 


9358 


9425 


9492 


67 


645 


809560 


9627 


9694 


9762 


9829 


9896 


9964 


*oo3i 


^0098 


*oi65 


67 


646 


810233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 


67 


647 


0904 


0971 


1039 


1106 


"73 


1240 


1307 


1374 


144 1 


1508 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 


67 


649 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 


67 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


w 


73 


7 


15 


22 


29 


37 


44 


51 


58 


66 


73 


H 


72 


7 


14 


22 


29 


36 


43 


50 


58 


6s 


72 


0< 


7i 


7 


14 


21 


28 


36 


43 


50 


57 


64 


7i 


. 


70 


7 


14 


21 


28 


35 


42 


49 


56 


63 


70 


O 


6q 


7 


14 


21 


2S 


35 


4i 


48 


55 


62 


69 


& 


68 


7 


14 


20 


27 


34 


4i 


48 


54 


61 


68 

Diff. 

1 




Diff. 


I 


2 


3 


4 


5 


* 


7 


8 


9 



LOGARITHMS OF NUMBERS 



S3 1 



N, 


O 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

67 


650 


812913 


2980 


3047 


3114 


3181 


3247 


33H 


3381 


3448 


35i4 


651 


35Si 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 


67 


652 


4248 


43i4 


43Si 


4447 


4514 


4581 


4647 


4714 


4780 


4847 


67 


653 


4913 


4980 


5046 


5113 


5i79 


5246 


5312 


5378 


5445 


55i 1 


66 


654 


5578 


5<M4 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


816241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 


66 


656 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 


66 


657 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


659 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 


66 


660 


819544 


9610 


9676 


9741 


9807 


9873 


9939 


*ooo4 


*oo7o 


^0136 


66 


661 


820201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 


66 


662 


0858 


0924 


0989 


1055 


1120 


1 186 


1251 


1317 


1382 


1448 


66 


663 


1514 


1579 


1645 


1710 


1775 


184 1 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 


65 


665 


822822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 


65 


666 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


4321 


4386 


4451 


45i6 


458i 


4646 


4711 


65 


668 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


536i 


65 


669 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 


65 


670 


826075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 


65 


673 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


829304 


9368 


9432 


9497 


956i 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


*OOII 


*oo75 


*oi39 


*0204 


*0268 


*o332 


*0396 


^0460 


*<>525 


64 


677 


830589 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1 166 


64 


678 


1230 


1294 


1358 


1422 


i486 


1550 


1614 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 


64 


680 


832509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 


64 


681 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


372i 


64 


682 


3784 


3848 


3912 3975 


4039 


4103 


4166 


4230 


4294 


4357 


64 


683 


4421 


4484 


4548 


461 1 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 


63 


685 


835691 


5754 


5817 


5881 


5944 


6007 


6071 


6i34 


6197 


6261 


63 


686 


6324 


6387 


6451 


65H 


6577 


6641 


6704 


6767 


6830 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 


63 


688 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156 


63 


689 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 


63 


690 


838849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415 


63 


6gi 


9478 


954i 


9604 


9667 


9729 


9792 


9855 


9918 


9981 


*oo43 


63 


692 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608 


0671 


63 


693 


0733 


0796 


0859 


0921 


0984 


1046 


1 109 


1172 


1234 


1297 


63 


694 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


i860 


1922 


63 


695 


841985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484 


2547 


62 


6g6 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 


62 


697 


3233 


3295 


3357 


3420 


3482 


3544 


3606 


3669 


3731 


3793 


62 


698 


3855 


3918 


3980 


4042 


4104 


4166 


4229 


4291 


4353 


4415 


62 


699 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5 36 


62 


N. 


Diff. 


I 


2 


3 4 


5 


6 


7 


8 


9 


Diff. 




67 


7 


13 


20 


27 


34 


40 


47 


54 


60 


67 


h 


66 


7 


13 


20 


26 


33 


40 


46 


53 


59 


66 




65 


7 


13 


20 


26 


33 


39 


46 


52 


59 


65 


6 


l A 


6 


13 


19 


26 


32 


38 


45 


5i 


58 


64 


04 


63 


6 


13 


19 


25 


32 


.38 


44 


50 


57 


63 


62 


6 


12 


19 


25 


3i 


37 


43 


50 


56 


62 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



532 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 5 


6 


7 


8 


9 


Diff. 
62 


700 


845098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


701 


5718 


578o 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 


62 


703 


6955 


7017 


7079 


714I 


7202 


7264 


7326 


7388 


7449 


75i 1 


62 


704 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 


62 


705 


848189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 


62 


706 


8805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 


61 


707 


9419 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


991 1 


9972 


61 


708 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0585 


61 


7og 


0646 


0707 


0769 


0830 


0891 0952 


1014 


1075 


1 136 


1 197 


61 


710 


851258 


1320 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 


61 


711 


1870 


193 1 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


713 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 


61 


714 


3698 


3759 


3820 


3881 


394i 


4002 


4063 


4124 


41S5 


4245 


61 


715 


854306 


4367 


4428 


4488 


4549 


4610 


4670 


473i 


4792 


4852 


6r 


716 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 


61 


717 


5519 


558o 


5640 


570I 


576i 


5822 


5882 


5943 


6003 


6064 


61 


718 


6124 


6185 


6245 


6306 


6366 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 


60 


720 


857332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


78i5 


7875 


60 


721 


7935 


7995 


8056 


8116 


8176 


8236 


8297 


8357 


8417 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8958 


9018 


9078 


60 


723 


9138 


9198 


9258 


93i8 


9379 


9439 


.,9499 


.9559 


9619 


9679 


60 


724 


9739 


9799 


9859 


9918 


9978 


*oo38 


*oo98 


*oi58 


*02l8 


*0278 


60 


725 


860338 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


1056 


1116 


1176 


1236 


1295 


1355 


14 15 


1475 


60 


727 


1534 


1594 


1654 


1714 


1773 


1833 


1893 


1952 


2012 


2072 


60 


728 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2549 


2608 


2668 


60 


729 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 


60 


730 


863323 


3382 


3442 


3501 


356i 


3620 


3680 


3739 


3799 


3858 


59 


731 


39i7 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 


59 


732 


45i 1 


4570 


4630 


4689 


4748 


4808 


4867 


4926 


4985 


5045 


59 


733 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


5578 


5637 


59 


734 


5696 


5755 


5814 


5874 


5933 


5992 


6051 


6110 


6169 


6228 


59 


735 


866287 


6346 


6405 


6465 


6524 


6583 


6642 


6701 


6760 


6819 


59 


736 


6878 


6937 


6996 


7055 


7114 


7173 


7232 


7291 


7350 


7409 


59 


737 


7467 


7526 


7585 


7644 7703 


7762 


7821 


7880 


7939 


7998 


59 


738 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 


59 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9 J 73 


59 


740 


869232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


74i 


9818 


9877 


9935 


9994 


*oo53 


*OIII 


*oi70 


*0228 


^0287 


*0345 


59 


742 


870404 


0462 


0521 


0579 


0638 


0696 


0755 


0813 


0872 


0930 


58 


743 


0989 


1047 


1 106 


1 164 


1223 


1281 


1339 


1398 


1456 


1515 


58 


744 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


I98 1 


2040 


2098 


58 


745 


872156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 


58 


746 


2739 


2797 


2855 


2913 


2972 


3030 


3088 


3146 


3204 


3262 


58 


747 


3321 


3379 


3437 


3495 


3553 


361 1 


3669 


3727 


3785 


3844 


58 


748 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 


4366 


4424 


58 


749 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5003 


58 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




62 


6 


12 


19 


25 


31 


37 


43 


50 


56 


62 


ft, 


61 


6 


12 


18 


24 


31 


37 


43 


49 


55 


61 




60 


6 


12 


18 


24 


30 


36 


42 


48 


54 


60 


O 


59 


6 


12 


18 


24 


30 


35 


4i 


47 


53 


59 




58 


6 


12 


17 


23 


29 


35 


4i 


46 


52 


58 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



533 



N. 


O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


75° 


875061 


5ii9 


5177 


5235 


5293 


535i 


5409 


5466 


5524 


5582 


58 


75i 


5640 


5698 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 


58 


752 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


6737 


58 


753 


6795 


6853 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


73i4 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 


755 


877947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 


57 


756 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9°39 


57 


757 


9096 


9*53 


9211 


9268 


9325 


9383 


9440 


9497 


9555 


9612 


57 


758 


9669 


9726 


97S4 


9841 


9898 


9956 


*ooi3 


*oo7o 


*OI27 


*oi85 


57 


759 


880242 


0299 


0356 0413 


0471 


0528 


0585 


0642 


0699 


0756 


57 


760 


880814 


0871 


0928 


0985 


1042 


1099 


1156 


1213 


1271 


1328 


57 


761 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


184 1 


1898 


57 


762 


1955 


2012 


2069 


2126 


2183 


2240 


2297 


2354 


2411 


2468 


57 


763 


2525 


2581 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


3037 


57 


764 


3093 


3150 3207 


3264 


3321 


3377 


3434 


349i 


3548 


3605 


57 


765 


883661 


37i8 1 3775 


3832 


3888 


3945 


4002 


4059 


4115 


4172 


57 


766 


4229 


4285 ■ 4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 1 4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


57 


768 


536i 


54i8 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


57 


769 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 


56 


770 


886491 6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 


56 


771 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


756i 


56 


772 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


8011 


8067 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 


56 


774 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


56 


775 


889302 


9358 


9414 


9470 


9526 9582 


9638 


9694 


9750 


9806 


56 


776 


9862 


9918 


9974 


*oo30 


*oo86 


*oi4i 


*oi97 


*0253 


#0309 


$0365 


56 


777 


890421 


0477 


0533 


0589 


0645 


0700 


0756 


0812 


0868 


0924 


56 


778 


0980 


1035 


1091 


1 147 


1203 


1259 


1314 


1370 


1426 


1482 


56 


779 


1537 


1593 


1649 


I705 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


892095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 


56 


781 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3i5i 


56 


782 


3207 


3262 


33i8 


3373 


3429 


3484 


354o 


3595 


3651 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 


55 


784 


43^6 


437i 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 


55 


7 l 5 


894870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5864 


5920 


55 


787 


5975 


6030 


6085 


6140 


6i95 


6251 


6306 


6361 


6416 


6471 


55 


788 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


55 


789 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


897627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


55 


794 


9821 


9875 


9930 


9985 


*oo39 


*oo94 


*oi49 


*0203 


*0258 


*03I2 


55 


795 


900367 


0422 


0476 


0531 


0586 


0640 


0695 


0749 


0804 


0859 


55 


796 


0913 


0968 


1022 


1077 


1131 


1 186 


1240 


1295 


1349 


1404 


55 


797 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 


54 


N. 

OQ 

H 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


57 


6 


II 


17 


23 


29 


34 


40 


46 


51 


57 


CU 


56 


6 


11 


17 


22 


28 


34 


39 


45 


50 


56 


• 


55 


6 


II 


17 


22 


28 


33 


39 


44 


50 


55 




54 


5 


II 


16 


22 


27 


32 


38 


43 


49 


54 


[ 


Diff. 


I 


2 


3 4 5 


6 


7 


8 


9 


Diff. 

.1 



534 



LOGARITHMS OF NUMBERS 



N. 


O 


I 


2 


3 


4 


5 


6 

1 


, 7 


8 


l 
9 


Diff. 


800 


903090 


3144 


3199 


3253 3307 


3361 


34i6 


3470 


3524 


3578 


54 


801 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


439i 


4445 


4499 


4553 


4607 


4661 


54 


803 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


804 


5256 


53io 


5364 


54i8 


5472 


5526 


558o 


5634 


5688 


5742 


54 


805 


905796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 


54 


807 


6874 


6927 


6981 


7°35 


7089 


7143 


71Q6 


7250 


7304 


7358 


54 


808 


741 1 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 


54 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 


54 


812 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


*oo37 


53 


813 


910091 


0144 


0197 


0251 


0304 


0358 


041 1 


0464 


0518 


0571 


53 


814 


0624 


0678 


0731 


0784 


0838 


0891 


0944 


0998 


1051 


1 104 


53 


815 


911158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 


53 


816 


1690 


1743 


1797 


1850 


1903 


1956 


2009 


2063 


2116 


2169 


53 


817 


2222 


2275 


2328 


2381 


2435 


2488 


2541 


2594 


2647 


2700 


53 


818 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3125 


3178 


3231 


53 


819 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 


3761 


53 


820 


913814 


3867 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


4290 


53 


821 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


5505 


5558 


561 1 


5664 


57i6 


5769 


5822 


5875 


53 


824 


5927 


5980 


6033 


6085 


6138 


6191 


6243 


6296 


6349 


6401 


53 


? 2 2 


916454 


6507 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


6927 


53 


826 


6980 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 


53 


827 


7506 


7558 


761 1 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8030 


8083 


8i35 


8188 


8240 


8293 


8345 


8397 


8450 


8502 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


830 


919078 


9130 


9183 


9235 


9287 


934o 


9392 


9444 


9496 


9549 


52 


831 


9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


*ooi9 


*oo7i 


52 


832 


920123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 


0541 


0593 


52 


833 


0645 


0697 


0749 


0801 


0853 


0906 


0958 


1010 


1062 


1114 


52 


834 


1 166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 


52 


835 


921686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 


52 


836 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 


52 


837 


2725 


2777 


2829 


2881 


2933 


2985 


3°37 


3089 


3 x 4o 


3192 


52 


838 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 


52 


839 


3762 


3814 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


924279 


4331 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


4796 


4848 


4899 


4951 


5°°3 


5°54 


5106 


5157 


5209 


5261 


52 


842 


53i2 


5364 


5415 


5467 


55i8 


557o 


5621 


5673 


5725 


5776 


52 


843 


5828 


5879 


593i 


5982 


6034 


6085 


6137 


6188 


6240 


6291 


5i 


844 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 


5i 


2 4 l 


926857 


6908 


6959 


701 1 


7062 


7114 


7165 


7216 


7268 


7319 


5i 


846 


737o 


7422 


7473 


7524 


7576 . 7627 


7678 


7730 


778i 


7832 


5i 


847 


7883 


7935 


7986 


8037 


8088 8140 


8191 


8242 


8293 


8345 


5i 


848 


8396 


8447 


8498 


8549 


8601 8652 


8703 


8754 


8805 


8857 


5i 


849 


8908 


8959 


9010 


9061 


9112 9163 


9215 


9266 


9317 


9368 


5 1 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
55 


H 


55 


6 


11 


17 


22 


28 


33 


39 


44 


50 


Ph 


54 


5 


11 


16 


22 


27 


32 


38 


43 


49 


54 


• 


53 


5 


11 


16 


21 27 


32 


37 


42 


48 


53 




52 


5 


10 


16 


21 26 


31 


36 


42 


47 


52 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



535 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


1 

\ 

Diff. 
51 


850 


929419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


9879 


851 


9930 


9981 


*0032 


♦0083 


*oi34 


*oi85 


*0236 


*0287 


*o 33 8 


*0389 


51 


852 


930440 


0491 


0542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


5i 


853 


0949 


1000 


1051 


1102 


1153 


1204 


1254 


1305 


1356 


1407 


51 


854 


1458 


1509 


1560 


1610 


1661 


1712 


1763 


1814 


1865 


1915 


51 


855 


931906 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


5 1 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


51 


857 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 


51 


858 


3487 


3538 


3589 


3639 


3690 


3740 


379i 


3841 


3892 


3943 


5i 


859 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 


5i 


860 


934498 


4549 


4599 


4650 


4700 


4751 


480 r 


4852 


4902 


4953 


50 


861 


5003 


5054 


5104 


5154 


5205 


5255 


53o6 


5356 


54o6 


5457 


50 


862 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


59io 


596o 


50 


863 


601 1 


6061 


6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 


50 


864 


65H 


6564 


6614 


6665 


6715 


6765 


6815 


6S65 


6916 


6966 


50 


865 


937016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


50 


866 


75i8 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


867 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


5° 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


50 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


50 


870 


939519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


50 


871 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 


50 


872 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 


50 


873 


1014 


1064 


1114 


1 163 


1213 


1263 


1313 


1362 


1412 


1462 


50 


874 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 


50 


* 75 


942008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 


50 


876 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 


50 


877 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


3593 


3643 


3692 


3742 


379i 


3841 


3890 


3939 


49 


879 


3989 


4038 


4088 


4137 


41S6 


4236 


4285 


4335 


4384 


4433 


49 


880 


944483 


4532 


458i 


4631 


4680 


4729 


4779 


4828 


4877 


4927 


49 


881 


4976 


5025 


5074 


5 12 4 


5173 


5222 


5272 


5321 


537o 


5419 


49 


882 


5469 


55iS 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 


49 


883 


596i 


6010 


6059 


6108 


6157 ' 6207 


6256 


6305 


6354 


6403 


49 


884 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 


49 


S 5 


946943 


6992 


7041 


7090 


7140 


7189 


7238 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 


758i 


7630 


7679 


7728 


7777 


7826 


7875 


49 


887 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 


49 


888 


8413 


8462 


8511 


8560 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 


49 


890 


949390 


9439 


9488 


9536 


9585 


9634 


9683 


9731 


978o 


9829 


49 


891 


9878 


9926 


9975 


*0024 


*oo73 


*OI2I 


*oi70 


*02I9 


*o267 


*03i6 


49 


892 


950365 


0414 


0462 


051 1 


0560 


060S 


0657 


0706 


0754 


0803 


49 


893 


0851 


0900 


0949 


0997 


1046 


I095 


1 143 


1192 


1240 


1289 


49 


894 


1338 


1386 


1435 


1483 


1532 


I580 


1629 


1677 


1726 


1775 


49 


895 


951823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 


48. 


896 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 


48 


897 


2792 


2841 


2S89 


2938 


2986 


3034 


3083 


3131 


3180 


3228 


48 


898 


3276 


3325 


3373 


3421 


347o 


3518 


3566 


3615 


3663 


37i 1 


48 


899 


3760 


3808 


3856 


3905 


3953 


4OOI 


4049 


409S 


4146 


4194 


48 


N. 


Diff. I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


CO 

H 


5i 5 


TO 


15 


20 


26 


31 


36 


41 


46 


5i 


50 1 5 | 10 


15 


20 


25 


30 


35 


40 


45 


50 




49 


5 to 


15 


20 


25 


29 


34 


39 


44 


49 


48 


5 1 10 


14 


19 


24 


29 


34 


38 


43 


48 




Diff. 


1 2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



536 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


4677 


48 


901 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


5110 


5158 


48 


902 


5207 


5255 


5303 


535i 


5399 


5447 


5495 


5543 


5592 


5640 


48 


903 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


6313 


6361 


6409 


6457 


6505 


6553 


6601 


48 


905 


956649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080 


48 


906 


7128 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559 


48 


907 


7607 


7655 


7703 


775i 


7799 


7847 


7894 


7942 


7990 


8038 


48 


908 


8086 


8134 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


8516 


48 


909 


8564 


8612 


8659 


8707 


8755 


8803 


8850 


8898 


8946 


8994 


48 


910 


959041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


947i 


48 


911 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 


9900 


9947 


48 


912 


9995 


*0042 


^0090 


^0138 


*oi85 


*0233 


*028o 


#0328 


#0376 


^423 


48 


913 


960471 


0518 


0566 


0613 


0661 


0709 


0756 


0804 


0851 


0899 


48 


914 


0946 


0994 


1041 


1089 


1 136 


1 184 


1231 


1279 


1326 


1374 


48 


915 


961421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


2511 


2559 


2606 


2653 


2701 


2748 


2795 


47 


918 


2843 


2890 


2937 


2985 


3°3 2 


3079 


3126 


3174 


3221 


3268 


47 


919 


3316 


3363 


34io 


3457 


3504 


3552 


3599 


3646 


3693 


374i 


47 


920, 


963788 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4165 


4212 


47 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4684 


47 


922 


4731 


4778 


4825 


4872 


4919 


4966 


5 OI 3 


5061 


5108 


5155 


47 


923 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


5531 


5578 


5625 


47 


924 


5672 


5719 


5766 


5813 


5860 


59°7 


5954 


6001 


6048 


6095 


47 


925 


966142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 


47 


926 


661 1 


6658 


6705 


6752 


6799 


6845 


6892 


6939 


6986 


7033 


47 


927 


7080 


7127 


7173 


7220 


7267 


73H 


7361 


7408 


7454 


75oi 


47 


928 


7548 


7595 


7642 


7688 


7735 


7782 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8156 


8203 


8249 


8296 


8343 


8390 


8436 


47 


930 


968483 


8530 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8950 


8996 


9043 


9090 


9136 


9183 


9229 


9276 


9323 


9369 


47 


932 


9416 


9463 


9509 


9556 


9602 


9649 


9695 


9742 


9789 


9835 


47 


933 


9882 


9928 


9975 


*002I 


*oo68 


*oii4 


*oi6i 


*0207 


*o254 


*0300 


47 


934 


970347 


0393 


0440 


O486 


0533 


0579 


0626 


0672 


0719 


0765 


46 


935 


970812 


0858 


0904 


095I 


0997 


1044 


1090 


1137 


1183 


1229 


46 


936 


1276 


1322 


1369 


1415 


1461 


1508 


1554 


1601 


1647 


1693 


46 


937 


1740 


1786 


1832 


1879 


1925 


1971 


2018 


2064 


2110 


2157 


46 


938 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


939 


2666 


2712 


2758 


2804 


2851 


2897 


2943 


2989 


3035 


3082 


46 


940 


973128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


39*3 


3959 


4005 


46 


942 


4051 


4097 


4H3 


4189 


4235 


4281 


4327 


4374 


4420 


4466 


46 


943 


4512 


4558 


4604 


465O 


4696 


4742 


4788 


4834 


4880 


4926 


46 


944 


4972 


5018 


5064 


5IIO 


5156 


5202 


5248 


5294 


534o 


5386 


46 


945 


975432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 


46 


946 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 


46 


947 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 


46 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
49 


c/j 
H 


49 


5 


10 


15 


20 


25 


29 


34 


39 


44 


b 


48 


5 


10 


14 


19 


24 


29 


34 


38 


43 


48 




47 


5 


9 


14 


19 


24 


28 


33 


38 


42 


47 




46 


5 


9 


14 


18 


23 


28 


32 


37 


4i 


46 




Diff. 


I 


2 


3 


4 | 5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



537 



N. 



950 


• O 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


977724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 


46 


951 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 


46 


952 


8637 


8683 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 


46 


953 


9°93 


9138 


9184 


9230 


275 


9321 


9366 


9412 


9457 


9503 


46 


954 


9548 


9594 


9639 


9685 


973o' 


9776 


9821 


9867 


9912 


9958 


46 


955 


980003 


0049 0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 


45 


956 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 


45 


957 


0912 


0957 


1003 


1048 


1093 


1139 


1 184 


1229 


1275 


1320 


45 


958 


1366 


1411 


1456 


1 501 


1547 


1592 


1637 


1683 


1728 


1773 


45 


959 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 


45 


g6o 


982271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 


45 


96 1 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 


45 


962 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


358i 


45 


963 


-3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 


45 


964 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4482 


45 


965 


984527 


4572 


46i7 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


45 


966 


4977 


5022 


5067 


5112 


5i57 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


55i6 


5561 


5606 


5651 


5696 


574i 


5786 


5830 


45 


968 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 


45 


969 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 


45 


970 


986772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7i75 


45 


97i 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 


45 


972 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 


45 


973 


8113 


8i57 


8202 


8247 


8291 


8336 


8381 


8425 


8470 


8514 


45 


974 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 


45 


975 


989005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 


45 


976 


945o 


9494 


9539 


9583 


9628 


9672 


9717 


9761 


9806 


9850 


44 


977 


9895 


9939 


9983 


*0028 


^0072 


*oii7 


*oi6i 


*0206 


*0250 


*o294 


44 


978 


990339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 


44 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1 182 


44 


980 


991226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 


44 


981 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 


44 


983 


2554 


2598 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 


44 


984 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392 


44 


9 & 


993436 


3480 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


3833 


44 


986 


3877 3921 


3965 


4009 


4053 


4097 


4141 


4185 


4229 


4273 


44 


9 ll 


4317 


436i 


4405 


4449 


4493 


4537 


4581 


4625 


4669 


4713 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


5152 


44 


989 


5196 


5240 


5284 


5328 


5372 


54i6 


546o 


5504 


5547 


5591 


44 


990 


995635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 


44 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


992 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 


44 


993 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 


44 


994 


7386 


7430 


7474 


7517 


756i 


7605 


7648 


7692 


7736 


7779 


44 


995 


997823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 


44 


996 


8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 


44 


997 


8695 


8739 


8782 


8826 


8869 


8913 


8956 


9000 


9°43 


9087 


44 


998 


9*3* 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 


44 


999 


9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 


N. 


Diff. 


I 


2 3 


4 


5 


' 


7 


8 


9 


Diff. 




46 1 5 


9 14 


18 


23 


28 


32 


37 


41 


46 


Oh 


45 I 5 j 9 i 14 


18 


23 


27 


32 


36 


41 


45 


1 

PR. 


44 1 4 1 9 I 13 


18 


22 


26 


3i 


35 


40 


44 


43 4 


9 1 13 


17 


22 


26 


30 


34 


39 


43 
Diff. 




Diff. I 1 


2 


3 


4 


5 


6 


7 


8 


9 



538 



LOGARITHMS OF NUMBERS 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


IOOO 


000000 


0043 


0087 


0130 


0174 


0217 


0260 


0304 


0347 


0391 


43 


IOOI 


0434 


0477 


0521 


0564 


0608 


0651 


0694 


0738 


0781 


0824 


43 


I002 


0868 


0911 


0954 


0998 


1041 


1084 


1128 


1171 


1214 


1258 


43 


1003 


1301 


1344 


1388 


1431 


1474 


1517 


1561 


1604 


1647 


1690 


43 


1004 


1734. 


1777 


1820 


1863 


1907 


1950 


1993 


2036 


2080 


2123 


43 


1005 


002166 


2209 


2252 


2296 


2339 


2382 


2425 


2468 


2512 


2555 


43 


1006 


2598 


2641 


2684 


2727 


2771 


2814 


2857 


2900 


2943 


2986 


43 


1007 


3029 


3073 


3116 


3159 


3202 


3245 


3288 


333i 


3374 


34i7 


43 


1008 


3461 


3504 


3547 


3590 


3633 


3676 


3719 


3762 


3805 


3848 


43 


ioog 


3891 


3934 


3977 


4020 


4063 


4106 


4149 


4192 


4235 


4278 


43 


IOIO 


004321 


4364 


4407 


4450 


4493 


4536 


4579 


4622 


4665 


4708 


43 


IOII 


4751 


4794 


4837 


4880 


4923 


4966 


5009 


5°52 


5095 


5138 


43 


1012 


5181 


5223 


5266 


5309 


5352 


5395 


5438 


548i 


5524 


5567 


43 


1013 


5609 


5652 


5695 


5738 


578i 


5824 


5867 


5909 


5952 


5995 


43 


1014 


6038 


6081 


6124 


6166 


6209 


6252 


6295 


6338 


6380 


6423 


43 


1015 


006466 


6509 


6552 


6594 


6637 


6680 


6723 


6765 


6808 


6851 


43 


1016 


6894 


6936 


6979 


7022 


7065 


7107 


7150 


7i93 


7236 


7278 


43 


1017 


7321 


7364 


7406 


7449 


7492 


7534 


7577 


7620 


7662 


7705 


43 


1018 


7748 


7790 


7833 


7876 


7918 


7961 


8004 


8046 


8089 


8132 


43 


1019 


8174 


8217 


8259 


8302 


8345 


8387 


8430 


8472 


8515 


8558 


43 


1020 


008600 


8643 


8685 


8728 


8770 


8813 


8856 


8898 


8941 


8983 


43 


102 1 


9026 


9068 


9111 


9153 


9196 


9238 


9281 


9323 


9366 


9408 


42 


1022 


9451 


9493 


9536 


9578 


9621 


9663 


9706 


9748 


9791 


9833 


42 


1023 


9876 


9918 


9961 


*ooo3 


*oo45 


*oo88 


*oi30 


*oi73 


*02I5 


*02 5 8 


42 


1024 


010300 


0342 


0385 


0427 


0470 


0512 


0554 


0597 


0639 


0681 


42 


1025 


010724 


0766 


0809 


0851 


0893 


0936 


0978 


1020 


1063 


1 105 


42 


1026 


1 147 


1190 


1232 


1274 


1317 


1359 


1401 


1444 


i486 


1528 


42 


1027 


1570 


1613 


1655 


1697 


1740 


1782 


1824 


1866 


1909 


1951 


42 


1028 


1993 


2035 


2078 


2120 


2162 


2204 


2247 


2289 


2331 


2373 


42 


1029 


2415 


2458 


2500 


2542 


2584 


2626 


2669 


2711 


2753 


2795 


42 


1030 


012837 


2879 


2922 


2964 


3006 


3048 


3090 


3132 


3174 


3217 


42 


103 1 


3259 


33oi 


3343 


3385 


3427 


3469 


35ii 


3553 


3596 


3638 


42 


1032 


3680 


3722 


3764 


3806 


3848 


3890 


3932 


3974 


4016 


4058 


42 


1033 


4100 


4142 


4184 


4226 


4268 


43io 


4353 


4395 


4437 


4479 


42 


1034 


4521 


4563 


4605 


4647 


4689 


4730 


4772 


4814 


4856 


4898 


42 


1035 


014940 


4982 


5024 


5066 


5108 


5150 


5192 


5234 


5276 


53i8 


42 


1036 


5360 


5402 


5444 


5485 


5527 


5569 


561 1 


5653 


5695 


5737 


42 


1037 


5779 


5821 


5863 


5904 


5946 


5988 


6030 


6072 


6114 


6156 


42 


1038 


6197 


6239 


6281 


6323 


6365 


6407 


6448 


6490 


6532 


6574 


42 


1039 


6616 


6657 


6699 


6741 


6783 


6824 


6866 


6908 


6950 


6992 


42 


1040 


017033 


7075 


7117 


7159 


7200 


7242 


7284 


7326 


7367 


7409 


42 


1041 


7451 


7492 


7534 


7576 


7618 


7659 


7701 


7743 


7784 


7826 


42 


1042 


7868 


7909 


795i 


7993 


8034 


8076 


8118 


8i59 


8201 


8243 


42 


1043 


8284 


8326 


8368 


8409 


8451 


8492 


8534 


8576 


8617 


8659 


42 


1044 


8700 


8742 


8784 


8825 


8867 


8908 


8950 


8992 


9033 


9075 


42 


1045 


019116 


9158 


9199 


9241 


9282 


9324 


9366 


9407 


9449 


9490 


42 


1046 


9532 


9573 


9615 


9656 


9698 


9739 


9781 


9822 


9864 


9905 


4i 


1047 


9947 


9988 


*oo30 


*oo7i 


*oii3 


*oi54 


*oi95 


*0237 


*0278 


*0320 


4i 


1048 


020361 


0403 


0444 


0486 


0527 


0568 


0610 


0651 


0693 


0734 


41 


1049 


0775 


0817 


0858 


0900 


0941 


0982 


1024 


1065 


1 107 


1 148 


41 


1050 


02 1 189 


1231 


1272 


1313 


1355 


1396 


1437 


1479 


1520 


1561 


4i 


N. 


Diff. 


I 


2 

9 


3 


4 


5 


6 


7 


8 


9 


Diff. 
44 


CO 

H 

0. 


44 


4 


13 


18 


22 


26 


31 


35 


40 


43 


4 


9 


13 


17 


22 


26 


30 


34 


39 


43 


a* 


42 


4 


8 


13 


17 


21 


25 


29 


34 


38 


42 


4i 


4 


8 


12 


16 


21 


25 


29 


33 


37 


4i 


1 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



0° LOGARITHMIC SIN., COS., TAN. AND COT * i^ 
, Table 62 79 



M. 



o 

1 
2 
3 
4 
5 
6 

7 
8 

9 

10 
11 
12 
13 

M 
15 



Sin. 



16 

17 
18 

19 
20 
21 
22 

23 
24 

25 

26 

27 
28 

29 

30 

3i 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 
48 

49 
50 
5i 
52 

53 
54 
55 

56 
57 
58 

59 
60 



6.463726 
.764756 
.940847 
7.065786 
7.162696 
.241877 
.308824 
.366816 
.417968 

7.463726 
.505118 
.542906 
.577668 
•609853 

7.639816 
•667845 
.694173 
.718997 
.742478 

7764754 
•785943 
.806146 
.825451 

•843934 
7.861662 
.878695 
.895085 
.910879 
.926119 

7.940842 
.955082 
.968870 
.982233 
.995198 

8.007787 
.020021 

.031919 
.043501 

.054781 

8.065776 
.076500 
.086965 
.097-83 
.107167 
8.116926 
.126471 
.135810 
•144953 
•153907 
8.162681 
.171280 
.179713 
.187985 
.196102 
8.204070 
.211895 
.219581 
.227134 

•234557 
8.241855 



D, i' 



Cos. 



5017.17 
2 934.85 
2082.32 
1615.17 
1319-68 
1115-78 
966.53 

852.53 
762.63 

689.87 
629.80 
579-37 
536.42 
499.38 
467.15 
438.80 

413.73 
39L35 
371.27 

353.15 
336.72 

321.75 
308.05 

295.47 
283.88 

273.17 
263.23 
254-00 
245.38 

237.33 
229.80 
222.72 
216. c8 
209.82 
203.90 
198.30 
193.03 
188.00 
183.25 

178.73 
174-42 
170.30 
166.40 
162.65 
159-08 
155.65 
152.38 
149-23 
146.23 

143.32 
*40.55 
137.87 
135.28 
132.80 
130.42 
128.10 
125.88 
123.72 
121.63 



Cos. 



10.000000 
.000000 
.000000 
.000000 
.000000 
10.000000 
9-999999 
•999999 
.999999 

•999999 
9.999998 

•999998 
.999997 
.999997 
.999996 
9.999996 
•999995 
•999995 
•999994 
•999993 

9-999993 
.999992 
.999991 
•999990 
•999989 

9.999989 
.999988 

•999987 
.999986 

•999985 
9.999983 
.999982 
.999981 
.999980 
.999979 
9.999977 
•999976 
•999975 
•999973 
•999972 

9.999971 
.999969 
.999968 
.999966 
.999964 

9.999963 
.999961 

•999959 
•999958 
.999956 

9-999954 
•999952 
.999950 
•999948 
•999946 

9.999944 
.999942 
•999940 
. 99993 S 
•999936 

9-999934 



D. 1 



Sin. 



D. 1' 



.00 
.00 
.00 
.00 
.02 
.00 
.00 
.00 
.02 

.00 
.02 
.00 
.02 
.00 
.02 
.00 
.02 
.02 
.00 

.02 
.02 
.02 
.02 
.00 
.02 
.02 
.02 
.02 
.03 
.02 
.02 
.02 
.02 

•03 
.02 
.02 

•03 
.02 
.02 

•03 
.02 

•03 
•03 
.02 

•03 
•03 
.02 

•03 
•03 

•03 

•03 

•03 

.03 

•03 

•03 

.03 

.03 • 

•03 

.03 



D. i> 



Tan. 



D. 1". 



6.463726 
.764756 
•940847 
7.065786 
7.162696 
.241878 
.308825 
.366817 
•417970 

7.463727 
.505120 
.542909 
•577672 
.609857 

7.639820 
.667849 
.694179 
.719003 
.742484 

7-764761 
•785951 
.806155 
.825460 
.843944 

7.861674 
.878708 

•895099 
.910894 
•926134 

7.940858 
.955100 
.968889 
•982253 

.995219 
8.007809 
.020044 
•031945 
•043527 
.054809 

8.065806 
.076531 
.086997 
.097217 
.107203 

8. 1 16963 
.126510 

•135851 
.144996 
•153952 

8.162727 
.171328 
.179763 
.188036 
.196156 

8.204126 

•2H953 
219641 
.227195 
.234621 
8.241921 



15017.17 

! 2934.85 
2082.32 
1615.17 
I3I9.70 
III5.78 
966.53 

852.55 
762.62 

689.88 
629.82 
579-38 
536.42 
499-38 
467.15 
438.83 

413.73 
39L35 
37L28 

353.17 
336.73 
321.75 
308.07 

295.50 
283.90 
273.I8 
263.25 
254-00 
245.40 

237.37 
229.82 
222.73 
2I6.IO 
209.83 
203.92 
198.35 
I93.03 
188.03 
183.28 

178.75 
174.43 
170.33 
166.43 
162.67 
159.12 
155-68 
152.42 
149.27 
146.25 

143.35 
140.58 
137.88 

135.33 
132.83 

130.45 
128.13 

125.90 

123.77 
121.67 



Cot. 



3.536274 
•235244 
•059153 
2.934214 
2.837304 
.758122 
.691175 
•633183 



2.536273 
.494880 

.457091 
.422328 

•390143 
2.360180 

•332151 
.305821 
.280997 
•257516 

2.235239 
.214049 

• I 93845 
.174540 
.156056 
2.138326 
.121292 
.104901 
.089106 
.073866 

2.059142 
.044900 
.031 11 1 
.017747 
.004781 

I.992191 
•979956 
.968055 

•956473 
.945191 

1.934194 
•923469 
.913003 
•902783 

•892797 
1.883037 
.873490 
.864149 
.855004 
.846048 

1.837273 
.828672 
.820237 
.811964 
.803844 

I-795874 
.788047 
•780359 
•772805 

•765379 
1.758079 



.582030 51 



Cot. 



D. 



Tan, 



50 
49 
48 

47 
46 

45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

II 

27 

26 

25 
24 

23 
22 
21 

20 

J! 

17 

16 I 

IS) 
M 
13 j 
12 

11 

10 



M 



*From Allen's 
1903, 1914. by C. 



"Field and Office Tables.' 
F. Allen. 



Copyright, 



89 



LOGARITHMIC SINES 



178 



M. 



Sin. 



o 
1 
2 
3 
4 
5 
6 

I 

9 
10 
11 
12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 

3o 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 

59 
60 



8. 241855 

• 249°33 
. 256094 
. 263042 
.269881 

8.276614 
. 283243 
. 289773 
. 296207 
. 302546 

8.308794 

.3H954 
.321027 
.327016 

• 332924 
8.338753 

• 344504 
.350181 

.355783 

.361315 

8. 366777 

.372171 

• 377499 
. 382762 
. 387962 

8.393101 
.398179 
.403199 
. 408161 
. 413068 

8.417919 
.422717 
. 427462 
.432156 
. 436800 

8.441394 

• 445941 
.450440 
.454893 

• 459301 

8.463665 

• 467985 
.472263 

• 47649S 
. 480693 
8. 484848 
.488963 
.493040 
. 497078 
. 501080 

8. 505045 

• 508974 
.512867 
.516726 
.520551 

8. 524343 
.528102 
.531828 

• 535523 
.539186 

8.542819 

Cos. 



D. i' 



119.63 
117.68 
115.80 

113.98 
112.22 
110.48 
108. 83 
107. 23 
105. 65 
104. 13 

102.67 
101. 22 

99.82 
98.47 
97.15 
95.85 
94.62 

93.37 
92. 20 
91.03 

89.90 
88.80 
87.72 
86.67 
85.65 
84.63 
83.67 
82.70 
81.78 
80.85 

79-97 
79.o8 
78.23 
77.40 

76.57 
75.78 
74.98 
74.22 

73-47 
72.73 
72. 00 
71.30 
70.58 
69.92 
69.25 
68.58 

67-95 
67.30 
66.70 
66.08 

65.48 
64.88 
64.32 
63.75 
63.20 
62.65 
62. 10 
61.58 
61.05 

60.55 
D. 1". 



Cos. D. 1". Tan. D. 1 



999934 
999932 
999929 
999927 
999925 
999922 
999920 
999918 
999915 
999913 
999910 
999907 
999905 
999902 

999899 
999897 
999894 
999891 



999885 



999879 
999876 
999873 
999870 
999867 
999864 
999861 
999858 
999854 
999851 
999848 
999844 
999841 

999838 
999834 
999831 

999827 
999824 
999820 

999816 
999813 
999809 
999805 
999801 
999797 
999794 
999790 
999786 
999782 

999778 
999774 
999769 
999765 
99976i 
999757 
999753 
999748 
999744 
999740 
999735 

Sin. 



,„ 



•°3 

.05 
.03 
• 03 
.05 
.03 
•03 
.05 
.03 
.05 

.05 
.03 
.05 
.05 
.03 
.05 
.05 
.05 
.05 
.05 

.05 
.05 
.05 
.05 
.05 
.05 
.05 
.05 
.07 
.05 

.05 
.07 ■ 

.05 
.05 
.07 
.05 
.07 
.05 
.07 
.07 

.05 
.07 
.07 
.07 
.07 

.05 
.07 
.07 
.07 
.07 

.07 
.08 
•07 
.07 
.07 
.07 
.08 
.07 
.07 
.08 

D. 1'.'. 



,241921 
,249102 
,256165 
,263115 
. 269956 
, 276691 
■ 283323 
,289856 
, 296292 
. 302634 

, 308884 
315046 
321 122 

,3271 14 

333025 
338856 
3446io 
,350289 
355895 
361430 

366895 
372292 
377622 



. 388092 
8. 393234 
.398315 
.403338 
. 408304 

.413213 
8. 418068 
. 422869 
.427618 
.432315 
. 436962 
8. 441560 
.446110 
.450613 

• 455070 

• 459481 

8. 463849 
.468172 

. 472454 
. 476693 
. 480892 

8. 485050 
.489170 

• 493250 

• 497293 
.501298 

8. 505267 
. 509200 
.513098 
.516961 
. 520790 

8.524586 

• 528349 
. 532080 

•535779 

• 539447 
8. 543084 

Cot. 



Cot. 



119.68 
117.72 
115.83 
114.02 
112.25 
110.53 
108. 88 
107. 27 
105. 70 
104. 17 

102. 70 
101. 27 
99.87 
98.52 
97.18 
95.90 
94.65 

93-43 
92.25 
91.08 

89.95 
88.83 

87.78 
86.72 
85.70 
84.68 
83.72 
82.77 
81.82 
80.92 

80.02 

79.15 

78.28 

77-45 
76.63 

75.83 
75.05 
74.28 
73.52 
72.80 

72.05 
71.37 
70.65 
69.98 
69. 30 
68.67 
68.00 
67.38 
66.75 
66.15 

65-55 
64.97 
64.38 
63.82 
63.27 
62.72 
62.18 
61.65 

61.13 
60.62 

D. I". 



1.758079 60 

• 750898 59 
.743835 
.736885 

• 730044 
1.723309 

.716677 

.710144 
. 703708 
.697366 

1.691116 

. 684954 
. 678878 
. 672886 
. 666975 
1. 661 144 

• 655390 
.649711 
.644105 
.638570 

1. 633105 

. 627708 

.622378 

.617111 

.611908 
1 . 606766 

.601685 

. 596662 

.591696 

.586787 

1. 581932 
.577131 
.572382 

.567685 

.563038 

1.558440 

. 553890 

• 549387 
. 54493° 
.540519 

I.536I5I 
.531828 

• 527546 

• 523307 
.519108 

1. 5H950 

• 510830 

• 506750 
. 502707 
. 498702 

1-494733 
. 490800 
. 486902 

• 483039 
.479210 

I-4754H 
.471651 
. 467920 
.464221 

.460553 
1. 456916 



Tan. 



91 



88° 



COSINES, TANGENTS, AND COTANGENTS 177' 



M. 



Sin. 






8.542819 


I 


. 546422 


2 


• 549995 


3 


• 553539 


4 


• 557054 


5 


8. 560540 


6 


• 563999 


7 


.567431 


8 


. 570836 


9 


.574214 


10 


8.577566 


11 


. 580892 


12 


.584193 


13 


• 587469 


*4 


.590721 


15 


8. 593948 


16 


.597152 


17 


.600332 


18 


. 603489 


19 


. 606623 


20 


8. 609734 


21 


.612823 


22 


.615891 


23 


.618937 


24 


.621962 


25 


8. 624965 


26 


. 627948 


27 


.630911 


28 


.633854 


29 


. 636776 


30 


8. 639680 


3i 


. 642563 


32 


. 645428 


33 


. 648274 


34 


.651102 


35 


8. 65391 1 


36 


. 656702 


37 


.659475 


38 


. 662230 


39 


.664968 


40 


8. 667689 


4i 


.670393 


42 


. 673080 


43 


.675751 


44 


. 678405 


45 


8.681043 


46 


.683665 


47 


. 686272 


48 


.688863 


49 


. 691438 


50 


8. 693998 


5i 


• 696543 


52 


.699073 


53 


• 701589 


54 


. 704090 


55 


8. 706577 


5b 


•709049 


5 l 


.711507 


5« 


.713952 


59 


.716383 


60 


8. 718800 



Cos. 



D. i' 



60.05 
59-55 
59.07 
58.58 
58.10 

57.65 
57.20 
56.75 
56.30 
55.87 

55-43 
55- 02 
54.60 
54.20 
53.78 
53.40 
53.oo 
52.62 
52.23 
51-85 
51.48 
5i.i3 
5o.77 
50.42 
50.05 
49.72 
49.38 
49.05 
48.70 
48.40 

48.05 
47-75 
47-43 
47.13 
46.82 
46.52 
46.22 
45.92 
45- 63 
45-35 

45.07 
44.78 
44.52 
44.23 
43-97 
43.70 
43-45 
43.18 
42.92 
42.67 

42.42 
42.17 

41.93 
41.68 

41.45 
41.20 

40.97 
40.75 
40. 52 
40.28 

D. 1". 



Cos. 



D. i' 



Tan. 



D. 



999735 
999731 
999726 
999722 
999717 

999713 
999708 

999704 
999699 
999694 

999689 
999685 
999680 

999675 
999670 
999665 
999660 

999655 
999650 
999645 

999640 
999635 
999629 
999624 
999619 
999614 
999608 
999603 
999597 
999592 

999586 
999581 
999575 
999570 
999564 
999558 
999553 
999547 
999541 
999535 

999529 
999524 
999518 
99951,2 
9995o6 
9995oo 

999493 
999487 
999481 
999475 

999469 
999463 
999456 
999450 
999443 
999437 
999431 
999424 
999418 
99941 1 
999404 

Sin. 



.07 
,08 

07 
08 
07 
,08 
07 
08 
08 
08 

07 
08 
08 
08 
08 
08 
08 
08 
08 
08 

08 
10 
08 
08 
08 
10 
08 
10 
08 
10 

08 
10 
08 
10 
10 
08 
10 
10 
10 
10 

08 
10 
10 
10 
10 
12 
10 
10 
10 
10 

10 
12 
10 
12 
10 
10 
12 
10 
12 
12 



D. 



8. 543084 
. 546691 
. 550268 

• 553817 

• 557336 
8. 560828 

.564291 
.567727 
.57H37 
.574520 

8.577877 
.581208 

.584514 

.587795 

.591051 

8. 594283 

• 597492 
.600677 

• 603839 
. 606978 

8.610094 
.613189 
.616262 
.619313 

• 622343 
8.625352 

. 628340 
.631308 
. 634256 
.637184 

8. 640093 
. 642982 

.645853 
. 648704 

•651537 
8. 654352 
.657149 
. 659928 
. 662689 

• 665433 

8.668160 
. 670870 

• 673563 
. 676239 
. 678900 

8.681544 
. 684172 
. 686784 
. 689381 

• 691963 

8. 694529 
.697081 
. 699617 
. 702139 
. 704646 

8. 707140 
.709618 
.712083 

• 7H534 
.716972 

8. 719396 

Cot. 



60. 12 

59.62 
59.15 
58.65 
58.20 
57.72 
57-27 
56.83 
56.38 
55-95 

55.52 
55.io 
54.68 
54.27 
53.87 
53.48 
53.o8 
52.70 
52.32 
51-93 

51.58 
51.22 
50.85 
50.50 
50.15 
49.80 

49-47 
49.13 
48.80 
48.48 

48.15 
47.85 
47.52 
47.22 
46.92 
46.62 
46.32 
46.02 
45-73 
45.45 

45.17 

44.88 
44.60 

44-35 
44.07 
43.8o 

43-53 
43.28 

43.03 
42.77 

42.53 
42.27 
42.03 
41.78 

41.57 
41.30 
41.08 
40.85 
40.63 
40.40 

D. i". 



Cot. 



1. 456916 

• 453309 

• 449732 
.446183 
. 442664 

1. 439172 

• 435709 
.432273 
. 428863 
.425480 

1. 422123 
.418792 
. 415486 
.412205 

• 408949 
1. 405717 

. 402508 

• 399323 
.396161 
. 393022 

1.389906 
.386811 
.383738 
.380687 

• 377657 
1.374648 

.371660 
. 368692 

. 365744 
.362816 

I.359907 
.357oi8 

. 354H7 
.351296 

• 348463 
1.345648 

. 342851 
. 340072 

-33731 1 

.334567 

1. 331840 

• 329130 
.326437 
. 323761 
.321100 

1. 318456 
.315828 
.313216 
.310619 
. 308037 

I-30547I 

• 302919 
. 300383 
.297861 

• 295354 
1.292860 

. 290382 
.287917 
. 285466 
. 283028 
1 . 280604 

Tan. 



92 



87 



LOGARITHMIC SINES 



176* 



M. 



o 
1 
2 
3 
4 
5 
6 

7 
8 

9 
10 
11 
12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 

26 

2 Z 
28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



93' 



Sin. 



8.718800 
. 721204 
. 723595 

• 725972 

• 728337 
8. 730688 

. 733027 

• 735354 

• 737667 
. 739969 

8. 742259 
.744536 
. 746802 

• 749055 
.751297 

8.753528 

• 755747 

• 757955 
.760151 

• 762337 
8. 76451 1 

. 766675 
.768828 
. 770970 
.773101 
8. 775223 

• 777333 

• 779434 
.781524 
.783605 

8.785675 

• 787736 
.789787 
. 791828 

.793859 

8.795881 

.797894 

• 799897 
. 801892 
. 803876 

8.805852 
.807819 
.809777 
.811726 
.813667 

8.815599 
.817522 
.819436 
.821343 
. 823240 

8.825130 
.827011 
.828884 
. 830749 
.832607 

8.834456 
. 836297 
.838130 
.839956 
.841774 

8.8 43585 
Cos. 



D. 1' 



40.07 

39.85 
39.62 

39.42 
39.18 

38.98 
38.78 
38.55 
38.37 
38.17 

37-95 
37.77 
37-55 
37-37 
37.18 
36.98 
36.80 
36.60 

36.43 
36.23 

36.07 
35-88 
35.70 
35.52 
35-37 
35.17 
35-02 

34.83 
34.68 

34.50 

34-35 
34.18 
34-02 
33.85 
33-70 
33-55 
33.38 
33-25 
33.07 
32.93 

32.78 
32.63 
32.48 
32.35 
32. 20 
32.05 
31.90 
31.78 
31.62 
31.50 

31.35 
31.22 
31.08 

30.97 
30.82 
30.68 
30.55 
30.43 
30.30 
30.18 

D. 1". 



Cos. 



999404 
999398 
999391 
999384 
999378 
999371 
999364 
999357 
999350 
999343 

999336 
999329 
999322 

999315 
999308 
999301 
999294 
999287 

999279 
999272 

999265 

999257 
999250 

999242 
999235 
999227 
999220 
999212 
999205 
999197 

999189 
999181 
999174 
999166 
999158 
999150 
999142 

999134 
999126 
9991 18 

9991 10 
999102 

999094 
999086 

999077 
999o69 
999061 

999053 
999044 
999036 

999027 
999019 
999010 
999002 
998993 
998984 
998976 
998967 
998958 
998950 
998941 

Sin. 



D. 1". 



Tan. 



D. 1". 



8. 719396 
.721806 
. 724204 
. 726588 

• 728959 
8.73I3I7 

• 733663 

• 735996 
.738317 
. 740626 

8. 742922 

• 745207 

• 747479 

• 749740 
■ 751989 

8. 754227 

. 756453 
. 758668 
. 760872 
. 763065 
8. 765246 

• 767417 
.769578 
.771727 
. 773866 

8. 775995 
.778114 
. 780222 
. 782320 
. 784408 

8. 786486 

.788554 
.790613 
. 792662 

• 794701 
8. 796731 

• 798752 
. 800763 
. 802765 
.804758 

8. 806742 
.808717 
.810683 
.812641 

.814589 
8.816529 
.818461 
. 820384 
. 822298 
. 824205 

8. 826103 
. 827992 
. 829874 
.831748 
.833613 

8.835471 
.837321 
.839163 
. 840998 
. 842825 

8. 844644 

Cot. 



D. i' 



40.17 
39-97 
39-73 
39.52 
39.30 
39.10 
38.88 
38.68 
38.48 
38.27 

38.08 
37.87 
37-68 
37.48 
37.30 
37- 10 
36.92 
36.73 
36.55 
36.35 
36.18 
36.02 
35.82 
35.65 
35.48 
35.32 
35.13 
34-97 
34.80 

34.63 

34-47 
34.32 
34.15 
33.98 
33-83 
33-68 
33o2 
33-37 
33-22 

33-07 

32.92 
32.77 
32.63 

32.47 
32.33 
32. 20 
32.05 
31.90 
31.78 
31.63 

31.48 
31-37 
31.23 
31.08 

30.97 
30.83 
30.70 
30.58 
30.45 
30.32 

D. 1". 



Cot. 



1.280604 


60 


.278194 


59 


. 275796 


58 


.273412 


57 


.271041 


56 


1.268683 


55 


. 266337 


54 


. 264004 


53 


.261683 


52 


. 259374 


5i 


1.257078 


50 


. 254793 


49 


.252521 


48 


. 250260 


47 


.248011 


46 


1.245773 


45 


. 243547 


44 


.241332 


43 


.239128 


42 


. 236935 


4i 


1.234754 


40 


. 232583 


39 


. 230422 


38 


. 228273 


37 


.226134 


36 


1.224005 


35 


.221886 


34 


.219778 


33 


.217680 


32 


•215592 


3i 


1.213514 


30 


.211446 


29 


. 209387 


28 


. 207338 


27 


. 205299 


26 


I . 203269 


25 


. 201248 


24 


. 199237 


23 


. 197235 


22 


. 195242 


21 


I. 193258 


20 


. i9 I2 83 


19 


. 189317 


18 


• 187359 


17 


.185411 


16 


1.183471 


15 


• 181539 


14 


. 1 79616 


13 


. 177702 


12 


• 175795 


11 


1. 173897 


10 


. 172008 


% 


. 1 70126 


. 168252 


7 


. 166387 


6 


1. 164529 


5 


. 162679 


4 


. 160837 


3 


. 159002 


2 


.157175 


1 


1. 155356 






Tan. 



86' 



COSINES, TANGENTS, AND COTANGENTS I75 c 



M. Sin. D. i". Cos. D. i". Tan. D. i". Cot. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 

io 

ii 

12 

13 
M 
15 
16 

17 
18 

19 

20 

21 
22 

23 
2 4 

25 
26 

27 
28 

29 

30 
31 

32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



8. 843585 

.8453S7 
.847183 
.848971 

.850751 

.854291 
. 856049 
.857S01 

• 859546 

8.S61283 
. 863014 
.864738 
.866455 
.868165 

8. 869868 
.871565 

• 873255 
.874938 
.876615 

8. 878285 
. 879949 
.881607 

• 883258 
.884903 

8. 886542 
.888174 



S. 



89142 1 
893035 

894643 
896246 
897842 
899432 
901017 
902596 
904169 
9 5736 
907297 
90S853 

910404 
.911949 
.913488 
.915022 
•916550 
. 918073 

■9I959I 
.921103 
.922610 
,924112 

. 925609 
.927100 
.928587 
. 930068 
.931544 
.933015 
.934481 
.935942 
• 937398 
■ 938850 
. 940296 

Cos. 



30-03 
29. 93 

29. So 
29.67 
29-57 
29.43 
29.30 
29. 20 
29.08 
28.95 
28.85 

28.73 
28.62 
28.50 
28.38 
28.28 
28.17 
28.05 1 

27.95 
27.83 

27-73 
27.63 
27.52 
27.42 
27.32 
27.20 
27. 12 
27.00 
26. 90 
26.80 

26.72 
26. 60 
26.50 
26.42 
26.32 
26.22 
26. 12 
26. 02 
25.93 
25.85 

25.75 

25.65 

25-57 

25.47 I 

25.38 

25.30 

25.20 

25.12 

25.03 

24.95 

24.85 

24.78 

24.68 

24. 60 

24.52 

24.43 

24.35 

24.27 

24. 20 

24. 10 



D. 1 



996941 
998932 
998923 
998914 

998905 
998896 
998887 

998869 
99S860 

998851 
99S841 
998832 
998823 

998813 
998804 

998795 
998785 
998776 
99S766 

998757 
998747 
99S738 
998728 
998718 
998708 
998699 
9986S9 

998679 
998669 

998659 
998649 
998639 
998629 
998619 
998609 
998599 
998589 
998578 
998568 

998558 
998548 

998537 
998527 
998516 
99S506 
998495 
998485 
998474 
998464 

998453 
998442 
998431 
998421 
998410 

998399 
998388 
998377 
998366 
998355 
99S344 

Sin. 



15 
15 
15 
15 
15 
15 
15 
15 
15 
15 

17 
15 
15 
17 
15 
15 
17 
15 
17 
*5 

17 

15 
17 
17 

17 

15 
17 
17 
17 
17 

17 
17 
17 

17 
17 
17 

17 
iS 

^7 
17 

17 
iS 

17 
iS 

17 

iS 

17 

iS 

17 

iS 

iS 

18 

17 

iS 

18 

18 

^8 
18 

18 

18 



D. 1' 



8. 844644 

• 846455 
. 848260 
. 850057 
.851846 

8. 853628 
.855403 
.857171 
.858932 
. 860686 

8.862433 
.864173 
.865906 
.867632 

• 869351 
8.871064 

.872770 
. 874469 
. 876162 
.877849 

8. 879529 
.881202 
.882S69 
.884530 
. 886185 

8.887833 
. 889476 
.891112 
. 892742 

• 894366 

8.895984 
.897596 
. 899203 
.900803 
. 902398 

8. 903987 

• 905570 
.907147 
.908719 
. 910285 

8. 91 1846 
.913401 
.9H95i 

• 916495 
.918034 

8.919568 
.921096 
.922619 
.924136 

• 925649 
8.927156 

. 928658 
.930155 
.931647 
.933134 
8. 934616 
.936093 
.937565 

• 939032 
. 940494 

8.941952 

Cot. 



'30. iS 
30.08 

29.95 
29.82 
29.70 
29.58 
29.47 
29.35 
29.23 
29. 12 

29.00 

28.88 

28.77 
28.65 

28.55 
28.43 
28.32 
28.22 
28.12 
28.00 

27.88 
27.78 
27.68 
27.58 
27.47 
27.38 
27.27 
27.17 
27.07 
26.97 
26.87 
26.78 
26.67 
26.58 
26.48 
26.38 
26.28 
26. 20 
26. 10 
26.02 

25.92 
25.83 
25.73 
25-65 
25.57 
25.47 
25. 38 
25.28 
25.22 
25.12 

25.03 
24.95 
24.87 
24.78 
24.70 
24.62 
24.53 
24.45 
24.37 
24.30 



D. 1". 



i. 155356 
• x 53545 
. 151740 

• 149943 
. H8154 

1. 146372 

• 144597 
. 142829 
. 141068 

• I393H 

1. 137567 

• 135827 
. 134094 
. 132368 

• 130649 
1. 128936 

. 127230 
.125531 
. 123838 
. 122151 

1. 120471 
.118798 

.117131 
.115470 

.113815 
1. 112167 
.110524 
. 10S888 
. 107258 
. 105634 

1. 104016 
. 102404 
. 100797 
.099197 
.097602 

1. 096013 
. 094430 
.092853 
.091281 
.089715 

1. 088154 
. 086599 
.085049 
.083505 
.081966 

1 . 080432 
. 078904 
.077381 

• 075864 
.074351 

1 . 072844 
.071342 
.069845 
.068353 
.066866 

1.065384 
. 063907 
.062435 
.060968 

• 059506 
1.058048 

Tan. 



94' 



85 



5° 



LOGARITHMIC SINES 



174^ 



M. 



Sin. 



D. r 



10 
11 
12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 
3o 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



8. 940296 
.941738 
•943174 
.944606 
. 946034 

8. 947456 

• 948874 
.950287 
.951696 
.953100 

8. 954499 

• 955894 
. 957284 
. 958670 
.960052 

8. 961429 
.962801 
.964170 

• 965534 
.966893 

8.968249 
. 969600 

. 970947 
. 972289 
. 973628 
8.974962 
. 976293 
.977619 
.978941 
. 980259 

8.981573 
. 982883 
.984189 
.985491 
. 986789 

8. 988083 

.989374 
. 990660 

.991943 
• 993 222 

8. 994497 
.995768 
.997036 
.998299 
.999560 

9.000816 
. 002069 
.003318 
.004563 
. 005805 

9. 007044 
.008278 
.009510 
.010737 
.011962 

9.013182 
.014400 
.015613 
.016824 
.018031 

9.019235 

Cos. 



24.03 

23.93 
23.87 
23.80 
23.70 
23.63 
23.55 
23.48 
23.40 
23.32 

23-25 
23.17 
23.10 

23.03 
22.95 
22.87 
22.82 

22.73 
22.65 
22.60 

22.52 
22.45 
22.37 
22.32 
22.23 
22.18 
22. 10 
22.03 
21.97 
21.90 

21.83 
21.77 
21.70 
21.63 

21-57 
21.52 

21.43 
21.38 
21.32 
21.25 

21.18 
21.13 
21.05 
21.02 
20.93 
20.88 
20.82 
20.75 
20. 70 
20.65 

20.57 

20.53 
20.45 
20.42 
20.33 
20.30 
20. 22 
20.18 
20. 12 
20.07 

D. 1". 



Cos. 



998344 
998333 
998322 
9983 1 1 
998300 
998289 
998277 
998266 
998255 
998243 
998232 
998220 
998209 

998i97 
998186 
998174 
998163 
998151 
998139 
998128 

9981 16 
998104 
998092 
998080 
998068 
998056 
998044 
998032 
998020 
998008 

997996 
997984 
997972 

997959 
997947 
997935 
997922 
997910 
997897 
997885 

997872 
997860 

997847 
997835 
997822 
997809 
997797 
997784 
997771 

997758 

997745 
997732 
997719 
9977o6 

997693 
997680 

997667 
997654 
997641 
997628 
997614 

Sin. 



D. 1". 



.18 
.18 
.18 
.18 
.18 
. 20 
.18 
.18 
. 20 
.18 

.20 
.18 
.20 
.18 
.20 
.18 
.20 
. 20 
.18 
.20 

. 20 
.20 
. 20 
. 20 
.20 
.20 
.20 
.20 
.20 
.20 

.20 
.20 
.22 
.20 
.20 
.22 
.20 
.22 
.20 
.22 

.20 
.22 
.20 
•22 
.22 
.20 
.22 
.22 
.22 
.22 

.22 
.22 
.22 
.22 
.22 
.22 
.22 
.22 
.22 
.23 



Tan, 



D. i' 



8.941952 
. 943404 

• 944852 

• 946295 

• 947734 
8. 949168 

• 950597 
.952021 

.953441 
• 954S56 

8. 956267 

• 957674 
. 959075 

• 960473 
.961866 

8.963255 

• 964639 
.966019 

• 967394 
. 968766 

8. 970133 
.971496 
.972855 

• 974209 
• 97556o 

8. 976906 
.978248 

• 979586 
. 98092 1 
.982251 

8.983577 

• 984899 
.986217 

• 987532 
. 988842 

8.990149 
.991451 
.992750 

• 994045 

• 995337 
8. 996624 

.997908 
. 999188 

9.000465 
.001738 

9. 003007 
. 004272 
.005534 
. 006792 
. 008047 

9. 009298 
.010546 
.011790 
.013031 
.014268 

9.015502 
.016732 
.017959 
.019183 
. 020403 

9.021620 

Cot. 



D. 1". 



24.20 

24.13 
24.05 

23.98 
23.90 
23.82 
23.73 
23.67 
23.58 
23.52 

23- 45 
23.35 
23.30 
23.22 

23.15 
23.07 
23.00 
22.92 
22.87 
22.78 

22.72 
22.65 
22. 57 
22.52 
22.43 
22.37 
22.30 
22.25 
22. 17 
22. 10 

22.03 
21.97 
21.92 
21.83 
21.78 
21.70 
21.65 
21.58 

21.53 
21.45 

21.40 

21.33 
21.28 
21.22 
21.15 
21.08 
21.03 
20.97 
20.92 
20.85 

20.80 
20.73 
20.68 
20.62 
20.57 
20.50 
20.45 
20.40 
20.33 
20.28 

D. 1". 



Cot. 



1.058048 
.056596 
.055148 

• 053705 
. 052266 

1.050832 

.049403 
.047979 

• 046559 
.045144 

I.043733 
.042326 
. 040925 

• 039527 
.038134 

1.036745 
. 035361 
.033981 
. 032606 
.031234 

1.029867 
. 028504 
.027145 
.025791 
. 024440 

1.023094 
.021752 
.020414 
.019079 
.017749 

1. 016423 
.015101 
.013783 
.012468 
.011158 

1. 009851 
. 008549 
. 007250 
. 005955 
.004663 

1.003376 
.002092 
.000812 

o. 999535 
. 998262 

o. 996993 
. 995728 

• 994466 
. 993 2 o8 
.991953 

o. 990702 

. 989454 
.988210 
.986969 
.985732 
o. 984498 
. 983268 
.982041 
.980817 
.979597 

o. 978380 
Tan. 



95' 



84' 



COSINES, TANGENTS, AND COTANGENTS jjj 



M. Sin. D. i". Cos. D. i". Tan. D. i". Cot 



o 

i 

2 

3 
4 
5 
6 

I 

9 
io 
ii 

12 

13 
M 
15 
16 

17 
18 

19 

20 
21 
22 

23 

2 4 

25 

26 

27 
28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

4i 

42 

43 
44 
45 
46 

47 
48 

49 
5o 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9.019235 
. 020435 
.021632 
.022825 
.024016 

9. 025203 
.026386 
.027567 
. 028744 
.029918 

9.031089 
.032257 
.033421 
.034582 

■035741 
9. 036896 

. 03S04S 

.039197 
.040342 
.041485 

9. 042625 
.043762 

.044895 
. 046026 

.047154 
9. 048279 
. 049400 
.050519 
.051635 
.052749 

9- 053859 
. 054966 
.056071 
.057172 
.058271 

9.059367 
.060460 
.061551 
. 062639 
.063724 

9.064806 
.065885 
. 066962 
.068036 
.069107 

9.070176 
.071242 
. 072306 
.073366 
.074424 

9. 075480 
.076533 
.077583 
.078631 
• 079676 

9.080719 
.081759 
.082797 
.083832 
. 084864 

9. 085894 

Cos. 



D. i' 



9.997614 
997601 
997588 
997574 
99756i 
997547 
997534 
997520 

997507 
997493 
99748o 
997466 
997452 
997439 
997425 
9974 1 1 
997397 
997383 
997369 
997355 

997341 
997327 
997313 
997299 
997285 
997271 

997257 
997242 
997228 
997214 

997199 
997i85 
997170 
997156 
997141 
997127 
9971 12 
997098 
997083 
997068 

997053 
997039 
997024 
997009 
996994 
996979 
996964 
996949 
996934 
996919 

996904 



996874 



996843 
996828 
996812 
996797 
996782 
996766 
996751 

Sin. 



.22 
.22 

.23 
.22 

.23 
.22 

.23 
.22 

.23 
.22 

.23 
•23 
.22 

.23 
.23 
.23 
.23 
.23 
.23 
.23 

.23 
.23 
•23 
•23 
.23 
.23 
.25 
.23 
•23 
.25 

•23 
.25 
.23 
.25 
•23 
.25 
.23 
.25 
.25 
.25 

.23 
.25 
.25 
.25 
.25 
.25 
.25 
.25 
.25 
.25 

.25 
.25 

.27 

.25 
.25 

.27 
.25 
.25 
.27 

•25 
D. 1". 



9.021620 
. 022834 
. 024044 
.025251 
.026455 

9- 027655 
. 028852 
. 030046 
.031237 
.032425 

9. 033609 
.034791 

.035969 
.037144 
.038316 

9- 039485 
.040651 
.041813 
.042973 
.044130 

9. 045284 
.046434 
.047582 
.048727 
. 049869 

9.051008 
.052144 
.053277 

• 054407 

• 055535 
9. 056659 

. 057781 
.058900 
.060016 
.061130 
9. 062240 
. 063348 

• 064453 
.065556 
.066655 

9. 067752 
.068846 
. 069938 
.071027 

.072113 
9.073197 
.074278 
.075356 
.076432 

.077505 
9. 078576 

.079644 
.080710 
.081773 
.082833 

9. 083891 
.084947 
.086000 
. 087050 
. 088098 

9.089144 

Cot. 



20.23 

20. 17 

20. 12 

20.07 

20.00 

9-95 

9.90 

9.85 

9.80 

9-73 
9.70 
9.63 
9.58 
9-53 
9.48 
9-43 
9-37 
9-33 
9.28 

9-23 
9.17 
9.13 
9.08 

9-03 
8.98 

8-93 
8.88 
8.83 
8.80 
8.73 
8.70 
8.65 
8.60 
8.57 
8.50 
8.47 
8.42 
8.38 
8.32 
8.28 

8.23 
8.20 

8.15 
8.10 
8.07 
8.02 
7-97 
7-93 
7.88 

7.85 
7.80 
7-77 
7.72 
7.67 
7.63 
7.60 

7-55 
7-50 
7-47 
7-43 



D. i". 



o. 978380 
.977166 
.975956 
•974749 

• 973545 
o. 972345 

.971148 

.969954 
.968763 

.967575 
o. 966391 
. 965209 
.964031 
. 962856 
. 9616S4 
0.960515 

•959349 

.958187 

.957027 
.955870 

0.954716 
.953566 
.952418 
.951273 
.950131 

o. 948992 

.947856 
.946723 

• 945593 
.944465 

o. 943341 
.942219 
.941100 

•939984 
.938870 

0.937760 
. 936652 
•935547 
•934444 
.933345 

o. 932248 

.931154 
.930062 

.928973 

. 927887 

o. 926803 

.925722 
.924644 
. 923568 
.922495 

0.921424 
. 920356 
.919290 
.918227 

.917167 

o. 916109 

.9!5053 
.914000 
.912950 
.911902 
0.910856 

Tan. 



60 
59 
58 
57 
56 
55 
54 
53 
^52 
5i 



96' 



83' 



LOGARITHMIC SINES 



I72< 



M. 



10 

ii 

12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 

30 

31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 

44 
45 
46 

47 

48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin, 



9. 085894 
. 086922 
.087947 
. 088970 
. 089990 

9.091008 
. 092024 

.093037 
. 094047 
. 095056 

9. 096062 
. 097065 
. 098066 
.099065 
. 100062 

9. 101056 
. 102048 
• 103037 
. 104025 
. 105010 

9. 105992 
. 106973 
. 107951 
. 108927 
. 109901 

9. 110873 
. 1 1 1842 
.112809 
•1 13774 
•"4737 

h 1 15698 
.116656 
.117613 
.118567 
.119519 

). 120469 
.121417 
. 122362 
. 123306 
. 124248 

9. 125187 
.126125 
. 127060 
. 127993 
. 128925 

9- 129854 
. 130781 
. 131706 
. 132630 
• I3355I 

9- I34470 

• 135387 

• 136303 
.137216 
.138128 

9- 139037 

• 139944 
. 140850 

• I4I754 

• 142655 
9- 143555 



D. 1". 



Cos. 



17-13 
17.08 

17.05 
17. 00 
16.97 
16.93 
16.88 
16.83 
16.82 
16.77 

16.72 
16.68 
16.65 
16.62 
16.57 
16.53 
16.48 
16.47 
16.42 
16.37 

16.35 
16.30 
16.27 
16.23 
16. 20 
16.15 
16. 12 
16.08 
16.05 
16.02 

15-97 
15-95 
15-9° 
15.87 
15-83 
15.80 

15-75 
15.73 
15-70 
15.65 

15-63 
15.58 
15.55 
15-53 
15.48 
15-45 
15.42 
15.40 

15.35 
15.32 

15.28 

15.27 
15.22 
15.20 

15.15 
15.12 
15.10 
15-07 
15.02 
15.00 



Cos. 



9.996751 

• 996735 
. 996720 

. 996704 

. 996688 

9. 996673 

• 996657 
. 996641 

• 996625 
.996610 

9.996594 
. 996578 
. 996562 
. 996546 

• 996530 
9.996514 

•996498 
. 996482 
. 996465 
.996449 

9- 996433 
.996417 
. 996400 
.996384 
.996368 

9-99635I 

• 996335 
.996318 
. 996302 
.996285 

9. 996269 
.996252 

• 996235 
.996219 
. 996202 

9.996185 
.996168 
.996151 
.996134 
.996117 

9.996100 
.996083 
. 996066 
. 996049 

• 996032 
9. 996015 

.995998 
. 995980 

• 995963 
. 995946 

9.995928 
•9959i 1 
.995894 
.995876 
.995859 

9. 995841 

• 995823 
. 995806 
.995788 
•995771 

9- 995753 



D. 1" 



Sin. 



D. 1' 



.27 

.25 
.27 
.27 

•25 
.27 
.27 
.27 

.25 
.27 

.27 
.27 
.27 
.27 

.27 
.27 
.27 
.28 

.27 
.27 

.27 

.28 

.27 
.27 
.28 

.27 
.28 

.27 
.28 
.27 

.28 
.28 

.27 
.28 
.28 
.28 
.28 
.28 
.28 
.28 

.28 
.28 
.28 
.28 
,28 
,28 
30 
28 
28 
30 
28 



.30 
.28 
.30 
.30 
,28 
30 
28 
30 



Tan. 



9.089144 
. 090187 
.091228 
. 092266 
. 093302 

9. 094336 

• 095367 
.096395 
. 097422 
.098446 

9. 099468 
. 100487 
. 10 1 504 
. 1025 19 
. 103532 

9. 104542 

• 105550 
. 106556 

. io7559 
. 108560 

9- 10 9559 
.110556 

.111551 
.112543 

•II3533 
9. 114521 

.115507 
. 1 1649 1 
.117472 
.118452 

9. 1 19429 
. 120404 
.121377 
. 122348 
.123317 

9. 124284 

• 125249 
. 1262 1 1 
. 127172 
. 128130 

9. 129087 
. 130041 
. 130994 
• I3I944 

• 132893 
9- 133839 

• 134784 

• 135726 
. 136667 
. 137605 

9- 138542 

• 139476 
. 140409 
. 141340 
. 142269 

9- 143196 
. 144121 

• 145044 
. 145966 
. 146885 

9. 147803 



D. 1' 



17.38 
17.35 
17.30 
17.27 
17.23 
17.18 

17.13 
17. 12 
17.07 
17.03 

16.98 

16.95 
16.92 
16.88 
16.83 
16.80 
16.77 
16.72 
16.68 
16.65 

16.62 
16.58 

16.53 
16.50 
16.47 
16.43 
16.40 
16.35 
16.33 
16.28 

16.25 
16. 22 
16.18 
16.15 
16.12 
16.08 
16.03 
16.02 
15.97 
15.95 

15.90 
15.88 
15.83 
15.82 

15.77 
15.75 
15.70 
15.68 
15.63 
15.62 

15.57 
15.55 
15.52 
15.48 
15.45 
15.42 
15.38 
15.37 
15.32 
15.30 



D. 1". 



Cot. 



o. 910856 60 



.909813 
.908772 

• 907734 
.906698 

o. 905664 

. 904633 

• 903605 
. 902578 

.901554 



o. 900532 50 



.899513 

. 898496 
.897481 
. 896468 
0.895458 
• 894450 
. 893444 

.892441 
. 891440 

o. 890441 

. 889444 



49 
48 

47 
46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 



.887457 
. 886467 
0.885479 
• 884493 
.883509 
. 882528 
.881548 

0.880571 30 
.879596 i 29 
.878623 28 
.877652 
. 876683 

0.875716 

.874751 
.873789 
. 872828 
.871870 

o. 870913 

• 869959 

. 869006 

. 868056 

. 867107 
0.866161 

.865216 

.864274 

.863333 
. 862395 

0.861458 
. 860524 

.859591 
. 858660 

.857731 
o. 856804 

.855879 
. 854956 
. 854034 
.853115 
0.852197 



Cot. 



D. 1". 



Tan. 



27 
26 
25 
24 
23 
22 
21 

20 

19 
18 

17 
16 

15 
M 
13 
12 
11 



M. 



97 



82 



COSINES, TANGENTS, AND COTANGENTS 171' 



M. 



Sin. 



o 
1 
2 
3 
4 
5 
6 

7 
8 

9 
10 
11 
12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



98° 



9. 143555 
144453 
H5349 
146243 
147 1 36 
14S026 
148915 
149802 
150686 
151569 

152451 
153330 
154208 

155083 
155957 
156830 
157700 
158569 
159435 
1 6030 1 

161164 
162025 
162885 

163743 
164600 

165454 
166307 
167159 
168008 
168856 

169702 

170547 
171389 
172230 
173070 
173908 
174744 
175573 
176411 
177242 

178072 
178900 
179726 
1 8055 1 
181374 
182196 
183016 

183834 
18465 1 
185466 

186280 
187092 
187903 
188712 
189519 
190325 
191130 

191933 
192734 

193534 
194332 

Cos. 



D. 



4-97 
4-93 
4.90 

4.88 

4.83 
4.82 
4.78 
4-73 
4.72 
4.70 

4.65 
63 
58 

57 
55 

50 



45 
45 
38 

4-35 
4-33 
4.30 
4.28 
4.23 
4.22 
4.20 
4.15 
4.13 
4. 10 

4.08 
4.03 
4.02 
4.00 
3-97 
3-93 
3-90 
3-88 

3-85 
3-83 
3.80 
3-77 
3-75 
3.72 
3.70 
3.67 
3.63 
3.62 
3.58 
3-57 

3-53 
3.52 
3.48 
3-45 
3-43 
3-42 
3.38 
3-35 
3-33 
3.30 



D. i". 



Cos. 



9- 995753 
•995735 
.995717 
.995699 
. 995681 

9. 995664 
. 995646 
. 995628 
.995610 
.995591 

9- 995573 

• 995555 

• 995537 
•995519 

• 995501 
9. 995482 

• 995464 

• 995446 

• 995427 

• 995409 

9- 995390 

• 995372 

• 995353 
. 995334 
. 9953i6 

9- 995297 
. 995278 
. 995260 

• 995241 
. 995222 

9- 995203 
.995184 
.995165 
.995146 
.995127 

9.995108 
. 995089 

• 995070 
.995051 

• 995032 

9-995013 

• 994993 

• 994974 

• 994955 

• 994935 
9. 9949i6 

. 994896 

• 994877 
.994857 

• 994838 

9.994818 
. 994798 
. 994779 

• 994759 

• 994739 
9. 994720 

. 994700 
. 994680 
. 994660 

• 994640 
9.994620 

Sin. 



D. 1" 



-30 
.30 
.30 
.30 
.28 
.30 
.30 
.30 
.32 
.30 

.30 
.30 
.30 
.30 
.32 
.30 
.30 
.32 
.30 
.32 

•30 
.32 

• 32 
.30 
.32 

• 32 
•30 
.32 

• 32 
.32 

.32 

• 32 
.32 
.32 
.32 

• 32 
.32 
.32 
.32 

• 32 

.33 
.32 
.32 

• 33 
.32 

• 33 

• 32 
•33 
.32 
•33 

•33 
.32 
•33 
•33 
•32 
•33 
•33 
•33 
•33 
•33 

D. 1" 



Tan. 



147803 
148718 
149632 
150544 
I5H54 
152363 
153269 

I54I74 
155077 
155978 

156877 

157775 
15867 1 

159565 
160457 

161347 
162236 
163123 
164008 
164S92 

165774 
166654 
167532 
168409 
169284 
170157 
171029 
171899 
172767 
173634 
174499 
175362 
176224 
177084 
177942 
178799 

179655 
180508 
181360 
182211 

183059 
183907 
184752 

185597 
186439 
187280 
188120 
188958 
189794 
190629 

191462 
192294 
193124 

193953 
1947S0 
195606 
196430 

197253 
198074 
198894 
199713 

Cot. 



D. 1 



Cot. 



5.25 
5-23 
5.20 

5.17 
5.15 
5-io 
5.08 

5.05 
5.02 

4.98 

4-97 
4-93 
4.90 
4.87 
4.83 
4.82 
4.78 
4-75 
4-73 
4.70 

4.67 

4-63 
4.62 

4.58 
4-55 
4-53 
4-50 
4-47 
4-45 
4.42 

4.38 
4-37 
4-33 
4.30 
4.28 

4.27 
4.22 
4.20 
4.18 
4.13 

4.13 
4.08 
4.08 

4.03 
02 



3.87 
3.83 
3.82 
3.78 
3-77 
3- 73 
3-72 
3-68 
3.67 
3.65 



D. 1". 



0.852197 
. 851282 
.850368 

• 849456 
.848546 

o. 847637 
.846731 
. 845826 
.844923 
. 844022 

0.843123 
. 842225 
.841329 
. 840435 

• 839543 
0.838653 

.837764 

c 836877 

.835992 
.835108 

o. 834226 

. 833346 
. 832468 

.831591 
.830716 

o. 829843 

.828971 
.828101 
.827233 

. 826366 

o. 825501 

. 824638 

.823776 

.822916 

. 822058 

0.821201 

. 820345 

.819492 

. 818640 

.817789 

0.8 1694 1 
.816093 
. 815248 
. 814403 
.813561 

0.812720 

.811880 

.811042 
.810206 

.809371 
0.808538 

. 807706 

. 806S76 

.806047 

. 805220 

o. 804394 

. 803570 

. 802747 

.801926 

.801106 

o. S00287 

Tan. 



8i° 



LOGARITHMIC SINES 



i7o ( 



M. 



10 
ii 

12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



Sin. 



9- 194332 
. 195129 

• 195925 
. 196719 

.197511 

9. 198302 

. 199091 

• 199879 
. 200666 
. 201451 

9. 202234 
. 203017 
. 203797 

• 204577 

• 205354 
9.206131 

. 206906 
. 207679 
. 208452 
. 209222 

9. 209992 
.210760 
.211526 
.212291 

.213055 
9.213818 

.214579 
.215338 
.216097 
.216854 

9.217609 
.218363 
.219116 
.219868 
.220618 

9.221367 
.222115 
.222861 
. 223606 
.224349 

9. 225092 
.225833 
.226573 
.227311 
. 228048 

9. 228784 
.229518 
. 230252 
. 230984 
.231715 

9.232444 
.233172 

.233899 
. 234625 

• 235349 
9. 236073 

.236795 
.237515 
. 238235 

. 238953 
9. 239670 

Cos. 



D. 1". 



13.28 
13.27 

13.23 

13.20 

13.18 
13.15 
13.13 
13.12 
13.08 
13-05 

13.05 
13.00 
13.00 
12.95 
12.95 
12.92 
12.88 
12.88 
12.83 
12.83 

12.80 
12.77 
12,75 
12.73 
12.72 
12.68 
12.65 
12.65 
12.62 
12.58 

12.57 
12.55 
12.53 
12.50 
12.48 
12.47 
12.43 
12.42 
12.38 
12.38 

12.35 
12.33 
12.30 
12.28 
12.27 
12.23 
12.23 
12.20 
12.18 
12.15 

12.13 
12. 12 
12. 10 
12.07 
12.07 
12.03 
12.00 
12.00 
11.97 
11-95 

D. 1". 



Cos. 



9. 994620 
. 994600 
. 994580 
. 994560 

• 994540 
9.994519 

•994499 
•994479 

• 994459 
.994438 

9.994418 

• 994398 
. 994377 
. 994357 
. 994336 

9.994316 
. 994295 

• 994274 
. 994254 
. 994233 

9.994212 
.994191 
.994171 
.994150 
.994129 

9. 994108 

• 994087 
.994066 

. 994045 
. 994024 

9. 994003 
.993982 
• 993960 
•993939 
• 9939i8 

9.993897 
.993875 

• 993854 
.993832 
.993811 

9- 993789 
.993768 
.993746 
. 993725 

• 993703 
9.993681 

. 993660 
•993638 
. 993616 

•993594 

9- 993572 
.993550 
.993528 

• 993506 
.993484 

9.993462 

•993440 
.993418 

• 993396 

• 993374 
9-993351 

Sin. 



D. 1' 



• 33 

• 33 

• 33 
•33 

• 35 

• 33 

• 33 
•33 

• 35 

• 33 

•33 

• 35 
•33 

• 35 
•33 
•35 

• 35 

• 33 

• 35 

• 35 

• 35 

• 33 

■ 35 

• 35 

• 35 

• 35 

• 35 

• 35 

• 35 

• 35 

• 35 

• 37 

• 35 

• 35 
•35 
•37 
•35 
•37 
>35 
•37 

-35 

• 37 

■ 35 
37 

■37 
■35 
■37 
■37 
37 
37 

37 
37 
37 
37 
37 
37 
37 
37 
37 
38 



D. r 



Tan. 



9. 199713 
. 200529 
.201345 
.202159 
.202971 

9. 203782 
. 204592 
. 205400 
. 206207 
. 207013 

9. 207817 
.208619 
. 209420 
.210220 
.211018 

9.211815 
.212611 
.213405 
.214198 
.214989 

9.215780 
.216568 
.217356 
.218142 
.218926 

9. 219710 
. 220492 
.221272 
. 222052 
. 222830 

9. 223607 
. 224382 
.225156 
. 225929 
. 226700 

9.227471 
. 228239 
.229007 
. 229773 

• 230539 
9. 231302 

. 232065 
. 232826 
. 233586 
.234345 
9- 235103 

• 235859 
.236614 
.237368 
.238120 

9. 238872 
. 239622 
.240371 
.241118 
. 241865 

9. 242610 

• 243354 
. 244097 
. 244839 

.245579 
9.246319 

Cot. 



D. 1". 



13.60 
13.60 
13.57 
13.53 
13.52 
13.50 
13.47 
13.45 
13.43 
13.40 

13.37 
13.35 
13.33 
13.30 
13.28 
13.27 

13.23 
13.22 
13.18 
13.18 

13.13 

13.13 
13.10 
13.07 
13.07 

13-03 
13.00 
13.00 
12.97 
12.95 

12.92 
12.90 
12.88 
12.85 
12.85 
12.80 
12.80 
12.77 
12.77 
12.72 

12.72 
12.68 
12.67 
12.65 
12.63 
12.60 
12.58 
12.57 
12.53 
12.53 
12.50 
12.48 
12.45 
12.45 
12.42 
12.40 
12.38 
12.37 
12.33 
12.33 

D. 1". 



Cot. 



o. 800287 

.799471 
.798655 
.797841 

• 797029 
0.796218 

• 795408 
.794600 

•793793 
.792987 

0.792183 
.791381 
. 790580 
. 789780 
. 788982 

o. 788185 
,787389 
.786595 
.785802 
.785011 

o. 784220 
. 783432 
. 782644 
.781858 
. 781074 

o. 780290 

.779508 
. 778728 
.777948 
.777170 

o. 776393 

.775618 

. 774844 
.774071 
.773300 

o. 772529 

.771761 
. 770993 
.770227 

. 769461 
o. 768698 

.767935 
.767174 

.766414 

. 765655 

o. 764897 

.764141 
. 763386 
. 762632 
. 761880 

0.761 128 

. 760378 
.759629 
. 758882 

. 758135 

o. 757390 

. 756646 
. 755903 
. 755161 
.754421 

o. 753681 
Tan. 



99 l 



80' 



io v 



COSINES, TANGENTS, AND COTANGENTS 169' 



M. 



Sin. 



10 
11 
12 
13 

14 

15 
16 

i7 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9. 239670 
. 240386 
.241101 
.241814 
. 242526 

9- 2 43237 

• 243947 
. 244656 

• 245363 
. 246069 

9. 246775 
. 247478 
.2481S1 
. 248883 

. 249583 

9. 250282 

. 250980 

.251677 

•252373 
. 253067 

9. 253761 

. 254453 
.255144 

• 255834 

• 256523 
9.257211 

.257898 
.258583 
. 259268 

.259951 
9. 260633 
.261314 
. 261994 
. 262673 
.263351 
9.264027 
. 264703 
.265377 
.266051 
. 266723 

9- 267395 
. 268065 
. 268734 
. 269402 
.270069 

9- 270735 
.271400 
. 272064 
. 272726 
.273388 

9- 274049 
. 274708 

• 275367 
. 276025 
. 276681 

9- 277337 
. 277991 
.278645 

. 279297 

. 279948 

9. 280599 

Cos. 



D. i' 



•93 
92 
,88 
,87 
85 
83 
82 
78 
77 
77 

72 
72 

70 

67 
65 
63 
62 
60 
57 
57 

53 
52 
50 
48 
47 
45 
42 
42 
38 
37 

35 
33 
32 
30 
27 
27 

23 

23 
,20 
,20 

17 

15 

13 

12 

, 10 

,08 

07 

03 

03 

.02 

0.98 
0.98 
o.97 
o.93 
o.93 
0.90 
o. 90 
0.87 
0.85 
0.85 



D. 1". 



Cos. 



9-993351 

• 993329 

• 993307 

• 993284 
. 993262 

9. 993240 
.993217 

.993195 
.993172 

.993149 

9.993127 

.993104 
.993081 

• 993059 
. 993036 

9- 993oi3 
.992990 

• 992967 
• 99 2 944 
.992921 

9.992898 

.992875 
. 992852 
. 992829 
. 992806 
9- 992783 
.992759 
. 992736 
.992713 
. 992690 

9. 992666 

. 992643 
.992619 

. 992596 
. 992572 
9- 992549 
. 992525 
.992501 

. 992478 
. 992454 

9-992430 
. 992406 
. 992382 
. 992359 
. 992335 

9. 99231 1 
. 992287 
. 992263 

.992239 
.992214 

9.992190 
.992166 
.992142 
.992118 

• 992093 
9. 992069 

• 992044 
. 992020 
.991996 
.991971 

9.991947 

Sin. 



D. 1". 



• 37 

• 37 
.38 

• 37 

• 37 
.38 

• 37 
.38 
.38 
•37 

.38 
.38 

• 37 
.38 
.38 
.38 
.38 
.38 
.38 
.38 

.38 
.38 
.38 
.38 
.38 
.40 
.38 
.38 
.38 
.40 

.38 
.40 
.38 
.40 
.38 
.40 
.40 

.38 
.40 
.40 

.40 
.40 
.38 
.40 
.40 
.40 
.40 
.40 
.42 
.40 

.40 
.40 
.40 
.42 
.40 
.42 
.40 
.40 
.42 
.40 

D. 1" 



Tan. 



9.246319 

• 247057 

• 247794 

• 248530 
. 249264 

9- 249998 
. 250730 
.251461 
.252191 
. 252920 

9- 253648 

• 254374 
.255100 

. 255824 

. 256547 

9. 257269 

• 257990 
.258710 

. 259429 
. 260146 

9. 260863 
.261578 
. 262292 
. 263005 
.263717 

9. 264428 
.265138 
. 265847 
. 266555 
.267261 

9. 267967 
.268671 
. 269375 
. 270077 
. 270779 

9.271479 
.272178 
. 272876 

• 273573 
. 274269 

9- 274964 
.275658 
.276351 

• 277043 
. 277734 

9. 278424 
.279113 
. 279801 
. 280488 
.281174 

9.281858 
. 282542 
. 283225 
. 283907 
. 284588 

9. 285268 
. 285947 
. 286624 
. 287301 
- 287977 

9. 288652 

Cot. 



D. 1". 



2.30 
2.28 
2.27 
2.23 
2.23 
2. 20 
2.18 
2.17 
2.15 
2.13 

2. 10 

2. 10 

2.07 

2.05 

2.03 

2.02 

2.00 

.98 

-95 

•95 

.92 
.90 

.88 
.87 
.85 
.83 
.82 
.80 

• 77 
•11 

• 73 

• 73 
•70 
.70 
.67 
.65 
.63 
.62 
.60 
.58 

• 57 

• 55 

• 53 
.52 
.50 
.48 

• 47 
.45 
-43 
.40 

.40 

.38 

• 37 
•35 
•33 
.32 
.28 
.28 
•27 
•25 



D. 1". 



Cot. 



o. 753681 

752943 
752206 

75M7o 
750736 
750002 
749270 

748539 
747809 
747080 

746352 
745626 
744900 
744176 

743453 
742731 
742010 
741290 
740571 
739854 

739137 
738422 
737708 

736995 
736283 
735572 
734862 

734153 
733445 
732739 

732033 
731329 
730625 

729923 
729221 
728521 
727822 
727124 
726427 
725731 
725036 
724342 
723649 
722957 
722266 
721576 
720887 
720199 
719512 
718826 

718142 
717458 
716775 
716093 
7I54I2 
714732 
7M053 
713376 
712699 
712023 
711348 

Tan. 



M. 



IOO 



.79' 



ir 



LOGARITHMIC SINES 



168 



M 



Sin< 



o 
i 

2 

3 
4 
5 
6 

7 
8 

9 

io 

ii 

12 

13 
14 
15 
16 

l7 o 
18 

19 

20 
21 
22 
23 

24 

25 
26 

27 

28 
29 

30 
31 
32 

33 
34 
35 
36 

H 
38 

39 
40 
4i 
42 
43 
44 
45 
46 

*l 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 

59 
60 



IOI 



9. 280599 

.281248 
.281897 
.282544 
.283190 
9.283836 
. 284480 
.285124 
. 285766 
. 286408 

9. 287048 



. 288326 
.288964 
. 289600 
9. 290236 
. 290870 
.291504 
.292137 
. 292768 

9- 293399 
. 294029 
. 294658 
. 295286 

.295913 
9. 296539 
.297164 
.297788 
.298412 
. 299034 

9- 299655 
. 300276 
. 300895 

.301514 
.302132 
9. 302748 
.303364 
.303979 
.304593 
. 305207 

9- 305819 
. 306430 
.307041 

• 307650 

• 308259 
9.308867 

. 309474 
. 310080 

• 310685 
.311289 

9- 3 1 1893 
.312495 
.313097 
.313698 
.314297 

9-3I4897 
.315495 
. 316092 
.3166S9 
.317284 

9.317879 



D. 1' 



0.82 
0.82 
0.78 

0.77 
0.77 

o.73 
o.73 
0.70 
0.70 
0.67 

67 

03 



o 
o, 

0.63 

0.60 
0.60 

0.57 
0.57 
0.55 
0.52 

0.52 

0.50 
0.48 
0.47 
0.45 
0.43 

0.42 
0.40 
o. 40 

0.37 
0.35 

0.35 
0.32 
0.32 
0.30 

o. 27 

0.27 
0.25 
0.23 
0.23 

o. 20 

0.18 
0.18 
0.15 
0.15 

o. 13 

O. 12 
O. IO 
O.08 

o. 07 
0.07 

0.03 
0.03 

0.02 

9.98 

IO.OO 

9-97 
9-95 
9-95 
9.92 
9.92 



Cos. j D. i' 



Cos. 



991947 
991922 
991897 
991873 
991848 
991823 
991799 

991774 
991749 
991724 

991699 
991674 
991649 
991624 
991599 
991574 
991549 
991524 
991498 

991473 
991448 
991422 

991397 
991372 
991346 
991321 
991295 
991270 
991244 
991218 

991 193 
991 167 
991 141 

99III5 
991090 
991064 
991038 
991012 
990986 
990960 

990934 
990908 
990882 

990855 
990829 

990803 
990777 
990750 
990724 
99o697 
990671 

990645 
990618 
990591 
990565 
990538 
9905 1 1 
990485 
990458 
990431 

990404 
Sin. 



D. if. 



Tan. 



288652 
289326 

289999 
290671 
291342 
292013 
292682 
293350 
294017 
294684 

295349 
296013 
296677 

297339 
298001 
298662 
299322 
299980 
300638 
301295 

301951 
302607 
303261 
3039H 
304567 
305218 
305869 
306519 
307168 
307816 

308463 
309109 

309754 
310399 
31 1042 

311685 
312327 
312968 
313608 
314247 

314885 
315523 
316159 
316795 
317430 
318064 
318697 
319330 
319961 
320592 

321222 

321851 

322479 
323106 

323733 
324358 
324983 
325607 
326231 
326853 
327475 



D. 1". I J Cot. 



D. 



1.23 
1. 22 
1. 20 
1. 18 
1. 18 
i- 15 
1. 13 
1. 12 
1. 12 
1.08 

1.07 
1.07 
1.03 
1.03 
1.02 
1. 00 

0-97 
0.97 

o.95 
o.93 

o.93 
0.90 
0.88 
0.88 
0.85 
0.85 
0.83 
0.82 
0.80 
0.78 

0.77 
o.75 
o.75 
0.72 
0.72 
0.70 
0.68 
0.67 
0.65 
0.63 

0.63 
0.60 
0.60 
0.58 
0-57 
o.55 
o.55 
0.52 
0.52 
0.50 

0.48 
0.47 
o.45 
o.45 
0.42 
0.42 
0.40 
0.40 
o.37 
0-37 



D. 1' 



Cot. 



0.71 1348 
.710674 
.710001 

• 709329 
. 708658 

o. 707987 
.707318 
. 706650 

• 705983 
.705316 

o. 704651 

. 703987 
. 703323 

. 702661 

. 701999 

o. 701338 
. 700678 
. 700020 

. 699362 
. 698705 

o. 698049 

.■697393 
. 696739 
. 696086 
. 695433 

o. 69^782 

.694131 
.693481 
. 692832 

.692184 

0.691537 

.690891 
. 690246 
.689601 

. 688958 

0.688315 

. 687673 

. 687032 

.686392 
.685753 

0.6851 15 
. 684477 
.683841 
. 683205 
. 682570 

0.681936 
.681303 

. 680670 
. 680039 
. 679408 

o. 678778 
.678149 
.677521 
. 676894 
. 676267 

0.675642 
.675017 

.674393 
. 673769 
.673147 

o. 672525 
Tan,. 



78' 



12° COSINES, TANGENTS, AND COTANGENTS zQf 



M. 



10 
ii 

12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 

24 

25 

26 
27 
28 
29 
30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9.317879 

.318473 
.319066 
.319658 
. 320249 

9.320840 
.321430 
.322019 
. 322607 
.323194 

9. 323780 
.324366 
. 324950 

• 325534 
.326117 

9. 326700 
.327281 
. 327862 
. 328442 
. 329021 

9- 329599 
.330176 

• 330753 
.331329 
•331903 

9- 332478 
•333051 
• 333 6 24 
•334195 

• 334767 

9- 335337 
• 3359o6 

• 336475 

• 337043 
.337610 

9-338176 

• 338742 

• 339307 
•339871 

• 340434 

9. 340996 
.341558 
.342119 

• 342679 

• 343239 
9- 343797 

• 344355 
• 3449 12 

• 345469 
. 346024 

9-346579 
•347134 
. 347687 
. 348240 

• 348792 
9- 349343 

• 349893 

• 350443 

• 350992 
•35i54o 

9. 352088 

Cos. 



D. i' 



9.90 
9.88 
9.87 
9.85 
9.85 
9.83 
9.82 
9.80 
9.78 
9-77 

9-77 
9-73 
9-73 
9.72 
9.72 
9.68 
9.68 
9.67 
9.65 
9.63 
9.62 
9.62 
9.60 
9-57 
9-58- 
9-55 
9-55 
9.52 
9-53 
9.50 

9.48 
9.48 
9-47 
9-45 
9-43 
9-43 
9.42 
9.40 
9.38 
9-37 

9-37 
9-35 
9-33 
33 
30 
30 
28 
28 
25 



9- 
9- 
9- 
9- 
9- 
9- 
9.25 

9.25 
9. 22 
9. 22 
9. 20 



9-13 



D. 1 



Cos. 



990404 
99037S 

990351 
990324 

990297 
990270 
990243 
990215 
990188 
990161 

99oi34 
990107 
990079 
990052 
990025 
989997 
989970 
9S9942 
989915 
989887 



D. 1' 



o 

989832 
989804 

989777 
989749 
989721 
989693 
989665 
989637 
989610 

989582 
989553 
989525 
989497 
989469 
989441 
989413 
989385 
989356 
989328 

989300 
989271 

989243 
989214 
989186 

989157 
989128 
989100 
989071 
989042 

989014 
988985 
988956 
988927 



988840 
98881 1 
988782 

988753 
988724 

Sin. 



43 
45 
45 
45 
45 
45 
47 
45 
45 
45 

45 

47 
45 
45 
47 
45 
47 
45 
47 
45 

47 
47 
45 
47 
47 
47 
47 
47 
45 
47 

48 
47 
47 
47 
47 
47 
47 
48 

47 
47 

48 
47 
48 
47 
48 
48 
47 
48 
48 
47 



Tan. 



D. i' 



D. i' 



9- 327475 

• 328095 

•328715 

• 329334 

• 329953 
9- 330570 

.331187 
.331803 
.332418 

• 333033 

9- 333646 

• 334259 
.334871 

• 335482 

• 336093 
9. 336702 

•3373II 
.337919 
. 338527 
•339!33 

9- 339739 
. 340344 
. 34094S 

• 341552 
.342155 

9.342757 

• 343358 

• 343958 

• 344558 

• 345157 

9. 345755 

• 346353 

• 346949 

• 347545 
.348141 

9- 348735 

• 349329 

• 349922 
.350514 
.351106 

9- 351697 

.352287 
.352876 

• 353465 

• 354053 
9- 354640 

• 355227 
.355813 

• 356398 
. 356982 

9.357566 
.358149 

• 358731 

• 359313 

• 359893 
9. 360474 

.361053 
.361632 
.362210 
.362787 
9- 363364 

Cot. 



10.33 
10.33 
10.32 
10.32 
10.28 
10.28 
10. 27 
10.25 
10.25 
10. 22 

10. 22 
10. 20 
10.18 
10.18 
10.15 
10.15 
10.13 
10.13 
10. 10 
10. 10 

10.08 
10.07 
10.07 
10.05 
10.03 
10. 02 
10.00 
10.00 
9.98 
9-97 

9-97 
9-93 
9-93 
9-93 
9.90 
9.90 
9.88 
9.87 
9.87 
9.85 

9.83 
9.82 
9.82 
9.80 
9.78 
9.78 
9-77 
9.75 
9-73 
9-73 
9.72 
9.70 
9.70 

9.67 
9.68 

9.65 
9-65 
9.63 
9.62 
9.62 



Cot. 



D. 1 



o. 672525 
.671905 
.671285 
. 670666 
. 670047 

o. 669430 

.668813 
.668197 
.667582 

. 666967 
o. 666354 

.665741 

.665129 

.664518 
. 663907 

o. 663298 

. 662689 
.662081 
.661473 
. 660867 

0.660261 

.659656 

• 659052 

. 658448 
. 657845 

o. 657243 
.656642 
. 656042 

• 655442 
. 654843 

o. 654245 

. 653647 
•653051 
•652455 

• 651859 

0.651265 
.650671 
. 650078 
. 649486 

. 648894 

o. 648303 

.647713 
.647124 

• 646535 

• 645947 

o. 645360 

•644773 

.644187 
. 643602 
.643018 

o. 642434 

.641851 

.641269 

. 640687 

.640107 

o. 639526 

. 638947 
.638368 

• 637790 
.637213 

o. 636636 
Tan. 



60 
59 
58 
57 
56 
55 
54 
53 
52 
5i 

50 
49 

48 

47 
46 

45 
44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

2 i 
28 

27 
26 

25 

24 

23 
22 
21 

20 

19 

18 

17 
16 

15 
14 
13 
12 
11 



I 

7 
6 

5 

4 
3 
2 
1 
o 

M. 



77' 



13* 



LOGARITHMIC SINES 



i66° 



M. 



Sin. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
14 
15 
16 

17 
18 

19 

20 

21 
22 

23 
2 4 

25 
26 

27 

28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9. 352088 

• 352635 
.353i8i 
.353726 
.354271 

9-3548I5 

• 355358 
.355901 
.356443 

• 356984 

9- 357524 

• 358064 
. 358603 

• 359HI 

• 359678 
9.360215 

. 360752 
.361287 
.361822 
. 362356 
9.362889 

• 363422 

• 363954 
. 364485 

• 365016 
9- 365546 

.366075 
. 366604 
.367131 

• 367659 
9.368185 

.368711 
. 369236 
.369761 
.370285 
9. 370808 
.371330 
.371852 
.372373 
.372894 

9-3734H 

• 373933 

• 374452 

• 374970 
. 375487 

9- 376003 
.376519 
. 377035 
•377549 
. 378063 

9- 378577 

• 379089 
. 379601 
.380113 
. 380624 

9-38ii34 
.381643 
.382152 
. 382661 
.383168 

9- 383675 

Cos. 



D. i' 



D. i' 



Cos. 



9.988724 
988695 
988666 
988636 
988607 
988578 



988519 
988489 
988460 

988430 
988401 

988371 
988342 
988312 
988282 
988252 
988223 

988193 
988163 

988133 
988103 
988073 
988043 
988013 
987983 

987953 
987922 
987892 
987862 

987832 
987801 
987771 
987740 
987710 

987679 
987649 
987618 
987588 
987557 
987526 
987496 
987465 

987434 
987403 
987372 

987341 
987310 
987279 
987248 

987217 
987186 

987155 
987124 
987092 
987061 
987030 
986998 
986967 
986936 
986904 

Sin. 



D. 1". 



.48 
.48 
.50 
.48 
.48 
.50 
.48 
.50 
.48 
•50 

.48 
.50 
.48 
.50 
.50 
.50 
.48 
.50 
•50 
•50 

■ -50 
.50 
.50 
•50 
.50 
•50 
.52 
.50 
.50 
.50 

.52 
.50 
.52 
.50 
.52 
.50 
.52 
.50 
.52 
.52 

.50 
.52 
.52 
•52 
.52 
.52 
.52 
.52 
.52 
.52 

.52 
.52 

• 52 

• 53 
.52 
.52 

• 53 
.52 

• 52 

• 53 

D. 1" 



Tan. 



9. 363364 
. 363940 
.364515 
. 365090 
. 365664 

9- 366237 
.366810 
.367382 

• 367953 

• 368524 

9. 369094 
. 369663 
. 370232 

• 370799 
.371367 

9-37I933 

• 372499 

• 373064 

• 373629 
.374193 

9- 374756 
.375319 
.375881 

• 376442 
- 377003 

9- 377563 
.378122 
.378681 

• 379239 

• 379797 

9- 380354 
.380910 
.381466 
. 382020 

.382575 

9.383129 

.383682 

• 384234 
.384786 

• 385337 
9.385888 

.386438 
.386987 

• 387536 
. 388084 

9.388631 
.389178 
. 389724 
. 390270 
. 390815 

9. 391360 
•39I903 

• 392447 

• 392989 
•393531 

9- 394073 
.394614 
.395154 

• 395694 

• 396233 
9. 396771 

Cot. 



D. i' 



D. 1". 



Cot. 



o. 636636 
. 636060 

.635485 
.634910 

• 634336 
o. 633763 

.633190 
.632618 
. 632047 
.631476 

o. 630906 

• 630337 
. 629768 

.629201 

.628633 

o. 628067 

.627501 

. 626936 

.626371 
. 625807 

o. 625244 

.624681 
.624119 

.623558 

.622997 

0.622437 
.621878 
.621319 
.620761 
. 620203 

0.619646 
.619090 

.618534 

.617980 

.617425 

0.616871 

.616318 
.615766 
.615214 
. 614663 

0.614112 

.613562 
.613013 

.612464 
.611916 
0.61 1369 
.610822 
.610276 

. 609730 
.609185 

o. 608640 
. 608097 

. 607553 

.607011 

. 606469 

o. 605927 

. 605386 

. 604846 
. 604306 

. 603767 

o. 603229 
Tan. 



103 



7 6« 



COSINES, TANGENTS, AND COTANGENTS 165' 



M. 



Sin, 



D. 1". 



Cos. 



o 
1 
2 
3 
4 
5 
6 

7 
8 

9 
10 
11 
12 
13 
M 
15 
16 

17 
18 

19 

20 
21 
22 

23 

24 

25 

26 I 

27 

28 

29 

30 

3i 

32 

33 

34 

35 

36 

37 

38 

39 

40 

4i 

42 

43 

44 

45 

46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9-383675 
.384182 
.384687 
.385192 

• 385697 
9. 386201 

. 386704 

. 337207 

• 387709 
.388210 

9. 38871 1 
.389211 
.389711 
.390210 
. 390708 

9.391206 

.391703 
.392199 

. 392695 
.393191 

9- 3936S5 
.394179 

• 394673 
.395166 

• 395653 
9. 396150 

.396641 
.397132 
.397621 
.398111 

9. 398600 
.399088 

• 399575 
. 400062 
.400549 

9.401035 
.401520 
. 402005 
. 402489 
.402972 

9- 403455 

• 403938 
. 404420 
.404901 

• 405382 
9- 405^62 

.406341 
. 406820 

• 407299 
.407777 

9.408254 
.408731 
. 409207 
. 409682 
.410157 

9.410632 
.411106 

.411579 

.412052 

.412524 

9.412996 

Cos. 



8.45 
8.42 
8.42 
8.42 
8.40 
8.38 
8.38 
8.37 
8-35 
8.35 

8-33 
8-33 
8.32 
8.30 
8.30 
8.28 
8.27 
8.27 
8.27 
8.23 

8.23 
8.23 
8.22 
8.20 
8.20 
8.18 
8. 18 
8.15 

8.17 

8.15 

8.13 
8.12 
8.12 
8.12 
8. 10 
8.08 
8.08 
8.07 
8.05 
8.05 

8.05 
8.03 
8.02 
8.02 
8.00 
7.98 
7.98 
7.98 
7-97 
7-95 

7-95 
7-93 ! 
7.92 1 

7.92 
7.92 
7.90 
7.88 
7.88 
7.87 
7.87 

D. 1". 



9. 986904 
.986873 

.986841 
. 986S09 
.986778 
9.9S6746 
.986714 
. 986683 
.986651 
.986619 

9.986587 

• 986555 
. 9S6523 
.986491 

• 986459 
9. 986427 

• 986395 
. 986363 
.986331 
. 986299 

9. 986266 

• 986234 
. 986202 
.986169 

.986137 
9.986104 
. 986072 
. 986039 
. 986007 

• 985974 
9. 985942 

• 985909 
.985876 

.985843 
.985811 

9- 985778 
.985745 
.985712 

. 985679 
. 985646 

9-985613 
.9855S0 

.985547 
.985514 

• 985480 

9- 985447 

.985414 
.985381 

.985347 

.985314 

9. 985280 

.985247 

•985213 
.985180 
.985146 

9-985113 
.985079 

• 9S5045 
.985011 

• 984978 
9. 984944 

Sin. 



D. 1' 



Tan. 



D. 1 '. 



D. 1 



9.396771 
397309 
397846 
3983S3 
398919 

399455 
399990 
400524 
401058 
401 59 1 

402124 
402656 

403 1 S7 
403718 
404249 
40477.8 
40530S 
405836 
406364 
406892 

407419 

407945 
408471 
408996 
409521 
410045 
410569 
4 1 1092 
411615 
412137 

41265S 

4I3I79 
413699 
414219 
4H738 
415257 
415775 
416293 
416810 
417326 

417842 
418358 
418873 
419387 
4 1990 1 
420415 
420927 
421440 
421952 
422463 

422974 

423484 
423993 
424503 
42501 1 

425519 
426027 

426534 
427041 

427547 
428052 

Cot. 



D. 



Cot. 



T " 
1 ' 



0.603229 
. 60269I 
.602154 
.60l6l7 
.6OIO8I 

o. 600545 
.60COIO 

. 599476 
. 598942 
.598409 

o. 597876 50 

.597344 

.596813 

. 596282 
•595751 

o. 595222 

• 594692 
.594164 

• 593636 
.593108 

o. 592581 

• 592055 

•591529 
.591004 

. 590479 

°. 589955 

.589431 
. 588908 

.588385 
.587863 

o. 587342 

.586821 
. 586301 

.585781 

. 585262 

o. 584743 

. 584225 
.583707 
.583190 
. 582674 

0.582158 
.581642 
.581127 
.580613 
. 580099 

o. 579585 

. 579073 
.578560 
.578048 

. 577537 

o. 577026 

.576516 

. 576007 

• 575497 

• 574989 
0.574481 

•573973 

• 573466 
.572959 

• 572453 
0.571948 

Tan. 



75' 



i5 ( 



LOGARITHMIC SINES 



i6 4 < 



M. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
M 
15 

16 

17 

18 

19 

20 
21 

22 

23 
2 4 

25 
26 

27 

28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



Sin. 



9.412996 
.413467 
.413938 
.414408 
.414878 

9-415347 
.415815 
.416283 
.416751 
.417217 

9.417684 
.418150 
.418615 
.419079 

.419544 

9. 420007 

. 420470 

• 420933 
.421395 
.421857 

9.422318 
.422778 
.423238 
. 423697 
.424156 

9.424615 
.425073 

• 425530 
. 425987 

• 426443 
9. 426899 

.427354 
. 427809 
.428263 
.428717 
9.429170 

• 429623 
.430075 
. 430527 
.430978 

9. 431429 

.431879 

• 432329 
.432778 
. 433226 

9- 433675 
.434122 

.434569 
.435016 

• 435462 

9- 435908 
. 436353 
.436798 

• 437242 
.437686 

9.438129 
. 438572 

• 439014 

• 439456 

• 439897 
9- 440338 



D. 1' 



Cos. 



85 
85 

83 
S3 

82 

80 
80 

So 

77 
78 

77 
75 
73 
75 
72 
72 
72 
70 
70 
68 

67 
67 
65 
65 
65 
63 
62 
62 
60 
60 

58 

58 
57 
57 
55 
55 
53 
53 
52 
52 

50 
50 
48 

47 
48 

45 
45 
45 
43 

43 

42 
42 
40 
40 
38 
38 
37 
37 
35 
35 



D. 1". 



Cos. 



). 984944 
.984910 
. 984876 
.984842 



9.984774 

• 984740 
. 984706 
. 984672 
.984638 

9. 984603 
.984569 
.984535 
.984500 
. 984466 

9. 984432 
.984397 
.984363 
.984328 

.984294 

9. 984259 
. 984224 
.934190 

• 984155 
.984120 

9. 984085 
. 984050 

• 984015 
.983981 

• 983946 

9-9839" 

.983875 
. 983840 

.983805 
. 983770 
9-983735 
. 983700 
. 983664 
.983629 

• 983594 

9- 983558 
.983523 
.983487 
.983452 
.983416 

9.983381 

• 983345 
. 983309 

• 983273 
.983238 

9. 983202 
.983166 
.983130 

. 983094 
.983058 

9. 983022 
. 982986 
. 982950 
.982914 
. 982878 

9. 982842 



D. 1' 



Sin. 



• 57 

• 57 

• 57 

• 57 
-57 

• 57 

• 57 
-57 
-57 
.58 

• 57 

• 57 
.58 
•57 

• 57 
.58 
-57 
.58 

• 57 
.58 

.58 
-57 
.58 
.58 
.58 
.58 
.58 

• 57 
.58 
.58 

.60 
.58 
.58 
.58 
■58 
.58 
.60 
.58 
.58 
.60 

.58 
.60 

.58 
.60 
.58 
,60 
.60 
.60 
58 
.60 

,60 
60 
60 
60 
60 
60 
60 
60 
60 
60 



Tan. 



D. 1' 



Cot. 



9- 



9- 



9- 



D. 1". 



9- 



428052 
428558 
429062 
429566 

, 430070 
430573 

■431075 
431577 
432079 
432580 

433080 
43358o 
434080 

434579 
435078 
435576 
436073 
436570 
437067 
437563 

438059 

438554 

439048 

439543 

440036 

440529 

.441022 

.441514 

. 442006 

■ 442497 
. 442988 

• 443479 
. 443968 
. 444458 
■444947 

■ 445435 

■ 445923 
,446411 

, 446898 

■ 447384 
447870 
448356 
448841 
449326 
449810 
450294 
450777 
451260 

451743 
452225 

452706 
453187 
453668 
454148 
454628 
455107 
455586 
456064 
456542 
457019 
457496 



Cot. 



8.43 
8.40 
8.40 
8.40 
8.38 
8.37 
8-37 
8-37 
8.35 
8-33 

8.33 
8.33 
8.32 
8.32 
8.30 
8.28 
8.28 
8.28 
8.27 
8.27 

8.25 
8.23 
8.25 
8.22 
8.22 
8.22 
8.20 
8.20 
8.18 
8.18 

8.18 
8.15 
8.17 
8.15 
8.13 
8.13 
8.13 
8.12 
8.10 
8.10 

8.10 
8.08 
8.08 
8.07 
8.07 
8.05 
8.05 
8.05 
8.03 
8.02 

8.02 
8.02 
8.00 
8.00 
7.98 
7.98 
7-97 
7-97 
7-95 
7-95 



D. 1". 



0.571948 
.57M42 

• 570938 

• 570434 
.569930 

0.569427 
. 568925 
.568423 
.567921 
.567420 

o. 566920 
.566420 

• 565920 
.565421 
. 564922 

o. 564424 

. 563927 
. 563430 
. 562933 
.562437 

0.561941 
. 561446 
.560952 
. 560457 
. 559964 

0.559471 
.558978 
.558486 
.557994 
. 557503 

0.557012 
.556521 
.556032 
. 555542 
. 555053 

o. 554565 

. 554077 
. 553589 
.553102 
.552616 

o. 552130 

.551644 
.551159 
. 550674 

• 550 1 90 
o. 549706 

. 549223 
. 548740 
. 548257 
.547775 

o. 547294 

.546813 
.546332 
.545852 
. 545372 

o. 544893 

.544414 
. 543936 
. 543458 
. 542981 

o. 542504 



105' 



Tan. M. 



i6< 



COSINES, TANGENTS, AND COTANGENTS 163* 



M. 



o 

1 
2 
3 
4 
5 
6 

7 
8 

9 

10 
11 
12 
13 
14 
15 
16 

17 

18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 



50 
5i 
52 
53 
54 

56 

5 l 
58 

59 
60 



Sin. 



9. 440338 
. 44077S 
.441218 
.441658 
. 442096 

9- 442535 

• 442973 
.443410 

.443847 
.444284 

9. 444720 

• 445155 
. 445590 
. 446025 

• 446459 
9. 446893 

. 447326 

• 447759 
.448191 
. 448623 

9. 449054 
. 449485 
.449915 

• 450345 

• 450775 
9. 451204 

.451632 
. 452060 
.452438 
.452915 



9. 453342 

• 453768 

•454194 
.454619 

. 455044 

35 9.455469 

36 . 455893 

37 .456316 



• 456739 
.457162 



40 9. 457584 

41 I .458006 

• 458427 
.458848 
. 459268 

9.459688 
.46010S 

• 460527 
. 460946 
. 461364 



9.461782 
.462199 
. 462616 
. 463032 

• 463448 
9. 463S64 

• 464279 
. 464694 
.46510S 
.465522 

9- 465935 



Cos. 



D. 1". 



7-33 
7.33 
7-33 
7.30 
7-32 
7-3o 
7.28 
7.28 
7.28 
7.27 

7.25 
7.25 
7.25 
7.23 
7.23 
7.22 
7. 22 
7. 20 
7. 20 
7.18 



Cos. 



D. 1' 



7.13 
7.13 
7-i3 
7. 12 
7. 12 

7. 10 
7. 10 
7.08 
7.0S 
7.08 
7.07 
7-05 
7-05 
7.05 
7-03 

7.03 
7.02 
7.02 
00 
00 
00 



6-95 

6-95 

6-93 

6-93 

6.93 

6.92 

6.92 

6.90 

6.90 I 

6.88 



D. i". 



9. 982842 
982805 
982769 

982733 
982696 
982660 
982624 
982587 

982551 
982514 

982477 
982441 
982404 
982367 
982331 
982294 
982257 
982220 
982183 
982146 

982109 
982072 
982035 
981998 
981961 
981924 
981886 
981849 
981812 
981774 

981737 
981700 
9S1662 
981625 
981587 
981549 
981512 
981474 
981436 
981399 

981361 
981323 
981285 
981247 
981209 
981171 

981 133 
981095 
981057 
981019 

980981 
980942 
980904 
980866 
980827 
980789 
980750 
980712 
980673 
980635 
980596 

Sin. 



.62 

.60 
.60 
.62 
.60 
.60 
.62 
.60 
.62 
.62 

.60 
.62 
.62 
.60 
.62 
.62 
.62 
.62 
.62 
.62 

.62 
.62 
.62 
.62 
.62 

.63 
.62 
.62 

.63 
.62 

.62 

.63 
.62 

.63 
.63 
.62 

.63 
.63 
.62 

.63 

.63 
.63 
.63 
.63 
.63 
.63 
.63 
.63 
.63 
.63 

.65 
.63 
.63 
.65 
.63 
.65 
.63 
.65 
.63 
.65 



Tan. 



D. 1' 



9- 457496 

• 457973 

• 458449 

• 458925 

• 459400 

9- 459875 
. 460349 
. 460823 
.461297 
.461770 

9.462242 
.462715 
.463186 
•463658 
.464128 

9- 464599 
. 465069 

• 465539 
. 466008 

• 466477 

9. 466945 
.467413 
. 467880 

• 468347 
. 46SS14 

9. 469280 

• 469746 
.470211 
. 470676 
.471141 

9.471605 
. 472069 

• 472532 

• 472995 

• 473457 
9-4739I9 

.474381 

• 474842 

• 475303 
.475763 

9. 476223 
.476683 
.477142 
. 477601 

• 478059 
9.478517 

•478975 

• 479432 
. 479889 

• 480345 
9. 480801 

.481257 
.481712 
.482167 
.482621 
9- 483075 

• 483529 
• 4839S2 

• 484435 
. 484887 

9- 485339 
Cot. 



D. 1' 



Cot. 



7-95 
7-93 
7-93 
7.92 
7.92 
7.90 
7.90 
7.90 
7. 88 
7.87 
7.88 
7.85 
7.87 
7.83 
7.85 
7.83 
7.83 
7.82 
7.82 
7.80 

7.80 
7.78 
7.78 
7.78 
7-77 
7-77 
7-75 
7-75 
7-75 
7-73 

7-73 
7.72 
7.72 
7.70 
7.70 
7.70 
7.68 
7.68 
7.67 
7.67 
7.67 
7.65 
7.65 
7.63 
7.63 
7.63 
7.62 
7.62 
7.60 
7.60 

7.60 
7.58 
7.58 
7.57 

57 

57 

55 

55 

53 

55 



D. 



o. 542504 

• 542027 

.541551 
041075 
. 540600 
0.540125 
.539651 
•539177 
.538703 
. 538230 

o. 537758 

• 537285 
.536814 
. 536342 

• 535872 
0.535401 

.534931 
. 534461 
. 533992 

. 533523 
o. 533055 

. 532587 
.532120 
.531653 

.531186 

o. 530720 

. 530254 
. 529789 

• 529324 
. 528859 

o. 528395 

.527931 
. 527468 
.527005 

• 526543 

o. 526081 

. 525619 
.525158 
. 524697 
. 524237 

o. 523777 

.523317 
.522858 

. 522399 

.521941 

0.521483 

.521025 

. 520568 
.520111 

.519655 

o. 519199 

.518743 
.518288 

.517833 
.517379 
0.516925 
.516471 
.516018 
•515565 
.515113 

o. 514661 
Tan. 



60 
59 
58 
57 
56 
55 
54 
53 
52 
5i 

50 
49 

4 8 

47 
46 
45 
44 
43 
42 

4i 
40 
39 
38 
37 
36 
35 
34 
33 
32 
3i 

30 
29 
28 

27 
26 

25 
24 

23 
22 
21 

20 

19 
18 

17 
16 

15 
M 

13 
12 
11 



7 
6 

5 

4 
3 
2 

1 
o 

M. 



>6° 



73' 



17° 



LOGARITHMIC SINES 



i6,2 £ 



M. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
14 
15 
16 

17 
18 

19 

20 
21 
22 
23 

24 

25 
26 

27 
28 

29 
30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

4 l 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 

59 
60 



IO7 



Sin. 



9- 465935 
. 466348 
. 466761 
.467173 
.467585 

9. 467996 
. 468407 
.468817 
. 469227 
.469637 

9. 470046 

. 470455 
. 470863 
.47T271 
.47T679 
9. 472086 
.472402 
. 47-1898 

.473304 
.473710 

9.474II5 

•4745*9 
.474923 
.475327 
.475730 

9-476 T 33 
. 476536 
.476938 
.477340 
.477741 

9. 478142 

• 478542 
. 478042 
. 470342 
•479 7 4i 

9.480140 

• 480539 

• 480937 
.481334 
.481731 

9.482128 
.482525 
.482921 
.483316 
.483712 

9. 484107 
. 484501 
. 484895 
.485289 
.485682 

9. 486075 
. 486467 
. 486860 
. 487251 

. 487643 
9. 488034 
. 488424 
.488814 
. 489204 

. 489593 
9. 489982 

Cos. 



D. i' 



Cos. 



D. i' 



6.88 
6.88 
6.87 
6.87 
6.85 
6.85 
6.83 
6.83 
6.83 
6.82 

6.82 
6.80 
6.80 
6.80 
6.78 
6.77 
6.77 
6.77 
6.77 
6-75 

6.73 
6-73 
6.73 
6.72 
6.72 
6.72 
6.70 
6.70 
6.68 
6.68 

6.67 

6.67 
6.67 
6.65 
6.65 
6.65 
6.63 
6.62 
6.62 
6.62 

6.62 
6.60 
6.58 
6.60 
6.58 
6.57 
6-57 
6.57 
6-55 
6-55 

6-53 
6.55 
6.52 
6.53 
6.52 
6.50 
6.50 
6.50 
6.48 
6.48 



D. I". 



9. 980596 
.980558 
.980519 
. 980480 
. 980442 

9. 980403 
. 980364 
. 980325 
. 980286 
.980247 

9. 980208 
.980169 
.980130 
. 980091 
. 980052 

9.980012 
. 9799^3 

• 979934 
. 979895 
.979855 

9.979816 
. 979776 
•979737 
.979697 
. 979658 

9.979618 

• 979579 

• 979539 

• 979499 
. 979459 

9.979420 
.97938o 

• 979340 
. 9793oo 
. 979260 

9. 979220 
.979180 
.979140 
.979100 
. 979059 

9.979019 

• 978979 
.978939 



.978858 
9.978817 
.978777 
.978737 
. 978696 

.978655 
9.978615 
.97S574 
. 978533 
.978493 
. 978452 
9. 97841 1 
. 978370 
. 978329 
. 978288 

• 978247 
9. 978206 

Sin. 



.63 
.65 
.65 
.63 
.65 
.65 
.65 
.65 
.65 
.65 

.65 
.65 
.65 
.65 
.67 
.65 
.65 
.65 
.67 
.65 

.67 
.65 
.67 
.65 
.67 
.65 
.67 
.67 
.67 
.65 

.67 
.67 
.67 
.67 
.67 
.67 
.67 
.67 
,68 
.67 

.67 
.67 
,68 

.67 

,68 

.67 
,67 
,68 
,68 
,67 

,68 
68 
67 
,68 

68 
68 
68 
68 
68 
68 



Tan. 



9- 485339 
.485791 
. 486242 
.486693 
.487143 

9- 487593 
.488043 
. 488492 
. 488041 

• 489390 

9.480838 
. 490286 

• 490^33 
.491180 
.491627 

9. 492073 
.492519 

.492965 
.493410 

.493854 

9. 494299 
•494743 
.495186 

. 495630 

. 496073 

9- 490515 

. 496957 

• 497399 
.497841 
.498282 

9. 498722 
.499163 

• 499603 
. 500042 
.500481 

9. 500920 

.501359 
.501797 
. 502235 
. 502672 

9.503109 

• 503546 
. 503982 
.504418 

. 504854 
9. 505289 

• 505724 
.506159 
.506593 
. 507027 

9.507460 

.507893 
. 508326 

. 508759 

. 509191 

9. 509622 

.510054 

.510485 

.510916 

.511346 

9. 51 1776 

Cot. 



D. 1". 



Cot, 



7-53 



52 
52 
50 
50 
50 
48 
48 
48 
47 



7-47 
7-45 
7-45 
7-45 
7-43 
7-43 
7-43 
7.42 
7.40 
7.42 

7.40 
7.38 
7.40 
7.38 
7-37 
7-37 
7-37 
7-37 
7-35 
7.33 

7-35 



7.28 
7.28 

7.28 
7.27 
7.27 



7. 22 

7. 22 
7. 22 
7. 22 
7. 20 
7.18 
7.20 
7.18 
7.i8 
7.17 
7.17 



D. 



o. 514661 
.514209 
.513758 
• 513307 
.512857 

0.512407 

.511957 
.511508 
.511059 
.510610 

o. 510162 

.509714 
.509267 
. 508820 

.508373 

o. 507927 

.507481 
. 507035 
. 506590 
. 506146 

0.505701 

.505257 
.504814 

. 504370 
. 503927 

o. 503485 

. 503043 

.502601 

. 502159 
.501718 

0.501278 

. 500837 
. 500397 
.499958 
.499519 

o. 499080 
.498641 
. 498203 

.497765 
.497328 

0.496891 

. 496454 

.496018 

.495582 
. 495146 

0.49471 I 
.494276 
.493841 
.493407 
.492973 

0.492540 

.492107 

.491674 
.491241 

. 490809 
o. 490378 

.489946 
.489515 

. 489084 

.488654 

o. 488224 
Tan. 



72° I 



l8° COSINES, TANGENTS, AND COTANGENTS xfo* 



M. Sin. D. i". Cos. D. i". Tan. D. i". Cot. 



9. 489982 
•49037I 
• 49°759 
.491147 
.491535 

9.491922 
. 492308 
. 49 26 95 
.493081 
.493466 



10 9. 493851 
.494236 
.494621 
. 495005 
.495388 
9- 495772 
.496154 

. 496537 
.496919 
• 497301 



11 
12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 

26 
27 
28 
29 

30 

3i 
32 
33 
34 

35 ! 

36 I 

37 1 
38| 
39 I 



9- 



40 
4i 
42 
43 
44 
45 
46 

47 

1 48 

49 

5o; 

5i I 
52 
53 
54 

55 
56 

57 
58 
59 
60 



497682 
498064 

498444 
.498825 
. 499204 
9- 499584 
•499963 
. 500342 
.500721 
. 501099 

9. 501476 
.501854 
.502231 
. 502607 
. 502984 

9- 503360 
. 503735 
.504110 

• 504485 
. 504860 

9- 505234 

• 505608 
.505981 

• 506354 

• 506727 
9. 507099 

.507471 

• 507843 
.508214 

.508585 

9. 508956 
. 509326 
.509696 
.510065 

.510434 
9. 510803 
.511172 
.511540 
.511907 
.512275 
9.512642 



6.48 

6.47 
6.47 
6.47 
6.45 
6.43 
6-45 
6.43 
6.42 
6.42 

6.42 
6.42 
6.40 
6.38 
6.40 

6-37 
6.38 

6.37 
6.37 
6-35 

6.37 
6-33 
6-35 
6.32 

6-33 
6.32 
6.32 
6.32 
6.30 
6.28 

6.30 
6.28 
6.27 
6.28 
6.27 
6.25 
6.25 
6.25 
6.25 
6.23 

6.23 
6. 22 
6. 22 
6. 22 



Cos. 



6.18 

6.17 
6.17 
6.15 
6.15 
6.15 
6.15 
6.13 
6. 12 

6.13 
6.12 



D. 1". 



9. 97S206 
.978165 
.978124 
.978083 
. 978042 

9.978001 

• 977959 
. 9779 J 8 
.977877 
•977835 

9- 977794 
•977752 
.977711 
. 977669 
. 977628 

9.977586 

• 977544 

• 977503 
.977461 

.977419 

9- 977377 

• 977335 
. 977293 
.977251 
. 977209 

9.977167 
.977125 
.977083 
. 977041 
. 976999 

9.976957 

.976914 
. 976872 
. 976830 
.976787 
9- 976745 
. 976702 
. 976660 
.976617 

• 976574 

9- 976532 
. 976489 
. 976446 

• 976404 
.976361 

9.976318 

• 976275 
. 976232 
.976189 
. 976146 

9. 976103 
.976060 
.976017 

• 975974 

• 975930 
9- 975887 

• 975844 
. 975800 

•975757 

.975714 

9. 975670 

Sin. 



.68 
.68 
.68 
.68 
.68 
•7o 
.68 
.68 
.70 
.68 

•70 
.68 
.70 
.68 
.70 
.70 
.68 
.70 
.70 
.70 

.70 

.70 
.70 
.70 
.70 
.70 
.70 
.70 
.70 
.70 

.72 
.70 
.70 
.72 
.70 
.72 
.70 
.72 
.72 
.70 

.72 
.72 
.70 
.72 
.72 
.72 
.72 
.72 
.72 
.72 

• 72 

.72 
.72 

• 73 
.72 
.72 

• 73 
.72 
.72 
•73 

D. 1" 



9.511776 
.512206 
•512635 
.513064 
.513493 

9-5I392I 
.5H349 
.514777 
. 515204 

.515631 

9- 5 l6 o57 

• 516484 
.516910 

.517335 
.517761 
9.518186 
.518610 
.519034 
.519458 
.519882 

9. 520305 
. 520728 
.521151 
.521573 

• 521995 
9.522417 

.522838 

• 523259 
. 523680 
. 524100 

9.524520 

• 524940 

• 525359 

• 525778 
.526197 

9. 526615 
. 527033 

• 527451 
.527868 
.528285 

9. 528702 
.529119 

• 529535 
.529951 

• 530366 
9- 530781 

.531196 
.531611 

• 532025 

• 532439 

9- 532853 

• 533266 

• 533679 

• 534092 

• 534504 
9- 5349i6 

• 535328 

• 535739 

• 536150 

• 536561 
9- 536972 

Cot. 



7.13 
7. 12 
7. 12 
7. 10 

7.12 
7. 10 
7.08 
7. 10 
7.08 
7.07 
7.07 

7.07 
7.07 

7- °5 

7.05 
7.05 
7-03 
7-03 
7- °3 
7.02 
7.02 
7.02 
7.00 
7.00 

7.00 
6.98 
6.98 
6.98 
6.97 

6-97 
6.97 

6-95 
6-95 
6-95 

6-95 
6-93 
6.93 
6.92 
6.92 
6.92 
6. 92 
6.90 
6.90 
6.90 

6.88 
6.88 
6.88 
6.87 
6.87 
6.87 
6.85 
6.85 
6.85 
6.85 



D. 1' 



o. 488224 

• 487794 

• 487365 
. 486936 
. 486507 

o. 486079 

.485651 

. 485223 

.484796 
.484369 

o. 483943 
.483516 
. 483090 
. 482665 
. 482239 

o. 481814 

. 481390 

. 480966 

. 480542 
.480118 

o. 479695 

.479272 

.478849 
.478427 
. 478005 

o. 477583 

.477162 
.476741 

.476320 

.475900 

o. 47548o 

. 475060 
.474641 
.474222 
. 473803 

o. 473385 

. 472967 
. 472549 
.472132 

.471715 

0.471298 

. 470881 
.470465 
. 470049 
. 469634 

0.469219 

. 468804 
.468389 

. 467975 
.467561 

o. 467147 

. 466734 
.466321 
. 465908 
. 465496 

o. 465084 
. 464672 
.464261 

. 463S50 
. 463439 

o. 463028 
Tan. 



108 



M. 



71' 



itf 



LOGARITHMIC SINES 



i6o c 



M. 



Sin. 



io 
ii 

12 

13 

M 
15 
16 

17 
18 

19 

20 

21 
22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 

48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
Go 



IOg 



512642 
513009 
513375 
5I374I 
514107 
514472 
514837 
515202 
515566 
515930 
516294 
516657 
517020 
5173S2 

517745 
518107 
51846S 
518829 
519190 
5I955I 

5I99II 
520271 
520631 
520990 

521349 
521707 
522066 
522424 
522781 
523138 

523495 
523852 
52420S 

524564 
524920 

525275 
525630 
525984 
526339 
526693 

527046 
527400 

527753 
528105 

528458 
528810 
529161 

529513 
529864 

530215 

530565 
530915 

53*265 

53*614 
531963 
532312 
532661 
533009 
533357 
533704 
534052 

Cos. 



D. 1' 



6. 12 
6. 10 
6. 10 
6. 10 
6.08 
6.08 
6.08 
6.07 
6.07 
6.07 

6.05 

6.05 



6.00 
6. 00 
5.98 
5.98 
5-97 
5.98 
5-97 
5-95 
5-95 
5-95 

5-95 
5-93 
5-93 
5-93 
5.92 
5.92 
5-90 
5-92 
5.90 
5-88 

5-9o 
5. 88 
5-87 
5-88 
5.87 
5- 85 
•5.87 
5.85 
5.85 
5-8 3 

5.83 
5.83 
5.82 
5.82 
5.82 
5.82 
5- 80 
5.8o 
5.78 
5.80 

D. I". 



Cos. 



975670 
975627 

975583 
975539 
975496 
975452 
975408 
975365 
975321 
975277 

975233 
975189 
975145 
975101 

975057 
975013 
974969 

974925 
974880 
974836 

974792 

974748 
974703 
974659 
974614 

974570 
974525 
974481 

974436 
974391 

974347 
974302 

974257 
974212 
974167 
974122 

974077 
974032 
9739S7 
973942 

973897 
973852 
973807 
973761 
973716 
973671 
973625 
97358o 
973535 
973489 

973444 
973398 
973352 
973307 
97326i 

973215 
973169 

973124 

973078 
973032 

9729S6 

Sin. 



D. r 



D. 1 



Tan. D. 1 



Cot. 



• 536972 
•537382 
.537792 
. 538202 
.538611 

• 539020 
.539429 
. 539837 
.540245 
.540653 

.541061 
.541468 

.541875 
. 542281 
. 542688 

• 543094 
.543499 
. 543905 
.5443io 

.544715 

.545119 
. 545524 
.545928 
.546331 
.546735 
■547138 
.547540 
•547943 
.548345 
.548747 

.549149 
. 549550 
.549951 
. 550352 
. 550752 
.551153 
.551552 
.55I95 2 
.552351 
.552750 

.553M9 
.553548 
. 553946 
.554344 
.554741 
. 555139 
. 555536 
. 555933 
.556329 
.556725 

.557121 
.557517 
.557913 
.558308 
. 558703 
. 559097 
.559491 
.5598S5 
■ 560279 
. 560673 
.561066 

Cot. 



6.83 
6.83 
6.83 
6.82 
6.82 
6.82 
6.80 
6.80 
6.80 
6.80 

6.78 
6. 78 

6.77 
6.78 

6.77 
6-75 
6.77 
6.75 
6.75 
6.73 

6.75 
6.73 
6. 72 

6-73 
6. 72 
6. 70 
6. 72 
6. 70 
6.70 
6.70 

6.68 
6.68 
6.6S 
6.67 
6.68 
6.65 
6.67 
6.65 
6.65 
6.65 

6.65 
6.63 
6.63 
6.62 
6.63 
6.62 
6.62 
6.60 
6.60 
6.60 

6.60 
6.60 
6.58 
6.58 
6-57 
6.57 
6-57 
6-57 
6-57 
6 -55 



D. 1' 



o. 463028 
.462618 
. 462208 
.461798 
. 461389 

o. 460980 

.460571 

. 460163 

.459755 
.459347 

o. 458939 

.458532 
.458125 

.457719 
.457312 

o. 456906 

.456501 
• 456095 
. 455690 
.455285 

o. 454881 

.454476 
. 454072 
. 453669 
.453265 

o. 452862 

. 452460 
. 452057 
. 451655 
.451253 

o. 450851 

. 450450 
. 450049 
.449648 
. 449248 

o. 448847 

. 448448 

. 448048 

. 447649 
.447250 

o. 446851 

. 446452 
. 446054 
.445656 
.445259 

o. 444861 

.444464 
.444067 
.443671 
.443275 
0.442879 
. 442483 

.442087 
.441692 

.441297 

o. 440903 

.440509 
.440115 
.439721 
.439327 
°. 43S934 

Tan. 



M. 



70' 



20 ° COSINES, TANGENTS, AND COTANGENTS 159 



M. Sin. D. 1". Cos. D. 1". Tan. D. 1". Cot 



9- 534052 

• 554399 

• 534745 
. 535092 

• 535438 

9- 535783 
.536129 

• 536474 
.536818 

• 537163 

9- 537507 
.537851 
.538194 
.538538 
.538S80 

9- 539223 

• 539565 

• 539907 
. 540249 
• 54O590 

9- 540931 
.541272 

.541613 
.541953 
.542293 
9. 542632 
.542971 
.5433io 

• 543649 
. 543987 

9- 544325 

• 544663 

• 5450oo 
.545338 

• 545674 
9. 54601 1 

.546347 

• 546683 

.547019 

• 547354 

9- 547689 
. 548024 

• 548359 
. 54S693 
• 549027 

9. 549360 

• 549693 

• 550026 

• 550359 

• 550692 

9.551024 
•551356 
.551687 
.552018 

• 552349 
9. 552680 

•5530io 

•553341 

• 553670 
. 554000 

9- 554329 



5-78 
5-77 
5.78 
5-77 
5-75 
5-77 
5-75 
5-73 
5-75 
5-73 



5. 
5- 
5- 
5- 
5- 
5- 
5-/ 



Cos. 



5-7o 
5-68 
5-68 

5-68 
5-68 
5.67 
5.67 
5.65 
5.65 
5.65 
5.65 
5.63 
5.63 

5-6 3 
5.62 
5.63 
5.60 
5.62 
5.60 
5.60 
5.60 
5.58 
5.58 

5.58 
5-58 
5-57 
5-57 
5-55 
5-55 
5-55 
5-55 
5-55 
5-53 

5-53 
5.52 
5.52 
5.52 
5.52 
5-50 
5-52 
5.48 
5.5o 
5.48 

D. 1". 



972986 
972940 
972S94 
972S48 
972802 

972755 
972709 
972663 
972617 
972570 

972524 
972478 
972431 

972385 
972338 
972291 

972245 
972198 
972151 
972105 

972058 
97201 1 
971964 
971917 
971870 
97^23 
971776 
971729 
971682 
971635 

971588 
97i54o 

97M93 
971446 
971398 
97I35I 
971303 
971256 
971208 
971161 

97III3 
971066 
971018 
970970 
970922 
970874 
970827 
970779 
970731 
970683 

970635 
9705S6 
970538 
970490 
970442 

970394 
970345 
970297 

970249 
970200 
970152 

Sin. 



D. i' 



9. 561066 

.561459 
.561851 
. 562244 

• 562636 
9. 563028 

.563419 
.563811 
. 564202 

• 564593 

9- 564983 

• 565373 

• 565763 
.566153 
. 566542 

9. 566932 
. 567320 
. 567709 
. 568098 
. 568486 

9-568873 
. 569261 
. 569648 
. 570035 
. 570422 

9. 570809 
.57H95 
.571581 
.571967 
•572352 

9- 572738 
.573123 

• 573507 

• 573892 
. 574276 

9. 574660 

• 575044 

• 575427 
.5758io 

• 576193 

9- 576576 

• 576959 
•577341 

• 577723 

• 578104 
9. 578486 

.578867 

• 579248 

• 579629 
. 580009 

9. 580389 
. 580769 
.581149 

.581528 

• 5S1907 

9. 5S2286 

.582665 

• 583044 
. 5S3422 
.583800 

9-584I77 

Cot. 



6.55 
6.53 
6.55 
6.53 
6.53 
6.52 
6.53 
6.52 
6.52 
6.50 

6.50 
6.50 
6.50 
6.48 

6.50 
6.47 
6.48 
6.48 
6.47 
6.45 

6.47 
6.45 
6-45 
6.45 
6-45 
6.43 
6-43 
6.43 
6.42 

6.43 
6.42 
6.40 
6.42 
6.40 
6.40 
6.40 
6.38 
6.38 
6.38 
6.38 

6.38 
6.37 
6.37 
6.35 
6.37 
6.35 
6.35 
6.35 
6.33 
6.33 

6.33 
6-33 
6.32 
6.32 
6.32 
6.32 
6.32 
6.30 
6.30 
6.28 



D. 



o- 438934 
.438541 
.438149 

• 437756 

• 437364 
o. 436972 

.436581 
.436189 

• 435798 
.435407 

0.435017 

• 434627 

• 434237 

• 433847 

• 433458 
o. 433068 

. 432680 
. 432291 
.431902 
.431514 
0.431127 

. 430739 
. 430352 
. 429965 
. 429578 

o. 429191 

. 42S805 

. 428419 
. 428033 
. 427648 

0.427262 
. 426877 

. 426493 

.426108 

. 425724 

o. 425340 

. 424956 
. 424573 

.424190 

.423807 

o. 423424 
. 423041 

.422659 
.422277 

.421896 

0.421514 
.421133 
.420752 
.420371 
.419991 

o. 419611 

.419231 

.418851 

.418472 

< 418093 

c.417714 

.417335 
.416956 
.416578 

.416200 

0.415823 

Tan. 



110 



69' 



21 



LOGARITHMIC SINES 



I58 c 



M. 



Sin. 



o 

i 

2 

3 
4 
5 

6 

7 
8 

9 
io 
ii 

12 

13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 

28 

29 
30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 

42 

43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



III 



9- 554329 

• 554658 
.554987 
.555315 

• 555643 
9- 555971 

• 556299 
. 556626 

• 556953 
.557280 

9.557606 

• 557932 
.558258 
.558583 
.558909 

9- 559234 

• 559558 
.559883 
. 560207 

• 560531 

9- 560855 
.561178 
. 561501 
.561824 
. 562146 

9. 562468 
. 562790 
.563112 

• 563433 
.563755 

9-564075 
.564396 
.564716 
. 565036 

• 565356 
9. 565676 

• 565995 
.566314 

• 566632 
.566951 

9. 567269 

.567587 

• 567904 
. 568222 

• 568539 
9.568856 

.569172 
.569488 
. 569804 
.570120 

9- 570435 
.570751 
.571066 
.571380 
.571695 

9. 572009 

• 572323 
.572636 

.572950 

• 573263 
9- 573575 

Cos. 



D. i' 



Cos. 



D. i' 



D. 1' 



9.970152 
. 970103 

• 970055 
. 970006 

• 969957 
9. 969909 

. 969860 
.969811 
. 969762 
.969714 

9. 969665 
.969616 

• 969567 
.969518 

. 969469 
9. 969420 
. 969370 
. 969321 
.969272 
. 969223 

9.969173 
.969124 
. 969075 
. 969025 
. 968976 

9. 968926 
. 968877 
. 968827 
.968777 
. 968728 

9. 968678 
. 968628 
.968578 
. 968528 
.968479 

9. 968429 
.968379 
.968329 
. 968278 
. 968228 

9. 968178 
.968128 
. 968078 
. 968027 
. 967977 

9. 967927 
. 967876 
.967826 

• 967775 

• 967725 
9.967674 

. 967624 

.967573 

.967522 

.967471 

9.967421 

• 967370 
.967319 
. 967268 
.967217 

9.967166 

Sin. 



.82 
.80 
.82 
.82 
.80 
.82 
.82 
.82 
.80 
.82 

.82 
.82 
.82 
.82 
.82 

.83 
.82 

.82 
.82 
.83 

.82 

.82 

.83 
.82 

.83 
.82 

.83 
.83 
.82 

.83 

.83 
.83 
.83 
.82 

.83 
.83 
.83 
.85 
.83 
.83 

.83 
•83 
.85 
.83 
.83 
.85 
.83 
.85 
.83 
.85 

.83 
.85 
.85 
.85 
.83 
.85 
.85 
.85 
.85 
.85 

D. 1". 



Tan. 



9.584177 
.584555 

• 584932 

• 585309 

• 585686 
9. 586062 

• 586439 
.586815 
.587190 
.587566 

9. 587941 
.588316 
. 588691 
. 589066 
. 589440 

9.589814 
.590188 

• 590562 
•590935 
.591308 

9.591681 

• 592054 

• 592426 

• 592799 
.593i7i 

9- 593542 
.593914 
.594285 

• 594656 

• 595027 

9.595398 
.595768 
.596138 
. 596508 
.596878 

9- 597247 
.597616 

• 597985 

• 598354 
.598722 

9. 599091 

• 599459 
. 599827 
.600194 
. 600562 

9. 600929 
.601296 
.601663 
. 602029 

• 602395 

9.602761 
.603127 
. 603493 
.603858 
. 604223 

9. 604588 

• 604953 
.605317 
. 605682 
. 606046 

9.606410 

Cot. 



D. 1' 



6.30 
6.28 
6.28 
6.28 
6. 27 
6.28 
6.27 
6.25 
6.27 
6.25 

6.25 
6.25 

6.23 
6.23 
6.23 
6.23 
6. 22 
6. 22 
6. 22 

6. 22 
6. 20 
6. 22 
6.20 
6.18 
6.20 
6.18 
6.18 
6.18 
6.18 

6. 17 
6. 17 
6. 17 
6.17 
6.15 
6.15 
6.15 

6.13 
6.15 
6.13 

6.13 
6. 12 

6. 12 
6. 12 
6. 12 
6. 10 
6. 10 
6. 10 

6. 10 
6. 10 
6.08 
6.08 
6.08 
6.08 
6.07 
6.08 
6.07 
6.07 

D. 1". 



Cot. 



0.415823 

.415445 
.415068 
.414691 
.414314 
0.413938 
.413561 
.413185 
.412810 
.412434 

0.412059 
.411684 
.411309 
.410934 
.410560 

o. 410186 
.409S12 
. 409438 
. 409065 
. 408692 

0.408319 
. 407946 

• 407574 
.407201 
. 406829 

o. 406458 
. 406086 

.405715 
.405344 
.404973 

o. 404602 

.404232 

.403862 

.403492 

.403122 
o. 402753 

. 402384 
.402015 

.401646 
.401278 

o. 400909 

.400541 
.400173 
. 399806 

• 399438 
0.399071 

. 398704 
. 398337 
.397971 
.397605 

o. 397239 

.396873 
. 396507 
.396142 

• 395777 
o.3954i2 

• 395047 

• 394683 , 
.394318 

• 393954 
o. 393590 



Tan. 



68° 



22 



COSINES, TANGENTS, AND COTANGENTS I57 t 



M. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
14 
15 
16 
17 
18 

19 

20 
21 
22 

23 
2 4 

25 
26 

27 

28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

5o 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9- 573575 
.573888 
. 574200 
.574512 

• 574824 
9- 575136 

• 575447 
.575758 
. 576069 

• 576379 
9.576689 

• 576999 

• 577309 
.577618 

.577927 
9. 578236 

.578545 
.578853 
.579162 

• 579470 

9- 579777 
.580085 

. 580392 
. 580699 
.581005 
9-581312 
.581618 
.581924 
. 582229 

• 582535 
9. 582840 

.583145 
. 583449 
.583754 
.584058 
9- 584361 
. 584665 
.584968 
. 585272 
.585574 

9.585877 
.586179 
. 586482 
.586783 
587085 
587386 
587688 

.587989 
. 588 2S9 
.588590 

. 588890 
.589190 
. 589489 
.589789 
. 590088 

• 590387 
. 590686 

. 590984 
.591282 
.591580 
.591878 

Cos. 



9- 



D. 1' 



5.22 
5.20 
5.20 
5.20 
5.20 



5-12 



5- 10 
5.10 
5.08 
5.10 
5.08 

5.08 
5.07 
5.08 
5-07 
5-05 
5-07 
5-05 
5-07 
5.03 
5-05 

5-03 
5.05 
5.02 

5.03 
5.02 

5-03 
5.02 
5.00 
5.02 
5.00 

5.00 
4.98 
5.00 

4.98 
4.98 
4.98 
4-97 
4-97 
4-97 
4-97 

D. 1". 



Cos. 



9.967166 
.967115 
. 967064 
.967013 
.966961 

9.966910 
. 966859 
. 966808 

• 966756 
. 966705 

9. 966653 
. 966602 
. 966550 
. 966499 

• 966447 
9- 966395 

• 966344 
. 966292 
. 966240 
.966188 

9. 966136 
. 966085 
. 966033 
.965981 
. 965929 

9. 965876 
. 965824 

• 965772 
. 965720 
. 965668 

9.965615 

• 965563 
.965511 

• 965458 
. 965406 

9. 965353 
.965301 
.965248 
.965195 
.965H3 

9. 965090 

.965037 
.964984 
.964931 

.964879 
9. 964826 

.964773 
.964720 
. 964666 
.964613 

9. 964560 

• 964507 

• 964454 
. 964400 

• 964347 
9- 964294 

. 964240 
.964187 

.964133 

. 964080 

9. 964026 

Sin. 



D. i' 



Tan. 



D. 1 



9.606410 
. 606773 
.607137 
. 607500 
. 607863 

9. 608225 
. 608588 
. 608950 
.609312 
. 609674 

9. 610036 
.610397 
.610759 
.611120 
.611480 

9.611841 
.612201 
.612561 
.612921 
.613281 

9-613641 
. 614000 

.614359 
.614718 

.615077 
9- 6i5435 
.615793 
.616151 
.616509 
.616867 

9.617224 
.617582 
.617939 
.618295 
.618652 

9. 619008 
.619364 
. 619720 
. 620076 
. 620432 

9. 620787 
.621142 
.621497 
.621852 
.622207 

9.622561 
.622915 
. 623269 
. 623623 
.623976 

9. 624330 
. 624683 
.625036 
.625388 
.625741 

9. 626093 
. 626445 
. 626797 
.627149 
.627501 

9. 627852 

Cot. 



D. 1' 



6.05 
6.07 
6.05 
6.05 
6.03 
6.05 
6.03 
6.03 
6.03 
6.03 

6.02 
6.03 
6.02 
6.00 
6.02 
6.00 
6.00 
6.00 
6.00 
6.00 

5.98 

5.98 
5.98 
5.98 
5.97 
5.97 
5-97 
5-97 
5-97 
5-95 



5.92 

5.92 

92 

92 
90 
90 
90 
90 



5.88 
5.90 

5.88 

5-88 
5.87 
5-88 
5.87 
5.87 
5.87 
5.87 
5.87 
5.85 

D. 1". 



Cot. 



o. 393590 
.393227 
.392863 
• 392500 
.392137 

o.39i775 
.391412 
.391050 
. 390688 
. 390326 

o. 389964 
. 389603 
. 389241 
. 388880 
.388520 

o. 388159 

.387799 
.387439 
. 387079 
.386719 

0.386359 

. 386000 

. 385641 
.385282 

. 384923 

o. 384565 

. 384207 

.383849 
.383491 
.383133 

o. 382776 

.382418 

. 382061 

.381705 
.381348 

o. 380992 

.380636 
. 380280 

.379924 
.379568 

0.379213 

.378858 
. 378503 
.378148 
.377793 
0.377439 
. 377085 
.376731 
.376377 
. 376024 

o. 375670 

.375317 
.374964 
.374612 

. 374259 

o. 3739°7 
•373555 
.373203 
.372851 
.372499 

0.372148 

Tan. 



112' 



6 7 " 



n" 



LOGARITHMIC SINES 



i56 ( 



M. Sin. D. i" 



10 
il 

12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



9. 591878 
.592176 
.592473 
. 592770 
. 59306/ 

9- 593363 

• 593659 

• 593955 
.594251 
. 594547 

9. 594842 
.595137 
. 595432 

• 595727 
. 596021 

9-5963I5 

• 596609 

• 596903 
.597196 

. 597490 

9.597783 
.598075 
.598368 
. 598660 

• 598952 
9- 599244 

. 599536 

• 599827 
.600118 
.600409 

9. 600700 
. 600990 
.601280 
.601570 
.601860 

9.602150 
. 602439 
.602728 
.603017 
.603305 

9. 603594 
. 603882 
. 604170 

• 604457 
. 604745 

9. 605032 
.605319 
. 605606 
. 605892 
.606179 

9. 606465 
. 606751 
. 607036 
. 607322 
. 607607 

9. 607892 
.608177 
.608461 
. 608745 
. 609029 

9.609313 

Cos. 



4-97 
4-95 
4-95 
4.95 
4-93 
4-93 
4-93 
4-93 
4-93 
4.92 

4.92 
4.92 
4.92 
4.90 
4.90 
4.90 
4.90 
4.88 
4.90 
4.88 

4.87 

4.88 

4.87 
4.87 
4.87 
4.87 
4.85 
4.85 
4.85 
4.85 

4.83 
4.83 
4.83 



83 

S3 
82 
82 

S2 

So 



4.82 

4.80 
4.80 
4.78 
4.80 
4.78 
4.78 
4.78 
4-77 
4.78 
4-77 

4-77 
4-75 
4.77 



4-73 



D. i' 



Cos. 



9. 964026 

• 963972 
.963919 
.963865 
.963811 

9- 963757 
.963704 
. 963650 
.963596 

• 963542 

9. 963488 

• 963434 
.963379 
.963325 
.963271 

9.963217 
.963163 
.963108 
. 963054 
.962999 

9. 962945 
. 962890 
. 962S36 
.962781 
.962727 

9. 962672 
.962617 
. 962562 
. 962508 
.962453 

9. 962398 

• 962343 
. 962288 
. 962233 
.962178 

9.962123 
. 962067 
.962012 
.961957 
.961902 

9.961846 
.961791 

.961735 

.961680 

.961624 

9.961569 

.961513 
.961458 
.961402 
.961346 
9.961290 

.961235 
.961179 
.961123 
.961067 
9. 961011 

• 960955 
. 960899 
. 960843 
. 960786 

9. 960730 

Sin. 



D. i ; 



Tan. 



D. 1 



9. 627852 
. 628203 
.628554 
.628905 
. 629255 

9. 629606 

• 629956 
. 630306 
.630656 
.631005 

9- 6 3i355 
.631704 
.632053 
.632402 
.632750 

9- 633099 
.633447 
.633795 
.634H3 
.634490 

9.634838 
.635185 
.635532 
.635879 
. 636226 

9. 636572 
.636919 
.637265 
.637611 

• 637956 
9. 638302 

.638647 

• 638992 

• 639337 
. 6396S2 

9. 640027 
.640371 
.640716 
. 641060 
.641404 

9.641747 
. 642091 
.642434 
.642777 
.643120 

9. 643463 
. 643806 
.644148 
.644490 
. 644832 

9.645174 
.645516 

.645857 
.646199 
. 646540 
9. 646881 
. 647222 
. 647562 

.647903 
. 648243 

9-648583 
Cot. 



D. i' 



D. 1 



Cot. 



0.372148 

.371797 
.371446 
.371095 

• 370745 
o. 370394 

• 370044 
. 369694 

• 369344 
.368995 

o. 368645 
. 368296 

. 367947 
.367598 
. 367250 

0.366901 

. 366553 
. 366205 

. 365857 
. 365510 

0.365162 

.364815 
. 364468 
.364121 
.363774 

o. 363428 

.363081 

.362735 
. 362389 
. 362044 

0.361698 

.361353 

.361008 
. 360663 
.360318 

o. 359973 

• 359629 

• 359284 
. 358940 

• 358596 

o. 358253 

• 357909 
.357566 

• 357223 
.356880 

o. 356537 
.356194 
. 355852 
.3555io 
.355168 

o. 354826 
.354484 
.354143 
.3538oi 
• 35346o 

o.353i 19 
. 352778 
. 352438 
.352097 
.351757 

0.351417 

Tan. 



"3' 



66' 



24^ 



COSINES, TANGENTS, AND COTANGENTS 155' 



M. 



Sin. 



o 


9. 6 °93i3 


I 


. 609597 


2 


. 609880 


3 


.610164 


4 


,610447 


| 


9.610729 


6 


.611012 


7 


.611294 


8 


.611576 


9 


.611S5S 


10 


9.612140 


ii 


,612421 


12 


.612702 


13 


.6129S3 


M 


.613264 


15 


9- 61 3545 


16 


.613825 


17 


.614105 


18 


.614385 


19 


.614665 


20 


9.614944 


21 


.615223 


22 


.615502 


23 


.6157S1 


24 


.616060 


25 


9.616338 


26 


.616616 


27 


.616894 


28 


.617172 


29 


.617450 


30 


9.617727 


31 


.61S004 


32 


.618281 


33 


.618558 


34 


.61S834 


ai 


9.619110 


36 


,619386 


37 


.619662 


38 


.619938 


39 


.620213 


40 


9. 620488 


4X 


. 620763 


42 


.621038 


43 


.621313 


44 


.621587 


4S 


9.621861 


46 


.622135 


47 


. 622409 


48 


. 622682 


49 


. 622956 


50 


9. 623229 


5i 


. 623502 


52 


.623774 


53 


. 624047 


54 


.624319 


55 


9.624591 


56 


. 624863 


57 


.625135 


58 


. 625406 


59 


. 625677 


60 


9. 625948 



Cos. 



D. 1 



4-73 
4.72 
4-73 
4.72 
4.70 
4.72 
4.70 
4.70 
4.70 
4.70 

4.68 
4.68 
4.68 
4.68 
4.68 
4.67 
4.67 
4.67 
4.67 
4.65 

4-65 
4-65 
4-65 
4-^5 
4-63 
4-63 
4.63 
4.63 
4-63 
4.62 

4.62 
4.62 
4.62 
4.60 
4.60 
4.60 
4.60 
4.60 
4.58 
4.58 



4-55 
4-57 
4-55 

4-55 
4-53 
4-55 
4-53 
4-53 
4-53 
4-53 
4.52 
4o2 
4.52 

D. 1". 



Cos. 



9. 960730 
.960674 
.960618 
.960561 
. 960505 

9. 960448 
. 960392 

. 960335 
. 960279 
.960222 

9.960165 
.960109 
.960052 

• 959995 
.959938 

9. 959882 

• 959825 

.959768 

.959711 
.959654 

9- 959596 
•959539 
.959482 

.959425 

• 95936S 
9- 9593io 

.959253 
.959195 
.959138 
. 9590S0 

9- 959023 
. 958965 
. 958908 
.958850 

• 958792 
9- 958734 

• 958677 
.958619 

.958561 
.958503 

9- 958445 
.9583S7 

• 958329 
.958271 

.95S213 
9-958I54 
. 958096 
.958038 
•957979 
.957921 

9- 957863 
. 957S04 

• 957746 
.957687 
. 957628 

9- 957570 
•9575II 
.957452 
•957393 

• 957335 
9.957276 

Sin. 



D. 1' 



D. 1". 



Tan. 



D. 1". 



9.648583 
.648923 
. 649263 
.649602 

• 649942 
9.650281 

. 650620 

.650959 
.651297 
.651636 

9.651974 
.652312 
.652650 
. 652988 
.653326 

9. 653663 
.654000 

.654337 

. 654674 
.655011 

9- 655348 
.6556S4 
. 656020 
. 656356 
. 656692 

9. 657028 

.657364 
.657699 
.658034 
.658369 

9.658704 

• 659039 
.659373 
.659708 
.660042 

9. 660376 
.660710 
.661043 
.661377 
.661710 

9. 662043 
.662376 
. 662709 
. 663042 

• 663375 
9. 663707 

. 664039 
. 664371 
. 664703 

• 665035 

! 9.665366 

1 . 665698 

. 666029 

. 666360 

. 666691 

9. 667021 

. 667352 

. 6676S2 

.66S013 

. 66S343 

9.668673 

Cot. 



D. 1' 



Cot. 



0.351417 
.351077 

• 350737 
.350398 
. 350058 

0.349719 
• 3493So 
.349041 
. 34S703 
. 34S364 

o. 348026 
.347688 

• 347350 
.347012 
. 346674 

o. 346337 
. 346000 

.345663 
. 345326 
. 3449S9 

o. 344652 

.344316 
. 343980 
. 343644 
.343308 

o. 342972 

. 342636 
. 342301 
.341966 
.341631 

0.341296 
.340961 
. 340627 
.340292 
. 339958 

o. 339624 

. 339290 
.338957 
. 338623 
. 33S290 

o. 337957 

• 337624 
.337291 

• 336958 
.336625 

o. 336293 
.335961 

• 335629 

• 335297 

• 334965 

o. 334634 

• 334302 
•333971 

• 333640 

• 333309 
o. 332979 

. 33264S 
.332318 

.331987 
.331657 

0.331327 

Tan. 



"4* 



65' 



25 c 



LOGARITHMIC SINES 



154' 



M. 



Sin. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
M 

15 

16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 
29 

3o 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



9. 625948 
.626219 
.626490 
. 626760 
. 627030 

9. 627300 
.627570 
.627840 
.628109 
.628378 

9. 628647 
.628916 
.629185 
.629453 
.629721 

9. 629989 
.630257 
.630524 

• 630792 
.631059 

9.631326 
.631593 
.631859 
.632125 
.632392 

9.632658 

• 632923 
.633189 

.633454 
.633719 

9-633984 

• 634249 
.6345H 
.634778 
. 635042 

9- 635306 

• 635570 

• 635834 
. 636097 
. 636360 

9. 636623 
. 636886 
.637148 
.637411 
.637673 

9- 637935 
.638197 
.638458 
.638720 
.638981 

9. 639242 
.639503 
. 639764 
. 640024 
. 640284 

9. 640544 
. 640804 
.641064 
.641324 

.641583 
9.641842 



D. 1". 



Cos. 



Cos. 



4.52 
4.52 
4.5o 



4.48 
4.48 

4.48 
4.48 
4-47 
4-47 
4-47 
4-47 
4-45 
4-47 
4-45 
4-45 

4.45 
4-43 
4-43 
4-45 
4-43 
4.42 

4-43 
4.42 
4.42 
4.42 

4.42 
4.42 
4.40 
4.40 
4.40 
4.40 
4.40 
4.38 
4.38 
4.38 

4.38 
4-37 
4.38 
4-37 
4-37 
4-37 
4-35 
4-37 
4-35 
4.35 

4-35 
4-35 
4-33 
4-33 
4-33 
4-33 
4-33 
4.33 
4-32 
4.32 

D. 1". 



D. 1". 



9.957276 
.957217 
.957158 

• 957099 
.957040 

9.956981 
.956921 
. 956862 
. 956803 
.956744 

9. 956684 
.956625 
.956566 

• 956506 
.956447 

9- 956387 

• 956327 
.956268 
. 956208 
.956148 

9. 956089 
. 956029 
.955969 

• 955909 

• 955849 
9- 955789 

.955729 
.955669 
.955609 
.955548 

9-955488 

• 955428 
.955368 
.955307 
.955247 

9-955186 
.955126 
.955065 
. 955005 
. 954944 

9- 954883 

• 954823 
. 954762 
.954701 
. 954640 

9- 954579 
.954518 
. 954457 
.954396 
•954335 

9- 954274 
.954213 
.954152 
.954090 
. 954029 

9. 953968 

• 9539° 6 
. 953845 
. 953783 
.953722 
9. 953660 

Sin. 



.98 
.98 



1. 00 
.98 
.98 
.98 

1. 00 



1. 00 



1. 00 
1. 00 



1. 00 
1. 00 



00 
00 
00 
00 
00 
00 
00 
00 
02 
00 



Tan. 



1. 00 
1. 00 
1.02 
1. 00 
1.02 
1. 00 
1.02 
1. 00 
1.02 
1.02 

1. 00 
1.02 
1.02 
1.02 
1.02 
1.02 
1.02 
1.02 
1.02 
1.02 

1.02 
1.02 
1.03 
1.02 
1.02 
1.03 
1.02 
1.03 
1.02 
1.03 

D. 1" 



9.668673 
. 669002 
.669332 
.669661 
. 669991 

9. 670320 
. 670649 

.670977 
.671306 
.671635 

9.671963 
.672291 
.672619 

• 672947 

• 673274 
9. 673602 

.673929 
.674257 
.674584 
.674911 

9.675237 
.675564 
. 675890 
.676217 

. 676543 

9. 676869 

.677194 

• 677520 
. 677846 
.678171 

9. 678496 
.678821 
. 679146 
.679471 

• 679795 
9.680120 

. 680444 
. 680768 
.681092 
.681416 

9.681740 
.682063 
.682387 
.682710 
. 683033 

9- 683356 
.683679 
.684001 
. 684324 
. 684646 

9. 684968 
. 685290 
.685612 
.685934 
.686255 

9. 686577 



D. 1". 



Cot. 



.687219 

. 687540 

.687861 

9. 688182 

Cot. 



5.48 
5.50 
5-48 



50 

48 
48 
47 
48 
48 
47 

5-47 
5-47 
5-47 
5-45 
5-47 
5-45 
5-47 
5-45 
5-45 
5-43 

5-45 

5-43 
5-45 
5-43 
5-43 



5-42 

5-42 
5.42 
5.42 
5-40 
5.42 
5-40 
5-40 
5.40 
5.40 
5-40 

5-38 
5.40 
5.38 
5-38 
5.38 
5.38 
5-37 
5-38 
5-37 
5-37 

5-37 
5-37 
5-37 
5-35 
5-37 
5-35 
5-35 
5-35 
5-35 
5-35 

D. 1". 



0.331327 
. 330998 
. 330668 

. 330339 

. 330009 

o. 329680 

.329351 
. 329023 
. 328694 
.328365 

o. 328037 
• 327709 
.327381 
.327053 
. 326726 

o. 326398 
.326071 

. 325743 
.325416 
. 325089 

o. 324763 

.324436 
.324110 

.323783 

. 323457 

0.323131 

. 322806 
. 322480 

.322154 

.321829 
o. 321504 

.321179 
.320854 
. 320529 
. 320205 

o. 319880 

.319556 
.319232 
.318908 

.318584 

0.318260 

.317937 
.317613 
.317290 
.316967 
0.316644 

.316321 

.315999 
.315676 

.315354 

0.315032 
.314710 
.314388 

.314066 

.313745 

0.313423 

.313102 

.312781 

.312460 

.312139 
0.311818 



Tan. 



115' 



64' 



2 6 c 



COSINES, TANGENTS, AND COTANGENTS I53 c 



M. 



Sin. 



10 
ii 

12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 
30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9- 



,641842 
.642101 
, 642360 
,642618 
. 642877 
643135 
■ 643393 
, 643650 
,643908 
,644165 

,644423 
, 644680 
644936 
645193 
645450 
645706 
645962 
646218 
646474 
646729 

646984 

647240 

. 647494 

• 647749 
. 648004 

9.648258 
.648512 
. 648766 
. 649020 
. 649274 

9. 649527 
.649781 
. 650034 
.650287 

• 650539 
9- 650792 

.651044 
.651297 

•651549 
.651800 

9. 652052 
. 652304 

.652555 
. 652806 

• 653057 
9. 653308 

.653558 

• 653808 
.654059 
.654309 

9- 654558 
. 654808 
.655058 
. 655307 
.655556 

9*655805 
. 656054 
. 656302 
.656551 

• 656799 
9. 657047 



D. i' 



Cos. 



D. 1' 



4.32 
4.32 
4.30 
4.32 
4.3o 
4.3o 
4.28 
4.30 
4.28 
4.30 

4.28 
4.27 
4.28 
4.28 
4.27 



4.25 
4-25 

4.27 
4-23 
4.25 
4.25 
4-23 
4.23 
4.23 
4-23 
4-23 
4.22 

23 

22 
22 
20 
22 
20 



4- 

4- 

4- 
4- 
4- 
4- 
4. 22 
4.20 
4.18 
4. 20 

4. 20 
4.18 
4.18 
4.18 
4.18 
4.17 
4.17 
4.18 

4.17 

4.15 

4.17 
4.17 
4.15 
4.15 
4.15 
4.15 
4.13 
4.15 
4.13 
4.13 



Cos. 



D. 



9. 95366o 

• 953599 
•953537 
. 953475 
.953413 

9- 953352 
. 953290 

• 953228 
.953166 
.953104 

9. 953042 
. 952980 
.952918 

• 952855 
. 952793 

9-95273I 
. 952669 
. 952606 

. 952544 
.952481 

9. 952419 

• 952356 

• 952294 
.952231 
.952168 

9. 952106 

.952043 
.951980 

.951917 
.951854 

9- 95i79i 
.951728 
.951665 
.951602 

.951539 

9-95I476 

.951412 

.951349 
.951286 
.951222 

9-95II59 
.951096 
.951032 
. 950968 

• 950905 
9- 950841 

•950778 
.950714 
. 950650 
.950586 

9.950522 

. 950458 
.950394 
.950330 
.950- 6 
9. 950202 
.950138 

.950074 
.950010 

• 949945 
9.949S81 

Sin. 



.02 
.03 
.03 
.03 
.02 

•03 
•03 
.03 
.03 
•03 

.03 

• 03 
•05 
■ 03 
.03 
•03 
.05 
.03 
.05 
.03 

.05 
.03 
•05 
•05 
.03 
.05 
.05 
.05 
.05 
.05 

•05 
.05 
•05 

• 05 
.05 
.07 
•05 
.05 
.07 
.05 

.05 

.07 

.07 
.05 
.07 
.05 

.07 

.07 

.07 
.07 

.07 
.07 

.07 
.07 

• 07 
.07 
.07 
.07 
.08 
.07 



D. i' 



Tan. 



9. 688182 
. 688502 
. 688823 
.689143 
. 689463 

9.689783 
.690103 
. 690423 
. 690742 
. 691062 

9-691381 
.691700 
.692019 

• 692338 
. 692656 

9- 692975 

• 693293 
.693612 

• 693930 
. 694248 

9- 694566 
.694883 
.695201 
•695518 
. 695836 

9.696153 
. 696470 
. 696787 
.697103 
. 697420 

9- 697736 
. 698053 
. 698369 
. 698685 
. 699001 

9.699316 
.699632 

• 699947 
. 700263 

. 700578 

9- 700893 
.701208 

.701523 
.701837 
.702152 
9. 702466 
. 702781 

• 703095 

• 703409 

• 703722 

9. 704036 

• 704350 
. 704663 

• 704976 
. 705290 

9. 705603 
. 705916 
. 706228 

. 706541 

• 706854 
9. 707166 

Cot. 



D. 



5-33 
5-35 
5-33 
5-33 



5-32 
5-32 
5-32 
5-30 
5-32 
5-30 
5-32 
5-30 
5.30 
5.30 

5-28 
5-30 
5-28 
5.30 
5-28 
5-28 
5-28 
5-27 
5-28 
5-27 
5-28 
5-27 
5-27 
5-27 
5-25 
5-27 
5-25 
5-27 
5.25 
5-25 

5-25 
5-25 
5-23 
5-25 
5-23 
5-25 
5-23 
5-23 

5-22 

5-23 

5.23 
5-22 
22 

23 
22 
22 
20 
22 
22 
20 



D. 1". 



Cot. 



0.311818 
.311498 

.311177 
.310857 

.310537 
o. 310217 

. 309897 

• 309577 
. 309258 
.308938 

0.308619 
. 308300 
.307981 
. 307662 

• 307344 
o. 307025 

. 306707 
.306388 

. 306070 

. 305752 

o. 305434 

.305117 
. 304799 
. 304482 
. 304164 

o. 303847 

. 303530 
.303213 
. 302897 
. 302580 

o. 302264 

. 301947 
.301631 

.301315 
. 300999 

o. 300684 

. 300368 
. 300053 
. 299737 

. 299422 

o. 299107 
. 298792 

.298477 

.298163 

. 297848 

o. 297534 
.297219 

. 296905 
. 296591 

. 296278 
o. 295964 

. 295650 

. 295337 
. 295024 
. 294710 

o. 294397 
. 294084 

. 293772 

. 293459 
.293146 

o. 292834 
Tan. 



116 



63* 



*7< 



LOGARITHMIC SINES 



152' 



M. 



O 

I 
2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
14 
15 
16 

17 
18 

19 

20 
21 
22 

23 
2 4 

25 

26 

27 

28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



117 



9- 657047 
. 657295 
.657542 
. 657790 
.65S037 

9.65S284 

.658531 
.658778 

. 659 02 5 
.659271 



D. 1" 



9- 



659517 
659763 
. 660009 
. 660255 
. 660501 
9. 660746 
. 660991 
.661236 
.661481 
.661726 

9.661970 
.662214 
. 662459 
. 662703 
. 662946 

9.663190 

• 663433 

• 663677 
. 663920 
.664163 

9. 664406 
. 664648 
.664S91 
.665133 

• 665375 
9.665617 

.665859 
.666100 
. 666342 
.666583 

9. 666824 
. 667065 
. 667305 
. 667546 
. 667786 

9. 668027 
. 668267 
. 668506 
. 668746 
. 668986 

9. 669225 
. 669464 

• 669703 
.669942 
.670181 

9.670419 
. 670658 
. 670896 
.671134 
.671372 

9. 671609 

Cos. 



4.13 
4.12 

4.13 
4.12 
4.12 
4.12 
4.12 
4.12 
4. 10 
4. 10 

4. 10 
4. 10 
4. 10 
4. 10 
4.08 
4.08 
4.08 
4.08 
4.08 
4.07 

4.07 
4.08 
4.07 

4.05 

4.07 

4-05 
4.07 
4-05 
4-05 
4-05 

4.03 
4-05 
4.03 
4-03 
4-03 
4-03 
4.02 

4.03 
4.02- 
4.02 

4.02 
4.00 
4.02 
4.00 
4.02 
4.00 

3.93 
4. 00 
4.00 
3.98 

3.98 
3.98 
3.98 
3.98 
3-97 
3.98 
3-97 
3-97 
3-97 
3.95 

D. 1". 



Cos. 



9. 949881 
. 949816 

• 949752 
. 949688 

• 949623 
9- 949558 

. 949494 

• 949429 

• 949364 
. 949300 

9- 949235 
.949170 

. 949105 
. 949040 

• 948975 
9. 948910 

. 948845 
. 948780 
.948715 
. 948650 

9. 948584 
.948519 

• 948454 
.948388 

• 948323 
9- 948257 

.948192 
.948126 
. 948060 
•947995 

9. 947929 
. 947863 

• 947797 
.947731 
. 947665 

9. 947600 
. 947533 
. 947467 

• 947401 
. 947335 

9. 947269 
. 947203 
.947136 

• 947070 

• 947004 

9.946937 
.946871 
. 946804 
.946738 
. 946671 

9. 946604 
.946538 
.946471 
. 946404 
. 946337 

9. 946270 
. 946203 
.946136 
. 946069 
. 946002 

9. 945935 

Sin. 



D. 1". 



1.08 
1.07 
1. 07 
1.08 
1.08 
1.07 
1.08 
1.08 
1.07 
1.08 

1.08 
1.08 
1.08 
1.08 
1.08 
1.08 
1.08 
1.08 
1.08 
1. 10 

1.08 
1.08 
1. 10 
1.08 
1. 10 
1.08 
1. 10 
1. 10 
1.08 
1. 10 



1. 10 
1. 10 
1. 10 
1. 10 
1.08 
1. 12 
1. 10 
1. 10 
1. 10 
1. 10 

1. 10 
1. 12 
1. 10 
1. 10 
1. 12 
1. 10 
1. 12 
1. 10 
1. 12 
1. 12 

1. 10 
1. 12 
1. 12 
1. 12 
1. 12 
1. 12 
1. 12 
1. 12 
1. 12 
1. 12 



Tan. 



9. 707166 
. 707478 
.707790 
.708102 
. 708414 

9. 708726 

• 709037 

• 709349 
. 709660 

• 709971 
9.710282 

. 710593 
. 710904 
.711215 

.711525 
9-711836 
. 712146 
.712456 
.712766 
. 713076 

9.713386 
.713696 
. 714005 
.714314 
.714624 

9-7I4933 
.715242 

.715551 
.715860 
. 716168 

9- 7i6477 
.716785 
.717093 
.717401 

• 717709 
9.718017 

.718325 
.718633 
. 718940 
.719248 

9- 719555 
. 719862 
. 720169 
. 720476 
. 720783 

9.721089 
.721396 
.721702 
. 722009 
.722315 

9. 722621 
.722927 

• 723232 
. 723538 

• 723844 
9.724M9 

• 724454 
. 724760 

. 725065 

- 725370 

9. 725674 

Cot. 



D. 



5.20 
5.20 
5.20 
5.20 



5.18 
5-i8 

5-i8 
5-17 
5.i8 

5.17 
5-i7 
5-i7 
5-i7 
5.17 



5 


17 


5 


15 


5 


15 


5 


*7 


5 


15 


5 


15 


5 


15 


5 


15 


5 


13 


5 


15 


5 


13 


5 


13 


5 


13 


5 


13 


5 


13 


5 


13 


5- 


13 


5- 


12 


5- 


13 


5- 


12 


5- 


12 


5- 


12 


5- 


12 


5- 


12 


5- 


IO 


5- 


12 


5- 


IO 


5- 


12 


5- 


IO 


5- 


IO 


5- 

5- 


IO 

oS 


5- 


IO 


5- 

5- 
5- 


IO 

oS 
oS 


5. 

5- 
5- 


IO 

oS 
08 


5.07 



Cot. 



D. 1". 



0. 292834 
. 292522 
. 292210 
. 291898 
. 291586 

o. 291274 

. 290963 
.290651 
. 290340 

-. 290029 

o. 289718 
, 289407 
. 289096 

. 288785 

.288475 

o. 288164 

.287854 
. 287544 
> 287234 
. 286924 

0.286614 
. 286304 
. 285995 
. 285686 
. 285376 

o. 285067 

. 284758 
. 284449 

. 284140 

. 283832 

o. 283523 

.283215 
. 282907 
. 282599 
. 282291 
o. 281983 

. 281675 
. 281367 

. 281060 

. 280752 

o. 280445 

. 280138 
.279831 
. 279524 

. 279217 
o. 278911 
. 278604 
. 278298 
. 277991 
. 277685 

o. 277379 

. 277073 
. 276768 
. 276462 

.276156 

o. 275851 

. 275546 
. 275240 

. 274935 
. 274630 

o. 274326 
Tan. 



62' 



28° COSINES, TANGENTS, AND COTANGENTS 151* 



M. Sin. D. 1". Cos. D, 1". Tan. D. i". Cot 



M. 


Sin. 





9.671609 


I 


.671847 


2 


. 672084 


3 


.672321 


4 


.672558 


5 


9.672795 


6 


. 673032 


7 


.673268 


8 


• 673505 


9 


. 673741 


10 


9. 673977 


11 


.674213 


12 


. 674448 


13 


. 674684 


M 


.674919 


15 


9-675I55 


16 


• 675390 


17 


. 675624 


18 


• 675859 


19 


.676094 


20 


9. 676328 


21 


. 676562 


22 


. 676796 


23 


. 677030 


24 


. 677264 


25 


9. 677498 


26 


.677731 


27 


. 677964 


28 


.678197 


29 


. 678430 


3o 


9.678663 


3i 


.678895 


32 


.679 1 2S 


33 


. 679360 


•34 


• 679592 


35 


9. 679824 


36 


. 680056 


37 


. 680288 


38 


.680519 


39 


.680750 


40 


9. 6809S2 


4i 


.681213 


42 


.681443 


43 


. 68 1 674 


44 


.681905 


45 


9. 6S2135 


46 


.682365 


47 


• 682595 


48 


. 6S2825 


49 


. 6S3055 


50 


9.683284 


5i 


.683514 


52 


.683743 


53 


. 683972 


54 


.6S4201 


55 


9. 684430 


56 


. 684658 


57 


. 6S48S7 


58 


.685115 


59 


.685343 


60 


9.685571 




Cos. 



3-97 

3-95 

3-95 

95 

95 
95 
93 
95 

93 



3-93 



3.90 
3-90 



3. 88 

3.87 
3-88 
3.87 
3.87 
3.87 
3.87 
3.87 
3.85 
3. 85 
3-87 

3.85 
3.83 
3.85 
3.85 

3.83 
3.83 
3.83 
3.83 
3.83 
3.82 

3.83 
3.82 
3.82 
3.82 
3.82 
3.80 
3.82 
3.8o 
3.8o 
3.80 



D. 1' 



9- 945935 
. 945868 
. 945800 

• 945733 
. 945660 

9- 945598 
•945531 
. 945464 

• 945396 

• 945328 

9. 945261 
.945193 
.945125 

• 945058 

• 944990 
9. 944922 

. 944854 
. 944786 
.944718 

• 944650 
9. 944582 

.9445M 
. 944446 

• 944377 

• 944309 
9.944241 

. 944172 
.944104 
. 944036 

• 943967 

9- 943899 

• 94383° 
.943761 

• 943693 

• 943624 
9- 943555 

• 943486 
.943417 

• 943348 

• 943279 

9. 943210 

•943 Mi 
. 943072 

• 943003 
.942934 

9. 942864 

• 942795 
. 942726 
.942656 
. 942587 

9-9425I7 

• 942448 
.942378 
. 942308 

• 942239 
9.942169 

.942099 
.942029 

•941959 

.941889 

9-94i8i9 

Sin. 



1. 12 

1. 13 
!•• 13 

1. 12 

1. 13 
1. 13 

1. 12 

i- 13 
i-i3 

1. 13 
i- 13 
1. 13 
1. 13 
1. 13 

1. 13 
1. 13 
1. 15 
1. 13 
1. 13 
1. 15 
i- 13 
1. 13 
1. 15 
1. 13 

1. 15 

1. 15 
1. 13 
1. 15 
1. 15 
1. 15 
1. 15 
1. 15 
1. 15 
1. 15 

i- 15 
1. 15 
1. 15 
1. 15 
1. 17 
1. 15 
i. 15 
1. 17 

i- 15 
1. 17 



15 
^7 
17 
15 
17 
17 
17 

17 
1. 17 
1. 17 



D. I' 



9- 725674 

• 725979 
. 726284 
.726588 
. 726892 

9. 727197 

• 727501 
. 727805 
. 728109 
.728412 

9. 728716 
. 729020 

.729323 
. 729626 

• 729929 
9- 730233 

• 730535 
. 730838 
.731141 
.73M44 

9.731746 

• 732048 
.732351 
. 732653 
.732955 

9- 733257 

• 733558 
. 733860 
• 734i62 

• 734463 

9- 734764 
• 735o66 

• 735367 
.735668 

• 735969 
9- 736269 

• 736570 
. 736870 
.737171 

• 737471 

9- 737771 
.738071 

• 738371 
.738671 

• 738971 
9- 739271 

• 739570 
. 739870 
. 740169 
. 740468 

9. 740767 

. 741066 

.741365 

.741664 

.741962 

9. 742261 

• 742559 
.742858 

.743156 

• 743454 
9- 743752 

Cot. 



5.08 
5.08 
5.07 
5-07 
5.08 

5.07 
5.07 
5.07 

5-05 
5-07 

5.o7 
5-05 
5-05 
5-05 
5- °7 
5- °3 
5-05 
5-05 
5.05 
5-03 

5.03 
5.05 
5- °3 
5- °3 
5.o3 
5.02 

5-03 
5-03 
5.02 
5.02 

5.03 
5.02 
5.02 
5.02 

5.00 
5.02 
5.00 
5. 02 
5.00 
5.00 

5.00 
5.00 

5- 00 
5- 00 
5.00 
4.98 
5.00 
4.98 
4.98 
4.98 

4.98 
4- 98 
4.9S 
4-97 
4.98 
4-97 
4.98 
4-97 
4-97 
4-97 

D. 1". 



o. 274326 

.274021 

.273716 

.273412 j 57 

.273108 I 56 
0.272803 j 55 

.272499 I 54 

• 272195 
.271891 
. 271588 

0.271284 50 

. 270960 4g 
.270677 | 48 
. 270374 
. 270071 
o. 269767 
. 269465 
. 269162 
. 268859 
.268556 

o. 268254 

. 267952 

. 267649 

. 267347 
. 267045 

o. 266743 
. 266442 
. 266140 

. 265838 
. 265537 

o. 265236 30 

. 264934 at 

.264633 a8 

• 264332 37 
. 264031 36 

0.263731 35 
.263430 I 34 
.263130 
. 262829 
. 262529 

o. 262229 20 

.261929 j 19 

. 261629 

. 261329 

.261029 
o. 260729 

. 260430 

. 260130 

.25983I j 12 
.259532 " 

o. 259233 

• 258934 
. 258635 
.258336 
. 258038 

o. 257739 

. 257441 
.257142 
. 256844 
. 256546 

o. 256248 



Tan. 



n8 ( 



6i° 



29' 



LOGARITHMIC SINES 



I50 l 



M. 



10 
11 
12 
13 
M 
15 
16 

17 
18 

19 

20 
21 
22 

23 

24 

25 
26 

27 
28 
29 

30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9- 6 S557i 
.685799 
. 686027 
. 686254 
.686482 

9. 686709 
. 686936 
.687163 
.687389 
.687616 

9.687843 
. 688069 
.688295 
.688521 
. 688747 

9. 688972 
.689198 
. 689423 
. 689648 
.689873 

9. 690098 
.690323 
. 690548 
.690772 
. 690996 

9.691220 
.691444 
.691668 
.691892 
.692115 

9. 692339 
.692562 
.6927S5 
. 69300S 
.693231 

9- 693453 
. 693676 
.693898 
.694120 
. 694342 

9 694564 
. 694786 
. 695007 
. 695229 

•695450 
9.695671 
. 695892 
.696113 
.696334 

• 696554 
9.696775 

• 696995 
.697215 

• 697435 

• 697654 
9. 697874 

. 698094 
.698313 
.698532 

.698751 
9. 698970 

Cos. 



D. 1". 



Cos. 



9418 19 
941749 
941679 
941609 

941539 
941469 
941398 
941328 
941258 
941 187 

941 1 17 
941046 
940975 
940905 
940834 
940763 
940693 
940622 

940551 
940480 

940409 
940338 
940267 
940196 
940125 
940054 
939982 

9399 1 1 
939840 
939768 

939697 
939625 
939554 
939482 
939410 

939339 
939267 

939195 
939123 
939052 
938980 
938908 
938836 

938763 
938691 
938619 
938547 
938475 
938402 

938330 

938258 
938185 
9381 13 
938040 
937967 
937895 
937822 

937749 
937676 
937604 
937531 



D. 1". |j Sin. 



D. 1" 



D. 1". 



Tan. 



9- 743752 
. 744050 

• 744348 

• 744645 

• 744943 
9. 745240 

. 745538 

• 745835 
.746132 

• 746429 
9. 746726 

• 747023 
.747319 
.747616 

.747913 
9. 748209 

. 748505 
.748801 

• 749097 

• 749393 

9. 749689 

• 749985 
.750281 

.750576 

. 750872 

9-75ii67 

.751462 

.751757 

• 752052 

• 752347 
9- 752642 

- 752937 
.753231 
. 753526 

• 753820 
9-754II5 

• 754409 
. 754703 

• 754997 
•755291 

9- 755585 
.755878 

• 756172 
. 756465 

• 756759 
9- 757052 

• 757345 

• 757638 
.757931 
.758224 

9.758517 
. 758810 
.759102 

• 759395 

• 759687 
9- 759979 

. 760272 

• 760564 
. 760856 
.761148 

9.76i439 

Cot. 



D. 1". 



Cot. 



o. 256248 

• 255950 

• 255652 

• 255355 

• 255057 
o. 254760 

. 254462 
. 254165 
. 253868 
.253571 

o. 253274 

. 252977 

. 252681 

. 252384 
. 252087 

o. 251791 

. 251495 
.251199 
. 250903 
. 250607 

0.25031 1 
. 250015 
.249719 
. 249424 

.249128 
o. 248833 

. 248538 
. 248243 
. 247948 
. 247653 

o. 247358 

. 247063 

. 246769 

. 246474 

. 246180 
o. 245885 

. 245591 
. 245297 
. 245003 
. 244709 

o. 244415 
. 244122 

. 243828 

. 243535 
.243241 

o. 242943 

. 242655 

. 242362 
. 242069 
. 241776 II 

o. 241483 10 
.241190 
. 240898 
. 240605 

.240313 

o. 240021 

. 239728 
. 239436 
.239144 
. 238852 
0.238561 



D. 1 



Tan. 



M. 



119' 



6o< 



30 v 



COSINES, TANGENTS, AND COTANGENTS 149' 



M. 



Sin. 



26 

27 
28 
29 

30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 



9. 698970 
.699189 

. 699407 
. 699626 
. 699S44 

9. 700062 
. 700280 
. 7004 9S 
.700716 
. 7°°933 

9.701151 
. 7 OI 3 68 
. 701585 
. 701802 
. 702019 

9. 702236 
. 702452 
. 702669 
.702885 
. 703 101 

9- 703317 
. 703533 
• 703749 
• 7039 6 4 
.704179 
25 ! 9-704395 



o 
1 
2 
3 
4 
5 
6 

I 

9 

10 
11 
12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 
23 
24 



. 704610 
. 704825 
. 705040 

. 705254 

9. 705469 

• 705683 
.705898 
.706112 
. 706326 

9- 706539 

• 706753 
. 706967 
.7071S0 
. 707393 



40 9. 

41 . 

42 . 

43 • 

44 • 

45 9- 

46 . 

47 • 

48 J • 

49 • 

I 

50 9- 
5i 
52 
53 
54 
55 
56 
57 
58 

59 
60 



J20 



9- 



707606 
707819 
708032 
708245 
708458 
708670 
708882 
709094 
709306 
709518 

709730 
709941 
710153 
710364 

710575 

710786 

.710997 

.711208 

.711419 
.711629 
.711839 

Cos. 



D. i> 



Cos. 



D. 1". 



Tan. 



D. i". 



65 
^3 
65 
63 

63 
^3 
^3 
63 

h 2 

63 

62 
62 

h 2 
62 

62 
60 
62 
60 
60 
60 

60 
hO 
58 
58 

hO 

58 
58 
58 

57 
58 

57 
58 

57 
57 
55 

57 
57 
55 
55 
55 

55 
55 

55 
55 

53 
53 
53 
53 
53 
53 

52 
53 
52 
52 
52 
52 
52 
52 
50 
50 



D. 1 



9-937531 

• 937458 
. 937385 
•937312 

• 937238 
9-937i65 

. 937092 
.937019 
. 936946 
. 936872 

9. 936799 

• 936725 
. 936652 

• 936578 

• 936505 
9-93643I 

.936357 
. 936284 
.936210 
.936136 

9. 936062 
.935988 
.9359H 

• 935840 

• 935766 
9- 935692 

• 9356i8 

• 935543 

• 935469 
. 935395 

9- 935320 

• 935246 
.935171 
. 935097 
. 935022 

9- 934948 
. 934873 

• 934798 
. 934723 

• 934649 

9- 934574 
.934^99 

• 934424 

• 934349 
. 934-274 

9- 934199 
.934123 

• 934048 

• 933973 
.933898 

9. 933822 

• 933747 
.933671 
- 933596 

• 933520 
•9-933445 

• 933369 
.933293 
.933217 
•933MI 

9- 933o66 

Sin. 



22 
22 
22 

23 
22 
22 
22 
22 

23 
22 

23 
22 

23 
22 

23 
23 
22 

23 
23 
23 

23 
23 
23 
23 
23 
23 
25 
23 
23 
25 

23 
25 
23 
25 
23 
25 
25 
25 
23 
25 

25 
25 
25 
25 
25 
27 
25 
25 
25 
,27 

25 

27 
25 

,27 

25 

.27 
,27 
.27 
.27 

.25 



D. 1 



9.761439 

.761731 
. 762023 
.762314 
. 762606 
9- 762897 
.763188 

• 763479 
.763770 
. 764061 

9- 764352 
. 764643 

• 764933 

• 765224 

• 7655H 
9. 765805 

• 766095 
. 766385 
. 766675 
. 766965 

9- 767255 
. 767545 

• 767834 
.768124 
.768414 

9- 768703 
. 768992 
. 769281 

.769571 
. 769860 

9. 770148 

. 770437 
. 770726 
.771015 

.771303 

9. 771592 

.771880 

.772168 

• 772457 
. 772745 

9- 773033 
.773321 
. 773608 
. 773896 
. 774184 

9.774471 

• 774759 

• 775046 
. 775333 
.775621 

9- 775908 
.776195 

. 776482 
. 776768 
- 777055 
9- 777342 
- 77762S 

.777915 
.778201 
. 778488 

9- 778774 

Cot. 



4.87 
4.87 



^5 
^7 
85 
^5 
85 



4 

4 

4 

4 

4 

4.85 

4.85 

4.85 

4.85 
4-83 
4.85 
4.83 
4.85 
4.83 
4.83 
4.83 
4-83 
4.83 

4.83 

4.82 

4.83 
4-83 
4.82 
4.82 
4.82 

4.83 
4.82 
4.80 

4. 82 
4.82 
4.82 
4. So 
4.82 
4.80 
4.80 
4. 82 
4.80 
4.80 



80 

78 
So 
80 

7^ 
So 
78 
7^ 
so 

78 

78 
78 

77 
7^ 
78 
77 
78 
77 
78 
4-77 



Cot. 



D. 1 



o. 238561 
. 238269 

• 237977 
. 237686 

. 237394 

0.237103 

. 236812 

• 236521 

• 236230 

• 235939 
o. 235648 

. 235357 
. 235067 

. 234776 
. 234486 

o. 234195 

. 233905 
. 233615 
. 233325 
. 233035 

o. 232745 

. 232455 

. 232166 

.231876' 

.231586 
0.231297 

. 231008 

.230719 
. 230429 

. 230140, 
o. 229852 

. 229563 
. 229274 
. 2289S5 

. 228697 

o. 228408 

. 228120 

. 227832 
. 227543 
. 227255 

o. 226967 
. 226679 

. 226392 

. 226104 

. 225816 

o. 225529 

. 225241 
. 224954 
. 224667 

. 224379 

o. 224092 

. 223805 
.223518 
.223232 
. 222945 

o. 222658 

.222372 

. 2220S5 

. 221799 

. 221512 

o. 221226 

Tan. 



M. 



59' 



31' 



LOGARITHMIC SINES 



I48 c 



M. 



Sin. 



10 
ii 

12 
13 

M 

15 
16 

: 7 a 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 

46 

47 ! 
48 

49 I 

5o 

5i 

52 

53 

54 

56 
57 
58 
59 
60 



7 1 1839 
712050 
712260 
7 1 2469 
712679 
712889 
713098 
71330S 

7I35I7 
713726 

713935 
714144 

714352 
714561 
714769 
714978 
715186 

715394 
715602 
715809 

716017 
716224 
716432 
716639 
716846 

717053 
717259 
717466 
717673 
717879 

718085 
718291 
718497 
718703 
718909 
719114 
719320 

719525 
719730 

719935 

720140 

720345 
720549 
720754 
720958 
721162 
721366 
721570 
721774 
721978 

722181 
722385 
722588 
722791 
722994 
723197 
723400 
723603 
723805 
724007 
724210 

Cos. 



D. 1". 



D. 1 



Cos. 



9. 933066 

• 932990 
.932914 
.932838 

• 932762 
9. 9326S5 

. 932609 

• 932533 
. 932457 
. 932380 

9. 932304 
.932228 
.932151 

• 932075 
.931998 

9-93I92I 
.931845 
.931768 
.931691 
.931614 

9- 931537 
.931460 

•931383 
.931306 
.931229 
9-93II52 
.93io75 

• 930998 
.930921 

. 930843 

9- 930766 
. 930688 
.930611 

• 930533 
- 930456 

9- 930378 
. 930300 

• 930223 

.930145 
. 930067 

9- 929989 
.929911 

• 929833 
.929755 

• 929677 
9- 929599 

. 929521 
. 929442 
. 929364 
. 929286 

9. 929207 
.929129 
. 929050 
.928972 
.928893 

9.928815 
. 92S736 
.928657 
.928578 
. 928499 

9. 928420 

Sin. 



D. i' 



1.27 
1.27 
1.27 
1.27 
1.28 
1.27 
1.27 
27 



1.28 
1.27 

1, 
1. 
1. 
1. 
1. 
1. 
1. 



1.28 
1.28 
1.28 

1.28 
1.28 
1.28 
1.28 
1.28 
1.28 
1.28 
1.28 
1.30 
1.28 



30 

28 



1. 

1. 

1.30 

1.28 

1.30 

1.30 

1.28 

1.30 

1.30 

1.30 

1.30 
1.30 
1.30 
1.30 

1.30 
3.30 
1.32 
1.30 
1.30 
1.32 
1.30 
1.32 
1.30 
1.32 
1.30 
1.32 
1.32 
1.32 
1.32 
1.32 



D. 1". 



Tan. 



9- 77S774 
. 779060 

• 779346 
. 779632 
.779918 

9. 780203 

. 780489 

• 780775 
.781060 
.781346 

9-781631 
.781916 
. 782201 
. 782486 
.782771 

9. 783056 

.783341 
.783626 
.783910 
.784195 

9- 784479 

. 784764 
. 785048 

• 785332 
. 785616 

9- 785900 
. 786184 



D. 1' 



. 786752 
. 787036 

9. 787319 
. 787603 
. 787886 
.788170 
.788453 

9-788736 
. 7S9019 
. 789302 

.7895.85 

. 789868 

9.790151 

. 790434 
. 790716 

• 790999 
.791281 

9-79I563 
. 791846 
.792128 
. 792410 
. 792692 

9. 792974 
. 793256 

• 793538 
.793819 
.794101 

9- 794383 
. 794664 
- 794946 
. 795227 
- 7955o8 

9- 795789 

Cot. 



4-77 
4-77 
4-77 
4-77 
4-75 
4-77 
4-77 
4-75 
4-77 
4-75 

4-75 
4-75 
4-75 
4-75 



4-73 

4-75 
4-73 
4-73 
4-73 
4-73 
4-73 
4-73 
4-73 
4-73 
4.72 

4-73 
4-72 
4-73 
4.72 
4.72 
4.72 
4-72 
4.72 
4-72 
4-72 

4.72 
4.7o 
4-72 
4-70 
4.70 
4.72 
4.70 
4.70 
4.70 
4-70 

4.70 
4.7o 
4.68 
4.70 
4.7o 
4.68 
4.70 
4.68 
4.68 
4.68 

D. 1". 



Cot. 



0.221226 
. 220940 
. 220654 
. 220368 
. 220082 

o. 219797 
.219511 
. 219225 
.218940 
.218654 

o. 218369 

.218084 

.217799 
.217514 

.217229 
o. 216944 

.216659 
.216374 

. 216090 

. 215805 

o. 215521 

.215236 
.214952 
. 214668 
. 214384 

o. 214100 
.2j 3 Si6 

.213532 
. 213248 

. 212964 
o. 2126S1 

.212397 

. 212114 

. 21 1830 

.211547 

0.21 1 264 
. 2IO981 
. 210698 
.210415 
. 2I0I32 

o. 209849 
. 209566 
. 209284 
. 20900 I 
. 208719 

o. 208437 

. 208154 

. 207872 

. 207590 
. 207308 

o. 207026 
. 206744 
. 206462 
. 206181 
. 205899 

o. 205617 

. 205336 
. 205054 
. 204773 

. 204492 
o. 20421 1 



Tan. 



INI. 



5 8° 



3 2° COSINES, TANGENTS, AND COTANGENTS 147* 



M. Sin. D. 1". I Cos. D. 1". Tan. D. 1". Cot. 



10 
11 
12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 

24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

5o 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



122 



9,724210 
.724412 
.724614 
.724816 

. 725017 
9.725219 
. 725420 
.725622 
. 725823 
. 726024 

9. 726225 
. 726426 
. 726626 
, 726827 
. 727027 

9. 727228 
. 727428 
. 727628 
.727828 
.728027 

9, 728227 
. 728427 
, 728626 
.728825 
. 729024 

9. 729223 
. 729422 
.729621 
. 729820 
. 730018 

9. 730217 

. 730415 
. 730613 
.730811 
.731009 
9. 731206 

. 731404 
.731602 

.731799 
. 731996 

9- 732193 
. 732390 

. 732587 
. 732784 

• 732980 
9.733177 

• 733373 

• 733569 

• 733765 

• 733961 

9- 734157 
. 734353 

• 734549 
. 734744 

• 734939 
9- 735135 

. 735330 

• 735525 
.735719 

• 7359H 
9. 736109 

Cos. 



3-37 
3-37 
3-37 
3-35 
3-37 
3-35 
3-37 
3-35 
3-35 
3-35 

3-35 
3-33 
3-35 
3-33 
3-35 
3-33 
3-33 
3-33 
3-32 
3-33 

3-33 
3-32 
3.32 
3-32 
3.32 
3-32 
3-32 
3-32 
3-30 
3-32 



30 

30 

30 

30 

28 

30 

30 

3.28 

3-28 

3.28 



28 

28 

28 

27 

2S 

27 
27 
27 
27 
27 
3-27 

3-27 
3-25 
3-25 
3-27 
3-25 



D. 1". 



9. 928420 
. 928342 
. 928263 
.928183 
.928104 

9. 928025 
. 927946 
. 927867 
.927787 
. 927708 

9. 927629 

• 927549 
.927470 
. 927390 
.927310 

9.927231 
.927151 
.927071 
. 926991 
.926911 

9. 926831 
.926751 
.926671 

. 926591 

.926511 

9.9264.31 

.926351 
. 926270 
.926190 
.926110 

9. 926029 

• 925949 
. 925868 
.925788 

• 925707 
9. 925626 

• 925545 

• 925465 

• 925384 

• 925303 
9.925222 

.925141 
. 925060 

• 924979 
. 924897 

9.924816 

• 924735 

• 924654 
.924572 

• 92449 1 

9. 924409 
. 924328 
. 924246 
, 924164 
. 924083 

9. 924001 
.923919 

• 923837 

• 923755 

• 923673 
9- 923591 

Sin. 



D. i" 



9- 795789 
. 796070 

.796351 

. 796632 

.796913 

9. 797194 

• 797474 

• 797755 
. 798036 
.798316 

9- 798596 
. 798877 

• 799157 
. 799437 
.799717 

9- 799997 
. 800277 
. 800557 
. 800836 
.801116 

9. 801396 
. 801675 
. 801955 
. S02234 
.802513 

9. 802792 
. 803072 
•803351 
. 803630 
. 803909 

9.804187 
. 804466 
. 804745 
. 805023 

• 805302 
9. 805580 

.805859 
.806137 
. 806415 
. S06693 

9. 806971 
. 807249 

• 807527 
. 807805 
. 808083 

9. 808361 
. 80S638 
. 808916 
. 809193 
.809471 

9. 809748 
.810025 
.810302 
. 810580 
.810857 

9.811134 
.811410 
.Si 1687 
.811964 
.812241 

9-812517 

Cot. 



4.68 
4.68 
4.68 
4.68 
4.68 
4.67 
4.68 
4.68 
4.67 
4.67 

4.68 
4.67 
4.67 
4.67 
4.67 
4.67 
4.67 
4.65 
4.67 
4.67 

4.65 
4.67 
4.65 
4.65 
4.65 
4.67 

4.65 
4.65 
4.65 
4.63 

4.65 
4.65 
4.63 
4.65 
4.63 
4.65 
4.63 
4.63 
4-63 
4-63 

4.63 
4.63 

4-63 
4.63 
4-63 
4.62 

4-63 
,4.62 

4-63 
4.62 

4.62 
4.62 

4-63 
4.62 
4.62 
4.60 
4.62 
4.62 
4.62 
4.60 

D. i". 



0.20421 1 


60 


. 203930 


59 


. 203649 


5« 


- 203368 


57 


. 203087 


56 


0. 202806 


55 


.,202526 


54 


. 202245 


53 


. 201964 


52 


. 201684 


51 


0. 201404 


50 


. 201123 


49 


. 200843 


48 


. 200563 


47 


. 200283 


40 


0. 200003 


45 


. 199723 


44 


. 199443 


43 


. 199164 


42 


. I9S884 


41 


0. 198604 


40 


• 198325 


39 


. 198045 


3« 


. 197766 


37 


. 197487 


3b 


0. 197208 


35 


. 196928 


34 


. 196649 


33 


. 196370 


32 


. 19609 I 


3i 


0. 195813 


30 


. 195534 


29 


. 195255 


28 


. 194977 


27 


. 194698 


2b 


0. 194420 


25 


. 194141 


24 


. 193863 


23 


. 193585 


22 


. 193307 


21 


0. 193029 


20 


. 192751 


\l 


. 192473 


. 192195 


17 


.191917 


ib 


0. 191639 


15 


. 191362 


14 


. 191084 


13 


. 190807 


12 


. 190529 


11 


0. 190252 


10 


. IS9975 


1 


. 189698 


. 189420 


7 


. 189143 


b 


0. 1 88866 


5 


. 188590 


4 


.188313 


3 


. 188036 


2 


. 187759 


1 


0. 1S74S3 





Tan. 


M. 



57' 



33 c 



LOGARITHMIC SINES 



146° 



M, 



o 

1 
2 
3 
4 
5 
6 

I 

9 
10 
11 
12 

13 

15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 
30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
5o 
5i 
52 
53 
54 
55 
56 
57 
58 

59 
60 



Sin. 



9. 736109 

. 736303 
.736498 
. 736692 
. 736886 
9. 737080 

• 737274 

• 737467 
. 73766i 

• 737855 
9. 738048 

• 738241 

• 738434 
. 738627 
. 738820 

9- 739oi3 

• 739206 

• 739398 

• 739590 

• 739783 

9- 739975 
. 740167 

• 740359 

• 740550 
. 740742 

9- 740934 
.741125 
.741316 
.741508 
. 741699 

9. 741889 
. 742080 
.742271 
. 742462 
. 742652 

9.742842 

• 743033 

• 743223 

• 743413 

• 743602 

9- 743792 

• 743982 
.744171 
. 74436i 

• 744550 
9- 744739 

. 744928 

.745117 
• 7453o6 

• 745494 
9- 745683 

.745871 
. 746060 
. 746248 

• 746436 
9- 746624 

.746812 

• 746999 

• 747187 

• 747374 
9- 747562 



D. 1 



3-23 
3-25 
3.23 
3-23 
3.23 
3-23 
3.22 

3.23 
3.23 
3-22 

3.22 
3.22 
3-22 
3.22 

3-22 
3.22 

3- 20 

3-20 

3.22 
3.20 

3.20 
3.20 

3.18 

3- 20 
3.20 ! 
3.i8 J 

3.18 ; 
3.20 j 
3.18 
3.17 

3.18 
3.18 
3.18 

3-17 

3-17 
3.18 
3-i7 
3.17 
3-i5 
3.17 

3.17 
3.15 
3.17 
3.15 
3.15 
3.15 



Cos. 



Cos. 



3.13 
3.15 
3.13 
3.13 
3.13 
3.13 
3.12 

3.13 
3.12 

3.13 
D. 1". 



9- 923591 

• 923509 
. 923427 
. 923345 
. 923263 

9-923181 
. 923098 
.923016 
. 922933 
. 922851 

9. 922768 
. 922686 
. 922603 
.922520 

• 922438 

9- 922355 
. 922272 
.922189 
.922106 
. 922023 

9. 921940 
.921857 
.921774 
.921691 
.921607 

9.921524 
.921441 

.921357 
.921274 
.921190 

9. 921107 
.921023 
. 920939 
. 920856 
. 920772 

9. 9206S8 
. 920604 
. 920520 

• 920436 
. 920352 

9. 920268 
. 920184 
. 920099 
.920015 
.919931 

9.919846 
.919762 
.919677 

• 919593 
. 919508 

9. 919424 

• 919339 
.919254 
.919169 

• 919085 
9.919000 

.918915 
. 918830 
.918745 
• 9*8659 
9- 918574 



D. 



1". Tan. 

I 



Sin. 



1-37 
1-37 
1-37 
1-37 
1-37 
1.38 

1-37 
1.38. 
i-37 
1.38 

i-37 
1.38 
1.38 
1-37 
1.38 
1.38 
1.38 
1.38 
1.38 
1.38 

1.38 
38 
38 
40 
38 
38 
40 
38 
40 
38 



1.40 
1.40 
1.38 
1.40 
1.40 
1.40 
1. 40 
1.40 
1.40 
1.40 

1.40 
1.42 
1.40 
1. 40 
1.42 
1. 40 
1.42 
1. 40 
1.42 
1.40 

1.42 
1.42 
1.42 
1.40 
1.42 
1.42 
1.42 
1.42 

1.43 
1.42 

D. 1". 



9.812517 
.812794 
.813070 

•813347 
.813623 
9.813899 
.814176 
.814452 
.814728 
.815004 

9.815280 

• 815555 
.815831 
.816107 
.816382 

9.816658 

• 816933 
.817209 
. 817484 
•817759 

9.818035 
.818310 
.818585 
. 818860 
.819135 

9..819410 
.819684 
. 819959 
. 820234 
. 820508 

9. 820783 
.821057 
.821332 
.821606 
.821880 

9.822154 
. 822429 
. 822703 
. 822977 

• 823251 

9. 823524 
.823798 
. 824072 

• 824345 
.824619 

9. 824893 
. 825166 

• 825439 
.825713 
. 825986 

9. 826259 

.826S32 
. 826805 
. 827078 
.827351 

9. 827624 
.827897 
.828170 
.828442 
.828715 

9. 828987 



Cot. 



D. 1' 



Cot. 



4.62 
4.60 
4.62 
4.60 
4.60 
4.62 
4.60 
4.60 
4.60 
4.60 

4.58 
4.60 
4.60 
4.58 
4.60 
4.58 
4. 60 
4.58 
4.58 
4.60 

4.58 
4.58 
4.58 
4.58 
4.58 
4-57 
4.58 
4.58 
4-57 
4.58 

4.57 
4.58 
4-57 
4-57 
4-57 

58 

57 

57 

57 

55 



4-57 
4-57 
4-55 
4-57 
4-57 
4-55 
4- 55 
4-57 
4-55 
4-55 

4-55 
4- 55 
4-55 
4-55 
4-55 
4-55 
4-55 
4-53 
4-55 
4-53 



o. 187483 j 60 

. 187206 

. 186930 

. 186653 

• 186377 
o. 186101 

. 185S24 

. 185548 

. 185272 

. 184996 

o. 184720 

. 184445 

. 184169 

. 183893 
. 183618 

o. 183342 

. 183067 
. 182791 
. 182516 

. 182241 

o. 181965 
. 181690 

.181415 

. 181 140 

. 180865 

o. 180590 
. 1803 16 
. 1 8004 1 

. 179766 

• 179492 

o. 179217 

.178943 
. 178668 
. 178394 

. 1 781 20 
o. 177846 

• 177571 
. 177297 
. 177023 
. 176749 

o. 176476 
. 176202 

. 175928 

• 175655 

• 175381 

o. 175107 

. 174834 
. I 74561 
. 174287 



59 
58 
57 
56 
55 
54 
53 
52 
5i 

50 

49 
48 

47 
46 

45 
44 
43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 

25 

24 

23 
22 
21 

20 

19 

18 

17 
16 

15 
M 
13 



174014 j 11 



D. 1 



o. 173741 
• 173468 

.173195 
. 172922 
. 172649 
o. 172376 
. 172103 

. 171830 
.171558 
. 17 1 285 

o. 171013 
Tan. 



10 

9 
8 

7 
6 

5 
4 
3 
2 

1 



123 



56 c 



34° COSINES, TANGENTS, AND COTANGENTS 145' 



M. Sin. D. 1". I Cos. D. 1". Tan. D. 1". Cot. 






9. 747562 


I 


. 747749 


2 


• 747936 


3 


.748123 


4 


. 748310 


5 


9. 748497 


6 


.748683 


7 


. 74S870 


8 


. 749 56 


9 


• 749243 


10 


9. 749429 


11 


• 7496i5 


12 


. 749S01 


13 


. 749987 


14 


.750172 


15 


9- 750358 


ifa 


. 750543 


17 


. 750729 


18 


■ 750914 


19 


. 751099 


20 


9. 751284 


21 


.75H69 


22 


. 75i654 


23 


.751839 


24 


• 752023 


25 


9- 752208 


2b 


• 752392 


27 


• 752576 


28 


. 752760 


29 


. 752944 


30 


9.753128 


3i 


.753312 


32 


• 753495 


33 


• 753679 


34 


.753862 


35 


9. 754046 


3b 


• 754229 


37 


.754412 


3» 


• 754595 


39 


.754778 


40 


9- 75496o 


4i 


.755143 


42 


.755326 


43 


•755508 


44 


• 755690 


45 


9- 755872 


46 


• 756054 


47 


. 756236 


48 


.756418 


49 


. 756600 


50 


9. 756782 


5i 


• 756963 


52 


•757144 


53 


.757326 


54 


. 757507 


55 


9. 757688 


5b 


• 757869 


57 


• 758050 


5« 


. 758230 


59 


.758411 


60 


9- 758591 



Cos. 



3.12 
3.12 
3 

3 
3 

3 
3 
3 
3 
3 



3.10 

3.10 
3-o8 
3- 10 
3.08 
3-io 
3- 08 
3.08 
3.08 

3.08 
3.08 
3.08 
3.07 
3.08 
3.07 
3.07 
3.07 
3-07 
3.07 

3.07 
3.05 
3- 



07 
05 
°7 
05 



3.05 
3-05 
3.05 
3.03 

3.05 
3.05 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 

02 
02 

03 
02 
02 



3. 

3. 

3- 

3- 

3- 

3.02 

3- 02 

3.00 

3.02 

3.00 

D. i". 



8574 
8489 
8404 
8318 
8233 
S147 
8062 
7976 
7891 
7805 
7719 
7634 
7548 
7462 
7376 
7290 
7204 
7118 
7032 
6946 

6859 

6773 
6687 
6600 
6514 
6427 
6341 
6254 
6167 
6081 

5994 
5907 
5820 

5733 
5646 
5559 
5472 
5385 
5297 
5210 

5123 
5035 
4948 
4860 

4773 
4685 
4598 
45 10 
4422 

4334 
4246 
4158 
4070 
3982 

3S94 
3806 
37i8 
3630 
354i 
3453 
3365 



Sin. 



D. 1". 



9. 828987 
. 829260 

• 829532 
. 829805 
. 830077 

9- 830349 
.830621 
.830893 
.831165 
.83M37 

9.831709 
.831981 
. 832253 
. 832525 

• 832796 
9.833068 

• 833339 
.833611 
.833882 

• 834154 

9- 834425 

• 834696 

• 834967 
.835238 

• 835509 
9- 835780 

.836051 

• 836322 

. 836593 
. 836864 

9.837134 

. 837405 
.837675 

• 837946 
.838216 

9.838487 
.838757 
. 839027 

• 839297 
.839568 

9.839838 
.840108 
.840378 
. 840648 
.840917 

9. 841187 
.841457 
.841727 
.841996 
.842266 

9- 842535 
. 842805 

• 843074 

• 843343 
.843612 

9.843882 
.844151 
.844420 
. 844689 

• 844958 
9- 845227 

Cot. 



4-55 
4-53 
4-55 
4-53 
4-53 
4-53 
4-53 
4-53 
4-53 
4-53 

4-53 
4-53 
4-53 
4.52 
4-53 
4.52 
4-53 
4.52 
4-53 
4.52 

4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4.50 

4.52 
4-5° 
4-52 
4-5° 
4.52 
4.50 
4-5° 
4.50 
4o2 
4-50 

4.50 
4.50 
4-50 
4.48 
4- 50 
4.50 
4-5o 
4.48 
4.50 
4.48 

4.50 

4.48 
4.48 
4.48 
4.50 
4.48 
4.48 
4.48 
4.48 
4.48 



D. i". 



o. 171013 
. 170740 
. 170468 
. 170195 
• 169923 

o. 16965 I 

. 169379 

. 169107 

. 168835 

. 168563 

o. 168291 
. 168019 

. 167747 
. 167475 

. 167204 
o. 166932 

. 166661 
. 166389 
.166118 
. 165846 

o. 165575 

. 165304 
. 165033 

. 164762 

. 164491 

o. 164220 

. 163949 
. 163678 
. 163407 
. 163136 

o. 162866 

. 162595 
. 162325 
. 162054 
. 161784 
0.161513 
. 161243 
. 160973 
. 160703 
. 160432 

o. 160162 

. 159892 
. 159622 
. 159352 
. 159083 

o. 158813 

. 158543 
. 158273 

. 158004 

• 157734 

o. 157465 

.157195 
. 156926 

. 156657 
. I563S8 

o. 156118 

. 155849 
. 155580 

.155311 
. 155042 

o. 154773 

Tan. 



124' 



55' 



35 v 



LOGARITHMIC SINES 



144 



M. 



Sin. 



o 
1 
2 
3 
4 
5 
6 

7 
8 

9 
10 
11 
12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 
30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 

49 
5o 
51 
52 
I 53 
54 
55 
56 
57 
58 
59 
60 



"5 



9- 758591 

.758772 

•758952 

.759132 

•759312 

9- 759492 

• 759672 

• 759852 
.760031 
.760211 

9. 760390 

• 760569 
. 760748 
. 760927 
.761106 

9.761285 
. 761464 
.761642 
.761821 
.761999 

9.762177 
. 762356 

• 762534 
.762712 
. 762889 

9. 763067 
.763245 
. 763422 
. 763600 
. 763777 

9- 763954 
.764131 

• 764308 
. 764485 
. 764662 

9.764838 

• 765015 
.765191 

• 765367 

• 765544 

9- 765720 
.765896 
. 766072 
. 766247 
. 766423 

9- 766598 

• 766774 

• 766949 
.767124 
.767300 

9- 767475 

• 767649 
. 767824 

• 767999 
.768173 

9.768348 
. 768522 
. 768697 
.768871 

• 769045 
9.769219 

Cos. 



D. 1' 



2.98 
2.98 
2.98 
2.98 
2.98 
2.98 
2.97 
2.98 
2.97 
2-97 
2.98 
2.97 
2.97 

2-95 
2.97 
2.97 

2-95 
2.97 

2.95 
2-95 

2.95 
2-95 
2-95 
2.95 
2-93 
2.95 
2.93 
2-93 
2.95 
2.93 

2.93 
2.93 
2.92 

2-93 
2.92 

2.93 
2.92 
2.92 

2-93 
2.92 

2.90 
2.92 
2.92 
2.90 
2.92 
2.90 
2.92 
2.90 
2.90 
2.90 



D. 1 



Cos. 



9- 9^365 
913276 
913187 

913099 
913010 
912922 
912833 
912744 
912655 
912566 

912477 
912388 
912299 
912210 
912121 
912031 
911942 

91 1853 
911763 
91 1674 

911584 

9^495 
91 1405 

911315 
911226 
91 1 136 
91 1046 
910956 
910866 
910776 

910686 
910596 
910506 
910415 
910325 
910235 
910144 
910054 
909963 
909873 
909782 
909691 
909601 
909510 
909419 
909328 
909237 
909146 

909055 
908964 

908873 
908781 
908690 
908599 

908507 
908416 
908324 

908233 
908141 
908049 
907958 



Sin. 



D. 1' 



Tan. 



D. 1". 



Cot. 



48 
48 

47 
48 

47 
48 

48 
43 
48 
48 

48 
43 
43 
48 
50 
48 

48 

50 

48 
50 

48 
50 
50 
43 
50 
50 
50 
50 
50 
50 

50 
50 
52 
50 
50 
52 
50 
52 
50 
52 

52 
50 
52 
52 
52 
52 
52 
52 
52 
52 

53 
52 
52 
53 
52 
53 
52 
53 
53 
52 



D. 1". 



9. 845227 
* . 845496 

.845764 

• 846033 
. 846302 

9. 846570 
.846839 
.847108 
.847376 

• 847644 

9- 847913 
.848181 
. 848449 
.848717 
. 848986 

9. 849254 

• 849522 

• 849790 

• 850057 

• 850325 

9- 850593 
. 850861 
.851129 

,851396 
.851664 

9-851931 
.852199 
. 852466 

• 852733 
. 853001 

9.853268 

• 853535 
.853802 

• 854069 

• 854336 
9. 854603 

.854870 
.855137 

• 855404 
.855671 

9- 855938 
. 856204 
.856471 

.856737 
. 857004 
9. 857270 
.857537 
.857803 
. 858069 
.858336 

9. 858602 
. 858868 

.859134 
. 859400 
. 859666 

9- 859932 
.860198 
. 860464 
. 860730 
.860995 

9. 861 261 

Cot. 



4.48 
4-47 
4.48 
4.48 
4-47 
4.48 
4.48 
4-47 
4-47 
4.48 

4-47 
4-47 
4-47 
4.48 
4-47 
4.47 
4.47 
4-45 
4-47 
4-47 

4-47 
4-47 
4-45 
4-47 
4-45 
4-47 
4-45 
4-45 
4-47 
4-45 

4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 

4-43 
4-45 
4-43 
4-45 
4-43 
4-45 
4-43 
4-43 
4-45 
4-43 

4-43 
4-43 
4-43 
4-43 
4-43 
4-43 
4-43 
4-43 
4.42 

4-43 
D. 1". 



o. 154773 
154504 
154236 
153967 
153698 
153430 
153161 
152892 
152624 
152356 

152087 
151S19 
!5i55i 
151283 
151014 
150746 
150478 
150210 
149943 
149675 
149407 

I49I39 
14887 1 
148604 
148336 
148069 
147801 

147534 
147267 
146999 

146732 
146465 
146 1 98 

14593 1 
145664 

145397 
I45I30 
144863 
144596 
144329 
144062 
143796 

143529 
143263 
142996 
142730 
142463 
142197 

I4I93I 
141664 

141398 
141132 
140866 
140600 

140334 
140068 
139802 
139536 
139270 
139005 
138739 

Tan. 



INI 



54' 



36 c 



COSINES, TANGENTS, AND COTANGENTS 143* 



M. 



10 
11 
12 
13 
14 
x 5 



Sin. 



D. 1". 



17 
18 

19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
3i 
32 
33 
34 

36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



126' 



9.7(39219 

769393 
769566 
769740 
769913 
770087 
770260 

770433 
770606 
770779 

770952 
771125 
771298 
771470 
771643 
771815 
771987 

772159 
772331 
772503 
772675 
772S47 
77301S 
773190 
77336 1 
773533 
773704 
773875 
774046 
774217 

774388 
774558 
774729 

774899 
775070 
775240 
7754IO 
77558o 
775750 
775920 

776090 
776259 
776429 
776598 
776768 

776937 
777106 

777275 
777444 
777613 

777781 
777950 
77S119 
77S2S7 

778455 
77S624 
778792 
778960 
779128 
779295 
779463 ! 

Cos. 



2.88 
2.88 
2.87 
2.S8 
2.S7 
2.S7 
2.87 
2.87 
2.S7 
2. 87 

2.87 
2.85 

2. S7 
2.85 
2.87 
2.85 
2.85 
2.85 
2.85 
2.85 

2.83 
2.S5 
2.83 
2.85 
2.83 
2.83 
2. S3 
2. S3 
2.83 
2. S3 

2.82 
2.83 
2.82 
2.83 
2.82 
2. 82 
2.S2 
2.82 
2.S2 
2. So 

2.82 

2. 82 

2.80 
2.80 
2.82 

2. SO 

2.80 

2. SO 
2.78 
2.8o 



Cos. 



D. 



Tan. 



D. 1". 



Cot. 



D. 1' 



9. 90795S 
. 907S66 

. 907774 
. 907682 

.907590 
9. 907498 
. 907406 
,907314 
,907222 
.907129 

907037 
906945 
906S52 
'906760 
906667 

906575 
9064S2 

9063S9 
906296 
906204 

9061 1 1 
906018 
905925 
905832 
905739 
905645 
905552 
905459 
905366 
905272 
905179 
9 5oS5 
904992 
904S98 
904804 
9047 1 1 
904617 
904523 
904429 
904335 
904241 
904147 
904053 
903959 
903S64 
903770 
903676 
903581 
903487 
903392 

903298 
903203 
903108 
903014 
902919 
902824 
902729 
902634 
902539 
902444 
902349 

Sin. 



53 
53 
53 
53 
53 
53 
53 
53 
55 
53 

53" 

55 
53 
55 
53 
55 
55 
55 
53 
55 

55 
55 
55 

55 

57 
55 

55 
55 
57 
55 

57 
55 
57 
57 
55 
57 
57 
57 
57 
57 

57 
57 
57 
5^ 
57 
57 
58 
57 
58 
57 

58 

5S 
57 
58 
58 
58 
58 
58 
58 
5^ 



D. 1". 



9.S61261 
.861527 
.861792 
. 86205S 
.862323 

9.S62589 
. 862854 
.863119 
.863385 
.863650 

9- 863915 
.864180 
. S64445 
.864710 

• 864975 
9. 865240 

. 865505 
. S65770 
. 866035 
. 866300 

9. 866564 
. 866829 
. 867094 
.867358 
. 867623 

9. 867887 
.868152 
.868416 
. 8686S0 
.868945 

9. 869209 
. 869473 
.869737 
.870001 
. 870265 

9. 870529 

• 870793 
.S71057 
.871321 
.S71585 

9- 871849 
.872112 
. 872376 
. 872640 
.87 2903 

9.873167 

• 873430 
.873694 

.873957 
. 874220 

9. 874484 

• 874747 
. 875010 

.S75273 
• S75537 

9. 875800 
. 876063 
.876326 
.876589 
.876852 

9.S77114 

Cot. 



4.43 

4.42 

4.43 
4.42 

43 

42 
42 
43 
42 



4.42 



4.42 
4.42 
4.42 
4.40 



4.42 
4.40 



4.38 
4.40 
4.4o 



4- 38 
4.40 

4.38 
4.3S 
4.38 
4.40 
4.38 
4. 38 
4- 38 
4.38 
4.38 
4-37 

D. i". 



o. 138739 

• 138473 
. 138208 
. 137942 

• 137677 
o. 137411 

• 137146 
. I 3688 I 
. 136615 
. 136350 

o. 136085 50 

• 135820 49 
• 1 35555 48 

• 135290 47 
.135025 J 46 

o. 134760 

• 134495 
. 134230 

• 133965 
. 133700 

o. 133436 
.133171 
. 132906 
. 132642 

• 132377 
o. 132113 

. 131848 

• 13 1 584 
.131320 

• 131055 
o. 130791 

. 130527 
. 130263 

• 129999 
.129735 

o. 1 2947 I 
. 129207 

. 128943 

. 128679 

. 1 284 15 

o. 128151 

. I278S8 

. 127624 

. 1 27360 

. 127097 

o. 126833 

.126570 

. 126306 

.126043 
. 125780 

o. 125516 

.125253 

. 1 24990 

.124727 
.124463 

o. 124200 

.123937 
.123674 
.123411 
.123148 

o. 1228S6 



Tan. 



M. 



53' 



37^ 



LOGARITHMIC SINES 



142 



M. 



Sin. 



D.I"., I 

I 



Cos. 



D. i' 



o 
1 
2 
3 
4 
5 
6 

7 
8 

9 
10 
11 

12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 
30 
31 
32 
33 

34 
35 
36 
37 
38 
39 
40 

4i 

42 

43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9- 779463 
.779631 
•77979$ 
. 779966 
.780133 

9. 780300 
. 780467 
. 780634 
.780801 
. 780968 

9.78ii34 
.781301 
.781468 
.781634 
.781800 

9.781966 
.782132 
. 782298 
. 782464 
. 782630 

9. 782796 
. 782961 
.783127 
. 783292 

• 783458 
9. 783623 

.783788 

• 783953 
.784118 
. 784282 

9. 784447 
.784612 
. 784776 
. 784941 
.785105 

9. 785269 

• 785433 

• 785597 
.785761 
.785925 

9. 786089 
. 786252 
.786416 

.786579 
.786742 
9. 786906 
. 787069 
.787232 
.787395 
.787557 

9. 787720 
.787883 
.788045 
. 788208 
.788370 

9- 788532 
. 788694 
. 788856 
.789018 
.789180 

9- 789342 

Cos. 



2.80 
2.78 
2.80 
2.78 
2.78 
2.78 
2.78 
2.78 
2.78 
2.77 

2.78 
2.78 
2.77 

2.77 

2.77 
2/77 
2.77 
2.77 
2.77 
2.77 

2.75 

2.77 

2.75 
2.77 

2.75 
2.75 
2.75 
2-75 
2-73 
2.75 

2-75 
2.73 
2-75 
2.73 
2.73 
2-73 
2.73 
2-73 
2-73 
2.73 
2.72 

2-73 
2.72 
2.72 

2-73 
2.72 
2.72 
2.72 
2.70 
2.72 

2.72 
2.70 
2.72 
2.70 
2.70 
2.70 
2.70 
2.70 
2.70 
2.70 

D. 1". 



902349 
902253 
902158 
902063 
901967 
901872 
901776 
90 168 1 

901585 
901490 

901394 
901298 
901202 
901 106 
901010 
900914 
900818 
900722 
900626 
900529 

900433 
9O0337 
900240 
900144 
900047 
899951 
899854 

899757 
899660 

899564 
899467 
899370 

S99 2 73 
899176 
899078 
898981 



898787 



898592 

898494 
898397 
898299 
898202 
898104 
898006 
897908 
897810 
897712 
897614 

897516 
897418 
897320 
897222 
897123 
897025 
896926 
896828 
896729 
896631 
896532 

Sin. 



.60 
.58 
.58 
,60 
58 
.60 
58 
60 
58 
60 

60 
60 
60 
.60 
60 
60 
60 
60 
62 
60 

60 
62 
60 
62 
60 
62 
62 
62 
60 
62 

62 
62 
62 

63 
62 
62 
62 

63 
62 

63 

62 

63 
62 

63 
63 
63 
63 
63 
63 
63 

63 
63 
63 
65 
63 
65 
63 
65 
63 
65 



Tan. 



D. 1". 



Cot. 



9. 8771 14 

.877377 
. 877640 
. 877903 
.878165 
9. 878428 
.878691 

.878953 
.879216 

.879478 

9. 879741 
. 880003 
. 880265 
. 880528 
. 880790 

9.881052 
.881314 

.881577 
.881839 
.882101 

9.882363 
. 882625 
. 882887 
.883148 
.883410 

9.883672 

.883934 
.884196 

.884457 
. 884719 

9. 884980 
.885242 
.885504 
. 885765 
. 886026 

9. 886288 
.886549 
.886811 
. 887072 
.887333 

9. 887594 
.887855 
.888116 
. 888378 
. 888639 

9. 888900 



. 889421 



D. 1 



• 889943 

9. 890204 
. 890465 

• 890725 
. 890986 
.891247 

9.891507 
.891768 
. 892028 
. 892289 
. 892549 

9.892810 

Cot. 



D. 1". 



22886 
22623 
22360 
22097 

21835 
21572 
21309 
21047 
20784 
20522 

20259 
19997 

19735 
19472 
19210 
18948 
18686 
18423 
18161 
17899 

17637 

17375 
17113 
16852 
16590 
16328 
16066 
15804 

15543 
15281 

15020 
14758 
14496 

14235 
13974 
13712 

1 345 1 
13189 
12928 
12667 

12406 
12145 
1 1 884 
11622 
11361 
1 1 100 
10839 

10579 
10318 
10057 

09796 

09535 
09275 
09014 

08753 
08493 
08232 
07972 
0771 1 

o745i 
07190 



Tan. 



127 



5* 



38 c 



COSINES, TANGENTS, AND COTANGENTS 



141' 



M. 



Sin. 



D. 1' 



Cos. 



9. 789342 

• 789504 

. 7S9665 

. 7S9827 

. 7S9988 

9. 790149 

• 79°3 10 
. 790471 
. 790632 

• 790793 

9- 790954 
.791115 
•791275 
. 791436 
• 79I59 6 

9- 791757 
.791917 
. 792077 
. 792237 

• 792397 

9- 792557 
.792716 
. 792876 

• 793035 

• 793195 
9- 793354 

.7935H 

• 793673 
• 793S32 

• 793991 

9- 794i5o 
. 7943oS 

• 794467 
. 794626 

• 794784 
9. 794942 

.795101 

• 795259 

•795417 

• 795575 



10 
11 
12 
13 

15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 

3o 
3i 
32 
33 
34 
35 
36 
37 
38 
39 

40 9. 795733 

• 795891 

• 796049 
. 796206 

• 796364 
9. 796521 

• 796679 
.796836 

• 796993 
.797150 



42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



I28 ( 



9- 797307 

• 797464 
. 797621 

•797777 

■ 797934 

9.798091 

• 798247 

• 798403 

• 798560 
.798716 

9- 798872 

Cos. 



2. 70 

2.68 
2. 70 
2.68 
2.68 
2.68 
2.68 
2.68 
2.68 
2.68 

2.68 
2.67 
2.68 
2.67 
2.68 
2.67 
2.67 
2.67 
2.67 
2.67 

2.65 
2.67 
2.65 
2.67 
2.65 
2.67 
2.65 
2.65 
2.65 
2.65 

2.63 



^5 
65 
^3 
63 
05 
63 
^3 
63 
63 
2.63 
2.63 
2.62 
2.63 
2.62 
2.63 
2.62 
2.62 
2.62 
2.62 

2.62 
2.62 
2.60 
2.62 
2.62 
2.60 
2.60 
2.62 
2.60 
2.60 

D. 1". 



9. 896532 

• 896433 

• 896335 
. 896236 
.896137 

9.896038 

• 895939 
. 895840 
.S95741 
.895641 

9- s 95542 
• s 95443 

• 895343 

• 895244 

• 895145 
9. 895045 

• 894945 



D. 1". 



• 894746 
. 894646 

9. 894546 
.894446 

• 894346 
. 894246 
.894146 

9. 894046 

• 893946 
.893846 

• 893745 
•893645 

9- 893544 

• 893444 

• 893343 

• 893243 
.893142 

9.893041 
. 892940 
.892839 

• 892739 
. 892638 

9.892536 
•892435 
.892334 
. 892233 
.892132 

9. 892030 
.891929 
.891827 
.891726 
.891624 

9. 891523 
.891421 
.891319 
.891217 
.891115 

9-891013 
.890911 
. 890809 
. 890707 
. 890605 

9- 890503 

Sin. 



1-65 
1.63 
1.65 

T.65 
1.65 
1.65 
1.65 
1.65 
1.67 
1.65 

1.65 
1.67 
1.65 
1.65 
1.67 
1.67 
1.65 
1.67 
1.67 
1.67 

1.67 
1.67 
1.67 

1.67 
1.67 
1.67 
1.67 
1.68 
1.67 
1.68 

1.67 
1.68 
1.67 
1.68 
1.68 
1.68 
1.68 
1.67 
1.68 
1.70 

1.68 
1.68 
1.68 
1.68 
1.70 
1.68 
1.70 
1.68 
1.70 
1.68 

1.70 
1.70 
1.70 
1.70 
1.70 
1.70 
1.70 
1.70 
1. 70 
1.70 



D. 1". 



Tan. 



9.892810 
. 893070 
.893331 
. 893591 
.893851 

9. S94111 

• 894372 
. 894632 
. S94892 
.S95152 

9.895412 

• 895672 
•805932 
.896192 
. 896452 

9.896712 
. 896971 
.897231 
. 897491 
.897751 

9. 898010 
. 898270 
.898530 
. 898789 

• 899049 
9. 899308 

.899568 
.899827 
. 900087 
. 900346 

9. 900605 
. 900864 
.901124 
.901383 
. 901642 

9. 901901 
. 902160 
. 902420 
. 902679 

• 902938 

9. 903197 
• 9 3456 
.903714 

• 903973 
. 904232 

9. 904491 

• 904750 
. 905008 
. 905267 
.905526 

9- 905785 
. 906043 
. 906302 
. 906560 
. 906819 

9. 907077 

• 907336 

• 907594 

• 907853 
.908111 

9. 908369 

Cot. 



D. 1' 



Cot. 



4.33 
4-35 
4-33 
4-33 
4-33 
4-35 
4-33 
4-33 
4-33 
4-33 

4-33 
4-33 
4-33 
4-33 
4-33 
4.32 
4-33 
4-33 
4-33 
4-32 

4-33 
4-33 
4.32 
4-33 
4.32 
4-33 
4.32 
4-33 
4.32 
4.32 

4.32 
4-33 
4.32 
4.32 
4.32 
4.32 
4-33 
4.32 
4.32 
4.32 

4.32 
4-3o 
4-32 

32 

32 

32 

30 

32 

32 



4 
4 
4 
4 
4 
4 
4.32 

4.30 
4.32 
4.30 
4.32 
4.30 
4.32 
4.3o 
4.32 
4-3o 
4.30 



D. 1". 



o. 107190 
. 106930 
. 106669 
. 106409 
. 106 149 

o. 105889 
. 105628 

. 105368 

. 105108 
. 104848 

o. 104588 

. 104328 

. 104068 

. 103808 
. 103548 

o. 103288 
. 103029 
. 102769 
. 102509 
. 102249 

o. 101990 

. 101730 

. 101470 

. IOI2II 
. I OO95 I 

o. 100692 
. 100432 
. 100173 
.099913 
. 099654 

o. 099395 

.099136 
. 098876 
. 098617 

.098358 

o. 098099 
. 097840 

. 097580 
.097321 
. 097062 

o. 096803 

. 096544 

. 096286 
. 096027 

. 095768 

o. 095509 

. 095250 
. 094992 

. 094733 
. 094474 

o. 094215 

. 093957 
. 093698 

.093440 
.093181 
o. 092923 
. 092664 
. 092406 

.092147 

.091889 
o. 091631 



60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

50 
49 
48 
47 
46 

45 
44 
43 
42 
4i 
40 
39 
38 
37 
36 
35 
34 
33 
32 
3i 

30 

3 

27 
26 
25 
24 
23 
22 
21 

20 

19 
18 

17 
16 

15 
M 

13 
12 
11 

10 

9 
8 

7 
6 

5 
4 
3 
2 

1 
o 

M 



51 



39 < 



LOGARITHMIC SINES 



140 



M. 



o 

1 

2 

3 

4 
5 
6 

7 
8 

9 
10 
ii 
12 
13 
M 
15 
16 

17 
18 

19 
20 
21 
22 
23 
24 
25 
26 

2 

2g 

30 
31 
32 
33 
34 
35 
36 

3 l 
38 

39 

40 

41 

42 

43 
44 
45 
46 

A l 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 



Sin. 



D. i' 



Cos. 



9. 798872 
. 799028 
• 799i84 

• 799339 

• 799495 
9. 799651 

. 799806 
. 799962 
.800117 
. 800272 

9. 800427 
. 800582 
. 800737 
. 800892 
.801047 

9. 801 201 
.801356 
.80151 1 
.801665 
.801819 

9.801973 
.802128 
.802282 
. 802436 
. 802589 

9. 802743 
. 802897 
. 803050 
. 803204 
.803357 

9. 80351 1 
. 803664 
.803817 
. 803970 
.804123 

9.804276 
.804428 
.804581 

• 804734 



805039 
805191 
805343 
805495 
805647 
805799 
805951 
806103 
, 806254 
. 806406 

,806557 
, 806709 
, 806860 
,807011 
.807163 
.807314 
. 807465 
.807615 
. 807766 
.807917 
. 808067 

Cos. 



2.60 
2.60 
2.5S 
2.60 
2.60 
2.58 
2.60 
2.58 
2.58 
2.58 

2.58 
2.58 
2.58 
2. 58 
2.57 
2.58 
2.58 
2-57 
2-57 
2.57 

2.58 
2-57 
2.57 
2-55 
2.57 
2-57 
2-55 
2-57 
2-55 
2-57 

2-55 
2-55 
2-55 
2-55 
2-55 
2.53 
2-55 
2.55 
2-53 
2-55 

2-53 
2.53 
2.53 
2.53 
2-53 
2-53 
2.53 
2.52 

2-53 
2.52 

2-53 
2.52 
2.52 
2-53 
2.52 
2.52 
2.50 
2.52 
2.52 
2.50 



D. 1' 



9. 890503 
890400 
890298 
890195 
890093 
889990 



889785 
889682 
8S9579 

889477 
889374 
889271 
889168 



888961 



888755 
888651 
888548 

888444 
888341 
888237 
888134 
888030 
887926 
887822 
887718 
887614 
887510 

887406 
887302 
887198 
887093 
886989 
886885 
886780 
886676 
886571 
886466 

886362 
886257 
886152 
886047 
885942 

885837 
885732 
885627 
885522 
885416 

8853 1 1 
885205 
8S5100 
884994 



884783 
884677 
884572 
884466 
884360 
884254 

Sin. 



D. 1' 



72 
70 

72 
70 
72 
70 
72 
72 
72 
jo 

72 
72 
72 
73 
72 
72 
72 
73 
72 
73 
72 
73 
72 
73 
73 
73 
73 
73 
73 
73 

73 
73 
75 
73 
73 
75 
73 
75 
75 
73 

75 

75 
75 
75 
75 
75 
75 
75 
77 
75 

77 

75 
77 
75 
77 
77 
75 
77 
77 
77 



D. i' 



Tan. 



D. 1". I Cot. 



9. 908369 
908628 



909144 
909402 
909660 
909918 
910177 

9 I0 435 
910693 

910951 
91 1209 
911467 
911725 
91 1982 
912240 
912498 
912756 
913014 
913271 

9 T 3529 
913787 
914044 
914302 
914560 
914817 
915075 
9*5332 
915590 
915847 
916104 
916362 
916619 
916877 

9 T 7i34 
917391 
917648 
917906 
918163 
918420 

918677 
918934 
919191 
919448 
919705 
919962 
920219 
920476 

920733 
920990 

921247 
921503 
921760 
922017 
922274 
922530 
922787 
923044 
923300 

923557 
923814 

Cot. 



4.32 
4-3o 
4-3o 
4-3o 
4-3o 
4.30 
4.32 
4-3o 
4-3o 
4-30 

4-3o 
4.30 
4.30 
4.28 
4-30 
4-30 
4-30 
4-30 
4.28 
4-30 

4- 3o 
4.28 
4.30 
4-30 
4.28 
4-30 
4.28 
4.30 
4.28 
4.28 

4.30 
4.28 



4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.2.8 

4.27 
4.28 
4.28 
4.28 
4.27 
4.28 
4.28 
4.27 
4.28 
4.28 

D. 1". 



0.091631 
.091372 
.091114 
. 090856 
. 090598 

o. 090340 
. 090082 
. 089823 
. 089565 
. 089307 

o. 089049 

. 08S79I 

.088533 
.088275 
. 088018 

o. 087760 
. 087502 
. 087244 

. 086986 
. 086729 

0.086471 
.086213 
. 085956 
. 085698 
.085440 

o. 085183 

. 084925 
.084668 

.084410 

.084153 

o. 083896 

.083638 
.083381 
.083123 
. 082866 

o. 0S2609 

.082352 

.082094 

.081837 
.081580 

0.081323 

.081066 
. 080809 
. 080552 
. 080295 
o. 080038 

.079781 
.079524 

. 079267 
.079010 

0.078753 
.078497 

. 078240 

- 077983 

.077726 

0.077470 
.077213 
. 076956 

. 076700 

. 076443 

0.076186 
Tan. 



129' 



50' 



COSINES, TANGENTS, AND COTANGENTS 139' 



M. 



Sin. 



D. i". 



Cos. 



10 
11 
12 
13 
14 
15 
16 

r 7 
18 

19 

20 

21 

22 

23 
24 

25 
26 

2 2 
28 

29 

30 
31 
32 
33 

34 

36 

38 
39 
40 

41 

42 

43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



808067 
808218 
808368 
808519 
808669 
808819 
808969 
8091 19 
809269 
809419 

809569 
809718 



0017 
0167 
0316 
0465 
0614 
0763 
0912 

1061 

1210 
1358 
1507 
1655 
1804 
1952 
2100 
2248 
2396 

2544 
2692 
2840 
2988 
3135 
3283 
3430 
3578 

3725 
3872 

4019 
4166 

4313 
4460 
4607 

4753 
4900 
5046 
5193 
5339 

5485 
5632 
5778 
5924 
6069 
6215 
6361 

6507 
6652 
6798 
6943 



Cos. 



2.52 
2.50 
2.52 
2.50 
2.50 
2.50 
2.50 
2.50 
2.50 
2.50 

2.48 
2.50 
2.48 
2.50 
2.48 
2.48 
2.48 
2.48 
2.48 
2.48 

2.48 
2.47 
2.48 

2-47 
2.48 
2.47 
2.47 
2.47 
2.47 
2.47 

2.47 
2.47 
2-47 
2.45 
2.47 
2-45 
2.47 
2-45 
2.45 
2.45 

2.45 
2.45 
2-45 
2-45 
2-43 
2.45 
2.43 
2.45 
2-43 
2.43 

2.45 
2.43 
2.43 
2.42 

2.43 
2.43 
2-43 
2.42 

2.43 
2.42 



D. 1' 



9.884254 
.884148 
. 884042 
.883936 
. 883829 

9.883723 
.883617 
.883510 
. 883404 
.883297 

9.883191 
. 883084 
. 882977 
.882871 
. 882764 

9- 882657 
.882550 
.882443 
.S82336 
.882229 

9.882121 
. 882014 
.881907 
.881799 
.881692 

9.881584 

.881477 
.881369 
.881261 
.881153 

9.881046 
. 880938 



.880722 

.880613 

9. 880505 

.880397 



. 880180 
.880072 

9. 879963 

.879855 
.879746 

. 879637 

. 879529 

9.879420 

.879311 
. 879202 

• 879093 
. 878984 

9.878875 
. 878766 
. 878656 
.878547 
.878438 

9.878328 
.878219 
.878109 
.877999 
.877890 

9.877780 

Sin. 



D. T ' 



77 
77 
77 
78 
77 
77 
78 
77 
78 
77 

78 
78 
77 
78 
78 
78 
78 
78 
78 
80 

78 
78 
80 
78 
80 
78 
80 
80 
80 
78 

80 
80 
80 
82 
80 
80 
80 
82 
80 
82 

80 
82 
82 
80 
82 
82 
82 
82 
82 
82 

82 

83 
82 
82 

83 

82 

83 

83 
82 

83 



Tan. 



D. 1' 



I 9-923814 
. 924070 
.924327 

• 924583 
. 924840 
9. 925096 
.925352 
. 925609 
.925865 
.926122 

9. 926378 
. 926634 
. 926890 
.927147 
. 927403 

9. 927659 
.927915 
.928171 
.928427 



9. 928940 
.929196 
.929452 
. 929708 

• 929964 
9. 930220 

• 930475 
.930731 

• 930987 
.931243 

9- 93H99 
.931755 
.932010 
.932266 
.932522 

9.932778 

• 933033 

• 933289 

• 933545 
. 933800 

9. 934056 
•9343.li 

• 934567 

• 934822 

• 935078 
9- 935333 

• 935589 

• 935844 
.936100 

• 936355 

9-9366ii 
. 936866 
.937121 
•937377 
. 937632 

9- 937887 
.938142 
.938398 

• 938653 
. 938908 

9.939163 
Cot. 



D. t". 



4.'27 
4- 

4. 



4.28 
4.27 

4.27 
4.27 
4.28 
4-27 



4.27 

4.27 
4.27 
4.27 
4.27 
4.27 
4.25 
4.27 
4.27 
4.27 
4.27 



4.25 
4.27 

4.25 
4.27 

4.25 
4.27 

4.25 
4.27 
4.25 
4.27 

4.25 
4.25 
4.27 
4.25 
4.25 
4.25 
4.27 
4.25 
4.25 
4.25 

D. 1". 



Cot. 



0.076186 
. 075930 

• 075^73 
.075417 
.075160 

0.074904 
. 074648 
.074391 

■074135 
.073878 

0.073622 
. 073366 
.073110 
.072853 

• 072597 
0.072341 

.072085 
.071829 

.071573 
.071316 

0.071060 
. 070804 

• 070548 
.070292 
. 070036 

o. 069780 
.069525 
. 069269 
.069013 

• 068757 

0.068501 

. 06S245 

.067990 I 28 

. 067734 

. 067478 
0.067222 

. 066967 

. 0667 1 1 

. 066455 

.066200 

0.065944 
. 065689 

. 065433 
.065178 
. 064922 
o. 064667 
.064411 
.064156 
. 063900 

. 063645 

o. 0633S9 

•063134 

. 062879 

. 062623 

. 062368 

0.062113 

.061858 

.061602 

. 06*347 

.061092 

0.060837 

Tan. 



I30 ( 



49' 



41 



LOGARITHMIC SINES 



I38 c 



M. 



Sin. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 
io 
ii 

12 

13 
M 
15 
16 

17 
18 

19 

20 
21 
22 
23 
24 
25 
26 

27 
28 

29 
30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



131 



9-816943 
.817088 

.817233 
.817379 
.817524 
9.817668 
.817813 
.817958 
.818103 
.818247 

9.818392 
.818536 
.818681 
.818825 
.818969 

9.819113 

• S19257 
.819401 

.819545 
.819689 

9.819832 
.819976 
.820120 
. 820263 
. 820406 

9. 820550 
. 820693 
.820836 
.820979 
.821122 

9.821265 
.821407 
.821550 
.821693 
.821835 

9-821977 
.822120 
.822262 
.822404 
.822546 

9. 822688 
.822830 
.822972 
.823114 
.823255 

9. 823397 
.823539 
. 823680 
,823821 
. 823963 

9. 824104 

• 824245 
. 824386 
. 824527 
. 824668 

9. 824808 

• 824949 
. 825090 
. 825230 
.825371 

9. 82551 1 

Cos. 



D. 1 



2.42 
2.42 

2.43 
2.42 
2.40 
2.42 
2.42 
2.42 
2.40 
2.42 

2.40 
2.42 
2.40 
2.40 
2.40 
2.40 
2.40 
2.40 
2.40 
2.38 

2.40 
2.40 

2.38 
2.38 
2.40 
2.38 
2.38 
2.38 
2.38 
2.38 

2.37 
2.38 

2.38 
2.37 
2.37 
2.38 
2-37 
2-37 
2-37 
2-37 

2.37 
2.37 
2-37 
2-35 
2-37 
2-37 
2.35 
2-35 
2-37 
2-35 

2.35 
2.35 
2.35 
2-35 
2-33 
2.35 
2.35 
2-33 
2-35 
2-33 

D. I". 



Cos. 



9- 87778o 
.877670 
. 877560 
.877450 
.877340 

9- 877230 
.877120 
.877010 
. 876899 
. 876789 

9. 876678 
. 876568 
.876457 
.876347 
.876236 

9.876125 
. 876014 
. 8759 4 
.875793 
, 875682 

9.875571 

• 875459 
.875348 

.875237 
.875126 

9- 875014 

• 874903 
.874791 
. 874680 

.874568 
9.874456 

.874344 
. 874232 
.874121 
. 874009 
9.873896 
.873784 
.873672 
. 873560 
.873448 

9- 873335 
.873223 
.873110 
. 872998 
. 872885 

9.872772 
.872659 
.872547 
.872434 
.872321 

9. 872208 
. 872095 
.871981 
.871868 

.871755 

9. 87 164 1 

.871528 

.8714M 

.871301 

.871187 

9.871073 

Sin. 



D. 1". 



1.83 
1.83 
1.83 
1.83 
1.83 
1.83 
1.83 
1.85 
1.83 
1.85 

1.83 
1.85 
1.83 
85 

85 
85 
83 
85 
85 
1.85 

1.87 
1.85 
1.85 
1.85 
1.87 
1.85 
1.87 
1.85 
1.8.7 
1.87 

1.87 
1.87 
1.85 
1.87 
1.88 
1.87 
1.87 
1.87 
1.87 
1.88 

1.87 
1.88 

1.87 
1.88 
1.88 
1.88 
1.87 
1.88 
1.88 
1.88 

1.88 
1.90 
1.88 
1.88 
1.90 
1.88 
1.90 
1,88 
1.90 
1.90 



D. 1" 



Tan. 



9-939i63 
. 939418 
. 939673 

• 939928 
.940183 

9. 940439 

• 940694 

. 940949 
.941204 

.941459 

9.94I7I3 
.941968 
.942223 
. 942478 

• 942733 
9. 942988 

.943243 

• 943498 

• 943752 
. 944007 

9. 944262 
.944517 
.944771 
. 945026 
.945281 

9- 945535 

• 94579° 
. 946045 

• 946299 
- 946554 

9. 946808 
. 947063 

• 947318 

• 947572 
.947827 

9.948081 

• 948335 
. 94859 
.948844 
.949099 

9- 949353 
. 949608 
. 949862 
.950116 

.95°37i 
9. 950625 

. 950879 
.951133 
.951388 
. 951642 

9. 951896 
.95215° 
• 9524°5 

• 952659 
.952913 

9.953167 
.953421 

• 953675 
. 953929 
.954183 

9- 954437 

Cot. 



D, 1' 



4.25 
4.25 
4.25 
4.25 
4.27 
4.25 
4-25 
4.25 
4.25 
4.23 

4.25 
4.25 
4.25 
4.25 
4.25 
4.25 
4.25 
4.23 
4.25 
4.25 

4.25 
4.23 
4.25 
4.25 
4.23 
4.25 
4.25 
4.23 
4.25 
4.23 

4.25 
4.25 
4.23 
4.25 
4.23 



4.25 
4.23 
4.23 
4.25 
4.23 
4.23 
4.23 
4.25 
4-23 
4-23 

4-23 
4.25 
4.23 
4.23 
4.23 
4.23 
4.23 
4.23 
4.23 
4-23 



D. 1 



Cot. 



o. 060837 
.060582 
. 060327 
. 060072 
.059817 

o. 059561 

. 059306 
.059051 
. 058796 
.058541 

o. 058287 
.058032 

.057777 

.057522 

. 057267 

0.057012 

. 056757 
. 056502 

. 056248 

.055993 

o. 055738 

. 055483 
. 055229 

. 054974 
.054719 

o. 054465 

. 054210 
. 053955 

.053701 

.053446 

0.053192 
. 052937 

.052682 
. 052428 

.052173 

0.051919 

.051665 

.051410 

.051156 
. 050901 

o. 050647 

. 050392 
.050138 

. 049884 
. 049629 

o. 049375 
.049121 
. 048867 

.048612 

.048358 

o. 048104 

. 047850 
. 047595 
.047341 

. 047087 
o. 046833 

. 046579 
. 046325 

.046071 

.045817 

o. 045563 



Tan. 



48' 



4 2° COSINES, TANGENTS, AND COTANGENTS i 37 c 



M. 



Sin. 



D. i". 



Cos. 



D. r 



Tan. 



D. i> 



Cot. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 

io 
ii 

12 

13 
14 
15 
16 

17 
18 

19 

20 
21 
22 
23 
24 
25 
26 

27 
28 

29 

30 
31 

32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

47 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



I32 ( 



.S25511 
.825651 
.825791 
.825931 
.826071 
.826211 
.826351 
.826491 
.826631 
. 826770 

. 826910 
.827049 
.827189 
.827328 
. 827467 
. 827606 
. 827745 
. 827884 
. 82S023 
.828162 

. 828301 
.828439 
.828578 
.828716 
.828855 
.828993 
.829131 
. 829269 
. 829407 

■ 829545 

. 829683 
.829821 

■ 829959 

■ 830097 
. 830234 
. 830372 
. 830509 
. 830646 
.830784 
. 830921 

.831058 

■83 1 195 
.831332 
.831469 
.831606 
.831742 
.831879 
.832015 
.832152 
. 832288 

. 832425 
.832561 
. 832697 

.832833 
. 832969 

• 833105 
.833241 

• 833377 
.833512 
.833648 
•833783 

Cos. 



2-33 
2-33 
2-33 
2-33 
2.33 
2.33 
2-33 
2-33 
2.32 

2.33 

2.32 

2.33 
2.32 

2.32 
2.32 
2.32 
2.32 
2.32 
2.32 
2.32 

2.30 
2.32 
2.30 
2.32 
2.30 

2.30 

2.30 

2.30 
2.30 
2.30 

2.30 
2.30 
2.30 
2.28 
2.30 
2.28 
2.28 
2.30 
2.28 
2.28 

2.28 
2.28 
2.28 
2.28 
2.27 
2.28 
2.27 
2.28 
2.27 
2.28 

2.27 

2.27 

2.27 

2.27 

2. 27 

2. 

2. 

2. 

2. 

2. 



D. 1". 



9.871073 
.870960 
. 870846 
. 870732 
. 870618 

9. 870504 
. 870390 
. 870276 
.870161 
. 870047 

9- 869933 
.869S18 
. 869704 
.869589 

• S69474 
9. 869360 
. 869245 
. 869130 
. 869015 
. 868900 

9.868785 
. 868670 

.868555 
. 868440 
. 868324 

9. 868209 
. 868093 
. 867978 
. 867862 
.867747 

9. 867631 
.867515 
. 867399 
.867283 
. 867167 

9.867051 
.866935 
.866819 
. 866703 
. 866586 

9. 866470 
.866353 
.866237 
.866120 
. 866004 

9.865887 
. 865770 
.865653 
.865536 
. 865419 

9. 865302 
.865185 
. 865068 
• 864950 
.864833 

9.864716 
.864598 
.864481 
.864363 
. 864245 

9.864127 

Sin. 





88 


9- 




90 






90 






90 






90 
90 


9- 




90 






92 






90 






90 






92 


9- 




90 






92 






92 






90 

92 


9- 




92 






92 






92 






92 






92 


9- 




92 






92 






93 






92 
93 


9- 




92 






93 






92 






93 






93 


9- 




93 






93 






93 






93 
93 


9- 




93 






93 






95 






93 






95 


9- 




93 






95 






93 






95 
95 


9- 




95 






95 






95 






95 






95 


9- 




95 






97 






95 






95 
97 


9- 




95 






97 






97 






97 


9- 



D. 1' 



954437 
, 954691 
954946 
955200 

955454 
9557o8 
955961 
956215 
956469 
956723 

956977 
957231 
957485 
957739 
957993 
958247 
958500 

958754 
959008 
959262 

959516 
959769 
960023 
960277 
960530 
960784 
961038 
961292 
96i545 
961799 
962052 
962306 
962560 
962813 
963067 
963320 

963574 
963828 
964081 
964335 
964588 
964842 
965095 
965349 
965602 

965855 
, 966109 
966362 
966616 
966869 

967123 
967376 
967629 
967883 
968136 
968389 
968643 
968896 
969149 
969403 
969656 

Cot. 



4-23 
4.23 
4.23 

4.23 
4.23 
4-23 
4.23 
4.23 
4. 22 
4-23 
4-23 
4.23 
4.23 
4.22 
4-23 
4-23 
4. 22 
4.23 
4-23 
4.23 
4. 22 
4 23 
4.22 

4.23 
4.23 
4.22 
4.23 
4.22 
4.23 
4.23 
4.22 

4.23 
4.22 

4.23 

4.22 

4.23 
4.22 
4.22 

4-23 
4.22 

4.23 
4.22 

4.23 
4.22 
4.22 
4.23 
4. 22 
4. 22 
4-23 
4. 22 
4. 22 
4-23 
4.22 



D. i> 



o. 045563 

• 045309 

• 045054 
. 044800 

• 044546 
o. 044292 

. 044039 
.043785 
•043531 
. 043277 

o. 043023 
. 042769 

•042515 

.042261 
. 042007 

0.041753 

.041500 
.041246 
. 040992 

. 040738 

o. 040484 
.040231 

• 039977 

.039723 

• 039470 

0.039216 
. 038962 

. 038708 
.038455 

. 038201 
o. 037948 

. 037694 
.037440 
.037187 

. 036933 

o. 036680 
. 0364 26 

.036172 
' 035919 
. 035665 

o, 035412 

•035158 
.034905 

.034651 

. 034398 
0.034145 

. 033891 
. 033638 
. 033384 
•033131 

o. 032877 

. 032624 
.032371 
.032117 
.031864 
0.031611 

.031357 
.031104 
.030851 
. 030597 

o. 030344 
Tan. 



47 



43 v 



LOGARITHMIC SINES 



136' 



M. 



Sin. 



10 
11 
12 
13 
14 

16 

17 
18 

19 

20 

21 
22 

23 
24 

25 

26 

27 

28 
29 

30 
3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
45 

4 Z 
48 

49 
50 
5i 
52 
53 
54 
55 
56 

5 l 
58 

59 
60 



9.833783 
►833919 

, 834054 
.834189 

.834325 
9. 834460 

.834595 
. 834730 
.834865 

• 834999 

9.835134 
. 835269 

• 835403 

.835538 
.835672 

9- 835807 
.835941 
.836075 
. 836209 
. 836343 

9. 836477 
.836611 

.836745 
. 836878 
.837012 
9.837146 
.837279 
.S37412 

• 837546 
.837679 

9.837812 

.837945 
. 838078 
.838211 
.838344 
9- 838477 
.838610 
.838742 
.838875 
. 839007 



9- 



839140 

839272 

839404 

. 839536 

. 839668 

9. 839800 

.839932 

. 840064 

.840196 

. 840328 

9. 840459 
.840591 
. 840722 
. 840854 
. 840985 

9.841116 
.841247 
.841378 
.841509 
.841640 

9-841771 

Cos. 



D. 1". 


| 


2.27 




2.25 




2.25 




2.27 




2.25 




2.25 




2.25 




2.25 




2.23 




2.25 




2.25 




2.23 




2.25 




2.23 




2.25 




2.23 




2.23 




2.23 




2.23 




2.23 




2.23 




2.23 




2. 22 




2.23 




2.23 




2.22 




2. 22 




2.23 




2. 22 




2. 22 




2. 22 




2. 22 




2. 22 




2. 22 




2. 22 




2. 22 




2. 20 




2. 22 




2. 20 




2. 22 




2. 20 




2. 20 




2. 20 




2. 20 




2. 20 




2. 20 




2. 20 




2. 20 




2. 20 




2.18 




2. 20 




2.18 




2. 20 




2.18 




2.18 




2.18 




2.18 




2.18 




2.18 




2.18 




D. 1". 





Cos, 



9.864127 
.864010 
. 863892 
.863774 
.863656 

9-863538 
. 863419 
.863301 
.863183 
. 863064 

9. 862946 
. 862827 
. 862709 
. 862590 
.862471 

9- 862353 
. 862234 
.862115 
.861996 
.S61877 

9.861758 
.861638 
.861519 
.86 1 400 
.861280 

9. 861161 
.861041 
. 860922 
.860802 
. 860682 

9. 860562 
. 860442 
. 860322 
. 860202 
. 860082 

9. 859962 
.859842 
.859721 
.859601 
. 859480 

9. 859360 

• 859239 
.859119 
.858998 
.858877 

9.858756 
.858635 
.858514 
.858393 
.858272 

9-858151 
. 858029 
.857908 
.857786 
.857665 

9.857543 
. 857422 

• 857300 
.857178 
. 857056 

9- 856934 
Sin. 



D. i' 



•95 
•97 
•97 
•97 
•97 
.98 
•97 
-97 
.98 
•97 



• 97 
.98 
.98 

• 97 
.98 
.98 
.98 
.98 
.98 

2. 00 



.00 
.98 
2.00 
1.98 
2.00 
2.00 
2.00 

2.00 
2. 00 
2.00 
2.00 
2.00 
2.00 
2.02 
2.00 
2.02 
2.00 

2.02 
2.00 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 

2.03 
2.02 
2.03 
2.02 
2.03 
2.02 
2.03 
2.03 
2.03 
2.03 



D. 1" 



Tan. 



9- 969656 
. 969909 
.970162 
.970416 
. 970669 

9. 970922 

.971175 
.971429 
.971682 
.971935 
9. 972188 
.972441 

• 972695 

• 972948 
.973201 

9- 973454 
. 973707 
• 9739 6 o 
.974213 

. 974466 
9. 974720 

• 974973 
. 975226 

• 975479 

• 975732 
9- 975985 

• 976238 
.976491 

• 976744 
. 976997 

9. 977250 

• 977503 
. 977756 
. 978009 
.978262 

9.9785I5 
. 978768 
.979021 
.979274 

• 979527 

9. 97978o 
. 980033 
. 980286 
.980538 
. 980791 

9. 981044 
.981297 
.981550 
.981803 
. 982056 

9. 982309 
. 982562 
.982814 
. 983067 
.983320 

9- 983573 
. 983826 

• 984079 
.984332 
.984584 

9. 9S4837 

Cot. 



D. 1". 



4.22 
4. 22 
4-23 
4. 22 



22 

22 

22 

22 

22 

22 

22 

4. 22 

4.22 

4.22 

4. 22 
4.22 
4.22 
4.22 



4. 

4- 
4- 
4- 
4- 
4. 22 

4. 22 
4. 22 
4. 20 

4. 22 
22 

22 
22 
22 
22 
22 



D. 1 



Cot. 



o. 030344 
.030091 
. 029838 
• 029584 
.029331 

o. 029078 

. 028825 
.028571 
.028318 
, 028065 

0.027812 

.027559 
.027305 
. 027052 

.026799 

o. 026546 

.026293 

. 026040 

.025787 
. 025534 

o. 025280 
.025027 

.024774 
.024521 

. 024268 
0.024015 
.023762 
. 023509 
.023256 
. 023003 

o. 022750 
. 022497 

.022244 
.021991 

.021738 
0.021485 
.021232 
. 020979 
.020726 

. 020473 

o. 020220 
.019967 

.019714 

.019462 

.019209 

0.018956 

.018703 

.018450 

.018197 

,017944 

0.017691 

.017438 

.017186 
.016933 
.016680 

0.016427 
,016174 
.015921 
.015668 
.015416 

0.015163 

Tan. 



133 



4 6° 



44 



COSINES, TANGENTS, AND COTANGENTS 



135 



M. 



o 

i 

2 

3 
4 
5 
6 

7 
8 

9 

io 
ii 

12 

13 
M 

15 
16 

17 
18 

19 

20 
21 
22 

23 
2 4 

25 
26 

27 

28 

29 

30 
31 

32 

33 
34 
35 
36 
37 
38 
39 
40 
4i 
42 
43 
44 
45 
46 

4 Z 
48 

49 

50 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9.841771 
.841902 
.842033 
.842163 
. 842294 

9. 842424 

■ 842555 
. 8426S5 
.842815 
. 842946 

9. 843076 
. 843206 

• 843336 
. 843466 

• 843595 
9- S43725 

. 843855 

• 843984 
.844114 
.844243 

9. 844372 

• 844502 
.844631 
. 844760 
. 844889 

9.845018 
.845147 
. 845276 
.845405 

• 845533 
9. 845662 

. 845790 
.845919 
. 846047 
.846175 
9. 846304 
.846432 
846560 
. 846688 
.846816 

9. 846944 
.847071 
.847199 
. 847327 

• 847454 
9- 847582 

.847709 
.847836 
. 847964 



9. 848218 

•848345 
. 84S472 
.848599 
. 848726 
9. 848852 
. 848979 
.849106 

• 849232 

• 849359 
9. S49485 

Cos. 



D. 1 



2. iS 
2.18 
2.17 
2.18 
2.17 
2.18 
2.17 
2.17 
2.18 
2. 17 



2.17 
2.15 
2.17 
2.15 
2.15 

2.17 
2.15 
15 



2.13 
2.15 
2.13 

2.13 
2.15 
2.13 
2.13 
2.13 

2.13 
2.13 



2. 12 
2. 12 



2. 
2. 
2. 
2. 
2. 
2. 
2. 
2. 

U. 1' 



Qos. 



9- 856934 
.856812 
. 856690 
. 856568 
. 856446 

9-856323 
. 856201 
. 856078 

• 855956 
.855833 

9.8557II 

.8555S8 

• 855465 
•855342 
.855219 

9.855096 

• 854973 
.854850 
.854727 
. 854603 

9. 854480 

• 854356 

• 854233 
.854109 
.853986 

9.853862 
.853738 
.853614 

• 853490 
.853366 

9- 853242 
.853118 
. 852994 
. 852869 

• 852745 
9. 852620 

. 852496 

•852371 
.852247 
.852122 

9-85I997 

.851872 

•851747 
.851622 

•851497 

9.851372 

.851246 

.851121 

• 850996 
. 850870 

9- 850745 
.850619 

• 850493 
.850368 
. 850242 

9.850116 

• 849990 
. 849864 
.849738 
. 8496 1 1 

9. S49485 

Sin. 



D. 1". 



2.03 
2.03 
2.03 
2.03 
2.05 
2.03 
2.05 
2.03 
2.05 
2.03 

2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.07 
2.05 

2.07 
2.05 
2.07 
2.05 
2.07 
2.07 
2.07 
2.07 
2.07 
2.07 

2.07 
2.07 
08 

07 
08 

07 
08 

07 
08 
oS 



2, 
2. 
2. 
2. 
2. 
2. 
2. 
2. 

2.08 
2.08 
2.08 
2.08 
2.08 
2. 10 
2.08 
2.08 
2. 10 
2.0S 



2. 10 



D. V 



Tan. 



9. 984837 
. 985090 

• 985343 

• 985596 
.985848 

9. 986101 

• 986354 
. 986607 
. 986860 
.987112 

9- 987365 
.987618 
.987871 
.988123 
. 988376 

9. 988629 
. 98SS82 

• 989134 
.989387 
. 989640 

9- 989893 
.990145 

• 990398 
.990651 

• 990903 
9. 991 156 

• 991409 
.991662 
.991914 
.992167 

9. 992420 
. 992672 

• 992925 
.993178 
.993431 

9- 993683 

• 993936 
.994 1 89 
.994441 

• 994694 

9- 994947 
.995199 

• 995452 

• 995705 

• 995957 
9.996210 

• 996463 
.996715 
. 996968 
.997221 

9- 997473 
- 997726 

• 997979 
.998231 

• 998484 
9- 998737 

• 998989 

• 999242 

• 999495 

• 999747 
o. 000000 

Cot. 



D. 1' 



4. 22 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 22 


4. 22 


4. 20 


4.22 


4. 22 


4. 22 


4.20 


4. 22 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 22 


4. 20 


4. 22 


4.22 


4. 20 


4. 22 


4.22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4. 20 


4. 22 


4. 22 


4.20 


4. 22 


4. 22 


4. 20 


4.22 


4,22 


4. 20 


4.22 


4. 22 


4. 20 


4. 22 


4.22 


4. 20 


4.22 



D. 1". 



Cot. 



0.015163 
.014910 

.014657 
.014404 
.014152 
0.013899 
. 013646 

•OI3393 
.013140 
.012888 

0.012635 
.012382 
.012129 
.011877 
.011624 

0.011371 
.011118 
.010866 
.010613 
. 010360 

o. 010107 
. 009855 
. 009602 
• 009349 
.009097 

o. 008844 
.008591 

.008338 
. 008086 
. 007833 

o. 007580 
. 007328 

. 007075 

. 006822 
. 006569 
0.006317 
. 006064 
.005811 

.005559 
. 005306 

o. 005053 
.004801 

. 004548 

. 004295 

. 004043 

o. 003790 

. 003537 
.003285 
. 003032 
.002779 

o. 002527 
.002274 
.002021 
.001769 
.001516 

0.001263 
.001011 
. 000758 
. 000505 
. 000253 

0.000000 

Tan. 



134' 



45 



5^4 



GENERAL REFERENCE TABLES 



Table 63. Giving the Weights of Different Materials per 

Cubic Foot 1 



Material 



Ash timber 

Brick (pressed) 

" (common building) 

Cement (Portland) 

(Natural 

Concrete 1:2:4 Mixture (Trap rock) 

(Gravel) 

" (Limestone) 

" (Sandstone) 

(Cinder) 

1:3:6 Mixture (about 5 lbs. less) 

Earth (common loam, loose and dry) 

" (common loam, moist and rammed) . . 

" (sand or gravel loose and dry) 

" (sand or gravel rammed) 

" (sand or gravel wet) 

Hemlock timber 

Hickory " 

Iron (cast) 

" (wrought) 

Maple timber 

Oak " (white) 

(black) 

Masonry (dressed granite or limestone) 

(mortar rubble) 

(dry " ) 

Pine (white) 

" (northern yellow) 

" (southern yellow) 

Steel 

Water 



Weight per Cu. Ft. 



75 
5o 



40 
150 
125 

to 90 

to 56 

155 
152 
150 

145 
no 

70 

IOO 
IOO 
120 
120 

25 

50 
450 
480 

50 

48 

40 

165 

155 

125 

25 

34 
40 
490 
62.5 



lbs. 



Miscellaneous Weights 

1 bbl. Portland cement 376 lbs. 

1 " natural " 235 

1 gal. water " 8.345 " 



1 For weight of road rocks, see Tables 21 and 22, page 99. 



MODULI OF ELASTICITY 



585 



Table 64. Giving Moduli of Elasticity, Working Stress 
and Ultimate Strength 



Moduli of Elasticity 



Material 



Lbs. per Sq. In. 



Concrete 

Hemlock 

Iron (cast) 

Iron (wrought) . 

Oak 

Pine (white) . . 
Pine (yellow) . . 
Steel (medium) 
Spruce 



900,000 

17,500,000 

29,000,000 

1,500,000 

1,600,000 

1,600,000 

30,000,000 

1,600,000 



Working Stresses in Lbs. per Square Inch 



Material 



Concrete 

Hemlock 

Iron (cast) . . . 
" (wrought) 

Oak 

Pine (white) . . 

" (yellow) . 

Steel (medium) 

Spuce 



Tension 



60 
600 

3,000 

10,000 

1,200 

700 

1,200 

1 2 ,000 

800 



Compression 



600 
W. G. 1 600 A. G. 2 150 

18,000 
8,000 
W. G. 1,200 A. G. 500 
W. G. 700 A. G. 200 
W. G. 1,200 A. G. 350 

12,000 
W G. 800 A. G. 200 



Shear 



60 to 100 
W. G. 100 A. G. 600 

5, 000 

8,000 
W. G. 200 A. G. 1,000 
W. G. 100 A. G. 500 
W. G. 150 A. G. 1,250 

12,000 
W. G. 100 A. G. 750 



Ultimate Strength in Lbs. per Square Inch 



Material 



Concrete 

Hemlock 

Iron (cast) . . . . 
" (wrought) . 

Oak 

Pine (white) . . . 

" (yellow) . . 

Steel (medium) 

Spruce 



Tension 



300 

6,000 

18,000 

50,000 

1 2 ,000 

7,000 

12,000 

60,000 

8,000 



Compression 



3,000 
W. G. 6,000 A. G. 



600 



90.000 

40,000 
W. G 7,000 A. G. 2 000 
W G. 5,500 A. G. 700 
W. G. 7,000 A. G. 1,400 

60,000 
W. G. 6,000 A. G. 700 



Shear 



1300 
W. G. 350 A. G. 2,500 

20,000 tO 30,000 

35,000 to 55,000 
W. G. 800 A. G. 4.000 
W. G 400 A. G. 2,000 
W. G. 600 A. G. 5,000 

50,000 to 70,000 
W. G. 400 A. G. 3,200 



1 W. G. — With Grain. 



2 A. G. — Across Grain. 



586 



GENERAL REFERENCE TABLES 



Table 65. Uniform Beams. Maximum Bending Moment 
and Deflections (Simple Cases) 



Case 1. Beam with ends free. Single concentrated load P in 
middle of span; weight of beam disregarded. 

The maximum moment occurs at 
the center of the span. 

P 4 




The maximum deflection occurs at 
the center of the span. 



Concentrated Load in Cen- 
ter of span 



D = 



PP 



48 EI 



Where D 
P 
' I 
E 



= the deflection in inches 
= load in pounds 
= span in inches 
= modulus of elasticity in lbs. 
per sq. inch 
/ = moment of inertia in inches 4 
Mp = maximum moment in inch 
pounds. 




Cantilever Beam 



Case 2. Cantilever beam con- 
centrated load P; weight of beam 
disregarded. 

The maximum moment occurs at 
the support. 

M = PI 

P 

D 



3 EI 



Case j. Beam with ends free. Uniformly distributed load. 
The maximum moment occurs at the center of the span. 

Wl 

8 




M = 



Uniform Load 



The maximum deflection occurs at 
the center of the span. 

D = j_wp 

384 EI 

In these formulas W equals the total 
uniformly distributed load. 



UNIFORM BEAMS 



587 



Case 4. Cantilever beam. Uniform load W 
Maximum moment occurs at the 
point of support. 

m = m 

2 

The maximum deflection occurs at 
the free end. 



D = 



WP 
8 EI 




Case 5. Beam with fixed ends, concentrated load P in center of 
span; weight of beam disregarded. 

The maximum bending moment 
occurs at the points of support and 
at the middle of the beam. 



if-2 



D = 



PP 



192 EI 




Case 6. Beam with fixed ends and a uniformly distributed load. 
Maximum bending moment occurs at the supports. 



M' 



Wl 



12 



m -m 

24 
Maximum deflection 



WP 
384 EI 




Resisting Moment of a beam is expressed by the formula 

u f ~tL 

e 

Where M r = moment of resistance in inch 
pounds 
p = maximum allowable fiber stress 

in lbs. per sq. inch. 
I = moment of inertia of the beam 

in inches 4 
e = distance in inches from the neu- 
tral axis to the outer fiber 



$88 GENERAL REFERENCE TABLES 

Table 66. Centers of Gravity of Ordinary Plane Figures 



K.Q. 





Squares, rectangles, parallelograms. Center of gravity is at 
the intersection of the diagonals or midway between the bases 
on a line drawn between the centers of those bases. 



Triangles 





Center of gravity is at the intersection of the medial lines 
a b and c d; a medial line is a line drawn from any apex to the 
middle of the opposite side The distance b (C. G.) = \ ab; that 
is, the center of gravity is on the medial line \ of the distance from 
the base to the apex. 

Trapezoid 



9 -*=^-- 



— -iCA. 



Graphic Method. Prolong b a to g, making a g = c d. Pro- 
long c d to h, making d h = a b. Connect g h. Bisect a b at e. 
Bisect cd at/. Connect ef: the intersection of g h and ej is 
the center of gravity. 

The distance/ (CG.) =^X 2 f , + °f 

3 ab + cd 




Any Quadrilateral 

Graphic Method. Draw 
the diagonals a c and b d 
intersecting at e. 

Lay off a / = e c 
Lay off b g = e d 

Bisect eg at h\ bisect ej 
at *. 

The intersection of / h and 
g i is the center of gravity 
of the figure. 



CENTERS OF GRAVITY 



589 



Circles 
Center of gravity at the center 




Semicircle, 

The center of gravity lies on the radius 
perpendicular to the diameter. The distance 
c (C. G.) = radius X 0.4244 




a 



Quadrant 

The center of gravity lies on the radius which 
bisects the Z. a c b. The distances (C.G.) = radius 
X 0.600? 




Sector 

The center of gravity lies on the radius bisect- 
ing the /_a c b. The distance c (C. G.) = f radius X c 
chord a b radius 2 X chord 



arc a d b 



3 X area 




Segment 



The center of gravity lies on the perpen- 
dicular erected at the center of the chord ab. 

The distance c (C G.) 



chord ab* 



1 2 X area of segment 




Table 67. Moments of Inertia of Simple Sections 



I = Moment of Inertia 
12 



— ; 


1 

1 



■tr- 



59° 



GENERAL REFERENCE TABLES 




Square 



/ = 



¥ 



12 




K— b — H 
Triangles 



36 




Circles 



/ = 0.7854^ 



ST** 






i b 



d' 
4:i 



7 = 



bd* - Vd'* 



12 



APPENDIX A 
TRAFFIC RULES AND REGULATIONS, STATE OF OHIO 

FOREWORD 

Inasmuch as Section 249 of the Cass Law, (G. C. 7246) directing 
the state highway commissioner to prepare and publish a set of 
traffic rules and regulations, is for the protection of life and limb, it 
is undoubtedly the most important section of the road laws of Ohio. 

After much thought and investigation of rules and regulations 
governing traffic conditions in a number of states, we submit the 
following in as condensed form as explicitness will permit, having 
selected, as we believe, the better parts of such laws and regulations 
governing the traffic of other states and municipalities, and putting 
them into a code of rules and regulations that will fit, as nearly as 
may be, all conditions and localities requiring a code of regulations, 
which will at the same time govern traffic on all the highways of 
Ohio. 

A cursory examination of these rules may lead many to the con- 
clusion that unreasonable restrictions have been imposed, but we 
believe a thoughtful study of each section will reveal an effort on 
the part of the State Highway Department to furnish the public 
with a code of traffic regulations, permitting of the greatest amount 
of freedom consistent with safety first. 

The original draft of the following regulations was submitted 
to Mr. W. A. Alsdorf, Secretary of the Ohio Good Roads Federation, 
Mr. Harry Gordon of Cincinnati, and Mr. Fred Caley of Cleveland, 
who carefully studied the entire code, section by section, and sug- 
gested many valuable and important changes. 

We now put forth the result of our efforts with the belief that if 
the prescribed rules and regulations are followed, many embarrassing 
situations and distressing accidents may be averted. 

Clinton Cowen, 
State Highway Commissioner. 

ARTICLE I — DEFINITIONS 

Sec. i — The term " vehicle" shall apply to a horse being rode 
or led, and to any conveyance except a baby carriage or street car. 

Sec. 2 — The term "street car" shall apply to any conveyance 
confined to tracks. 

Sec. 3 — The term "driver" shall apply to the rider, driver, or 
leader of a horse, a person who pushes, draws, propels, operates, or 
who is in charge of a vehicle. 

Sec. 4 — The term "road" shall apply to that part of a street 
or public highway intended for vehicles. 

59i 



592 



TRAFFIC RULES AND REGULATIONS 



Sec. 5. — The term "curb" shall apply to the boundary line of 
a road. 

Sec. 6 — The term "sidewalk" shall apply to a path or walk 
intended for pedestrians. 

Sec. 7 — The term "horse" shall apply to any draft animal or 
beast of burden. 

Sec. 8 — The term, "motor vehicle" shall apply to all vehicles 
propelled by power other than muscular, except a street car, traction 
engine, road roller, and police, fire or ambulance vehicles. 

ARTICLE II — RESPECTIVE RIGHTS AND DUTIES OF 
DRIVERS AND PEDESTRIANS 

Sec. 1 — Roads are primarily intended for vehicles, but pedestrians 
have the right to cross them in safety, and drivers shall exercise ail 
possible care not to endanger them. 

Sec. 2 — Pedestrians should observe the following precautions; 

1st. Avoid interference with vehicular traffic, and to this end not 
step onto the road without first looking to see what is approaching: 

2nd. Cross the road at right angles — at regular crossings where 
such exist, — and where a traffic officer is stationed, wait for his signal. 

Sec. 3 — Pedestrians will aid in expediting traffic on side-walks 
by keeping to the right, and when stopping for any purpose by doing 
so on one side and out of the way of a crossing or driveway. 



ARTICLE III — PASSING TURNING, STOPPING, 
STANDING AND STARTING 

Sec. 1 — A vehicle meeting another shall keep to the right, so as 
to leave half the road free for the coming vehicle. (6310 G. C.) 

Sec. 2 — A vehicle overtaking another shall pass to the left, the 
front vehicle giving half the road to the rear vehicle. (6310 G. C.) 

Sec. 3 — A vehicle turning into a road to the right shall turn the 
corner as near the right hand curb as practicable. 



This Way 



Sec. 4 — A vehicle turning into a road to the left shall pass around 
the point of intersection of the center lines of the two roads. 






+ . 



This Way 



Not this Way 



TRAFFIC RULES AND REGULATIONS 593 

Sec. 5 — A vehicle crossing from one side to the other of a road 
shall head in the same direction as the traffic on that side of the road. 



This Way Not this Way 

Sec. 6 — On heavy traffic roads, slow moving vehicles shall keep 
close to the right hand curb so as to leave the center of the road clear 
for overtaking traffic — the slower the speed the nearer the curb. 

Sec. 7 — A vehicle in passing around a circle shall keep to the right 
from entrance to exit. 

Sec. 8 — A vehicle on a road divided longitudinally by a parkway, 
walk, rope or other obstruction, shall keep to the right of such 
division. 

Sec. 9 — A vehicle shall not back to make a turn if by so doing it 
obstructs traffic, but shall go forward to a point where a turn can be 
made without backing. 

Sec. 10 — A vehicle shall not follow another too closely for safety. 

Sec. 11 — No vehicle shall stop in the road in such a position as 
to prevent the free passage of other vehicles in both directions at 
the same time. 

Sec. 12 — A vehicle shall not pass a street car which has stopped 
to receive or discharge passengers at a less distance than ten feet, 
nor at a greater speed than six miles per hour. A vehicle shall come 
to a stop if necessary to prevent interference or injury to such 
passengers. 

Sec. 13 — No horse or vehicle shall be driven, propelled or allowed 
to stand, on any side- walk except for purposes of crossing the same 
when necessary, and then only the shortest way from the road to 
the abutting premises. 

Sec. 14 — No vehicle shall stop in such a way as to interfere with 
the passage of pedestrians at regular crossings, or within 10 feet of 
a fire plug. 

Sec. 15 — No street car shall stop or stand within the intersection 
of any road. 

ARTICLE IV — LOADS, LOADING, WIDTH OF TIRE, 
TRAILERS, ETC. 

Sec. 1 — No traction engine or other vehicle whose wheels have 
tires equipped with lugs, spikes, chains or other projections seriously 
destructive to the surface, shall be driven over the road. (1342 1- 
12 G. C.) 

Sec. 2 — No vehicle or load, the total width of which is greater 
than twelve feet, shall be operated or drawn over a road unless said 
greater width will leave one-half the road free for passing vehicles. 

Sec. 3 — No more than thirty-four hundred pounds including 
weight of vehicle, shall be transported over a gravel, macadam or 
stone road in a vehicle having a tire less than three inches in width. 
(7477 G. C.) 



594 TRAFFIC RULES AND REGULATIONS 

Sec. 4 — For vehicles having tires three inches and over in width 
the load on any wheel per lineal inch of width of tire on any road shall 
not exceed six hundred pounds; and during such times as the road 
surface is soft, because of thawing or because of excessive rains, the 
load per lineal inch of width of tire on any wheel shall not exceed 
three hundred pounds on gravel or macadam roads. 

Sec. 5 — Trailers used in hauling over the road shall be so con- 
nected that the wheels of no two will follow in the same tracks. 

Sec. 6 — No vehicle carrying a load in excess of fifteen tons, 
including the weight of the vehicle, shall be moved over any 
road except under the written permission of the State Highway 
Commissioner. 

ARTICLE V— SPEEDS 

Sec. i — No motor vehicle shall operate on a road at a greater 
speed than: 

8 miles per hour in the business or closely built up portions of a 
municipality; 

15 miles per hour in other portions of a municipality; 

20 miles per hour outside of municipalities. (12604 G. C.) 

Sec. 2 — No vehicle shall operate on a road at a speed greater 
than is reasonable or proper or so as to endanger the property, life 
or limb of any person. (12603 G. C.) 

Sec. 3 — No motor or other power vehicle carrying a weight in 
excess of four tons including a vehicle shall be operated upon any 
road at a speed greater than 15 miles per hour; and no such vehicle 
carrying a weight in excess of eight tons including the vehicle shall 
be operated at a speed greater than 6 miles per hour when such vehicle 
is equipped with iron or steel tires, nor greater than 12 miles per 
hour when the vehicle is equipped with tires of rubber or other similar 
substance. 

Sec. 4 — No vehicle shall cross a road or make any turn at a 
dangerous speed. . 

Sec. 5 — Where " Danger" and "Go Slow" signs appear, the 
speed of any vehicles shall not exceed twelve miles per hour. 

Sec. 6 — Trucks and heavy wagons shall not be driven recklessly 
so as to endanger the public. 

Sec. 7 — No vehicle shall emerge from an alley, stable, garage 
or any private drive or entrance faster than a walk or six miles 
per hour. 

Sec. 8 — A vehicle upon approaching a cross road shall slow down 
sufficiently to prevent any danger from meeting other vehicles on 
the cross road. 

Sec. 9 — No person shall race any horse or motor vehicle on a 
road whether the running, racing or trotting be for trial or speed or 
for the purpose of passing another horse or vehicle. 

Sec. 10 — A motor vehicle, road roller or traction engine shall 
slow down when approaching a horse, if the horse appears to be 
frightened, and if the driver of the horse shall signal the driver of 
the vehicle the latter shall be brought to a stop, and if the circum- 
stances require it, the engine shall be stopped, provided such signal 



TRAFFIC RULES AND REGULATIONS 595 

be given in good faith and under circumstances of necessity. Such 
vehicle shall remain stationary so long as may be reasonable to allow 
such horse to pass. (12605 G. C.) 

Sec. 11 — In case of injury or damage to person or property, 
due to the operation of vehicle, the operator or driver of said vehicle 
shall stop, and, upon request of the person injured or any one present, 
give his name and address and that of the owner of the vehicle. 
(12606 G. C.) 



ARTICLE VI — SIGNALS, HORNS, SIGNS AND NOISES 

Sec. i — All motor vehicles and bicycles shall be equipped with 
a suitable bell or horn for signalling. (12614 G. C.) 

Sec. 2 — When a vehicle is slowing up or stopping, the driver 
shall give a timely signal to those in the rear, by raising the arm or 
whip vertically (preferably) or horizontally or by some other unmis- 
takable manner. 

Sec. 3 — When about to turn either from a standstill or while in 
motion, the driver of a vehicle shall give timely signal by hand or 
whip or in some other unmistakable manner, to indicate the direction 
of the turn. This is especially important when turning to the left. 

Sec. 4 — Before a vehicle is backed, the driver shall give timely 
warning. 

Sec. 5 — Sound signals are prohibited except for necessary warn- 
ing, and must be reserved for that purpose. Signals shall not be 
sounded by unauthorized persons on standing vehicles. 

Sec. 6 — All signs, signals and orders of a traffic officer shall be 
promptly complied with. 

Sec. 7 — Every driver of a motor vehicle shall give a timely warn- 
ing when overtaking a person or vehicle on a road or when approach- 
ing a crossing or curve where the sight of approaching vehicles may 
be obscured. 

Sec. 8 — No vehicle shall be so loaded as to cause an objectionable 
or unnecessary noise by parts of the load striking together or upon 
the vehicle. 

Sec. 9 — The use between the hours of 8 P. M. and 6 A. M. of 
the muffler cut-out or the production of any other unnecessarily 
loud noise on any vehicle, is prohibited within 100 yards of any 
residence or within such distance as might seriously disturb the in- 
habitants of such residence. 

Sec. 10 — No vehicle shall pass over any road which is closed 
against traffic to be repaired or constructed. A suitable sign or 
barricade shall be considered as sufficient evidence that such road 
is closed. (13421-9 G. C.) 



ARTICLE VII — RIGHT OF WAY 

Sec. 1 — Every driver of a vehicle approaching the intersection 
of a road where a traffic officer is not stationed, shall grant the right 
of way at such intersection to any vehicle approaching from his right. 



596 TRAFFIC RULES AND REGULATIONS 

Sec. 2 — A vehicle in front of a street car shall immediately turn 
out upon the signal of the operator of the car. 

Sec. 3 — A vehicle shall not so occupy any road as to obstruct 
traffic. 

Sec. 4 — When in the performance of duty, the following vehicles 
shall have the right of way: Police, Fire, Fire Patrol, Ambulance, 
U. S. Mail; also the militia. 

Sec. 5 — During blockades and stoppages a clear space shall be 
kept open between all street cars at crossings. 

Sec. 6 — Pedestrians about to get on, or just having been dis- 
charged from, a street car shall have the right of way and vehicles 
shall come to a stop when necessary to give such pedestrians the right 
of way. 

ARTICLE VIII — LIGHTS 

Sec. i — Motor vehicles shall display between 30 minutes after 
sunset and 30 minutes before sunrise, two white lights in front of 
sufficient power to be visible 200 feet away in the direction the vehicle 
is moving, and one red light visible in the opposite direction; also 
one rear white light which shall illuminate and make plainly visible 
the license number tag. Provided that motorcycles need have but 
one front light. (12614 G. C.) 

Sec. 2 — During the same period given in Sec. 1, bicycles shall 
have a light of sufficient power to be seen 200 feet in the direction 
the bicycle is moving. 

Sec. 3 — Bright lights on any vehicle or street car operated within 
the limits of the right of way of any road shall be dimmed or con- 
trolled while approaching and passing another vehicle so as to pro- 
tect from the direct glare, the eyes of a driver 200 feet ahead and whose 
eyes are 5 feet above the road surface. 

Sec. 4 — In order to avoid accidents and for the purpose of secur- 
ing the greatest possible safeguard to human life, all drivers of horse 
drawn vehicles are urged and requested to display a light at night 
that can be seen both in front and in the rear. 



ARTICLE IX — MISCELLANEOUS REGULATIONS 

Sec. i — The unnecessary emission of dense smoke from motors 
is forbidden. 

Sec. 2 — No horse or other domestic animal shall be allowed to 
run loose and unattended upon the road. 

Sec. 3 — No vehicle shall be used or so loaded as to permit its 
load to be scattered over the road in such a way as to be objectionable 
to traffic or detrimental to the road. In no case shall ashes, garbage 
or other vegetable matter be scattered over the road surface. 

Sec. 4 — No one shall ride on any vehicle without the consent of 
the driver. 

Sec. 5 — No road shall be blocked or obstructed by any farm 
implements or other machinery or obstructions except when the 
road is legally closed for repair or construction. (13421-11 G. C.) 



TRAFFIC RULES AND REGULATIONS 597 

Sec. 6 — No person shall operate a motor vehicle while in a state 
of intoxication. (1 2626-1 G. C.) 

Sec. 7 — Any special rules or regulations jor any road or portion 
of a road which are conspicuously displayed at either end of such 
road or have been made known to the driver of a vehicle by a road 
official, shall be strictly observed by all drivers of vehicles over the 
road. (7246 G. C.) 

Sec. 8 — Drivers of vehicles shall observe such care as is neces- 
sary to preserve the life of the road; — avoid following the tracks of 
a vehicle preceding them, and avoid driving in the ruts that may 
have started to form in the road surface. 

Sec. 9 — Any person operating a vehicle or moving a load, or 
who is responsible for the operating of a vehicle or the moving of a 
load over a road in violation of any of the rules and regulations apply- 
ing to such road, in addition to the fine imposed shall be responsible 
for all damage which said road may sustain as a result of such vio- 
lation. (13421-17 G. C.) 

While a good set of Traffic Rules and Regulations will be of great 
service to the public, yet in connection with any set of rules and regu- 
lations that may be in force, it will be necessary for drivers to exer- 
cise common sense and good judgment to avoid accidents and protect 
the roads. By a careful distribution of the traffic over a good road 
surface, roads may be made to last several times as long as they will 
last when all traffic concentrates in a single track. Every individual 
should remember that he helps build and maintain the roads regard- 
less of the direct taxes he pays, and hence it is to his interest that the 
roads be used in such a way as to preserve them and render the 
greatest service to the general public. 

APPENDIX 

Sec. 6290 (G. C.) ["Motor vehicle" defined.] The term 
"motor vehicle," as used in this chapter and in the penal laws, except 
where otherwise provided, shall be deemed to include all vehicles 
propelled by power other than muscular power, except road rollers, 
traction engines, police patrol wagons, police automobiles, public 
ambulances, vehicles run upon rails or tracks, fire engines, fire trucks 
or other vehicles or apparatus belonging to any police department, 
municipal fire department, volunteer fire company or salvage com- 
pany, organized under the laws of Ohio, or used by such police depart- 
ment, volunteer fire company, or salvage company, in the discharge 
of its functions or in transporting its officers, members, employes, 
men or articles necessary and proper for the proper discharge of 
such functions, to or from a fire or in response to any alarm of fire 
or to any other alarm or call to which it may respond. (100 v. 72; 
Am. 103 v. 763; 106 v. 139). 

Sec. 6310 (G. C.) [Meeting vehicle on highway.] A person 
driving a carriage or vehicle on a public turnpike, road or highway, 
on meeting a carriage or vehicle, shall keep to the right so as to leave 
half of the road free for the coming vehicle. 



598 TRAFFIC RULES AND REGULATIONS 

A person riding on horseback or on a bicycle, tricycle, or tandem 
bicycle, or driving a locomobile, automobile, or any motor vehicle 
operated by its own power, on meeting a carriage or vehicle drawn 
by horses or oxen, shall keep to the right so as to leave one-half of 
the road free for the use of the vehicle drawn by horses, mules or 
oxen. 

A person driving a carriage, vehicle, automobile, or any kind of 
vehicle, who desires to pass a vehicle going in the same direction on 
any public road or highway shall give an alarm or demand to the 
person or persons driving the vehicle in front and going in the same 
direction, of such desire, and the person so driving the front vehicle 
shall immediately give the half of the road to the rear vehicle, by 
turning to the right, so that the rear vehicle can pass to the left of 
the front vehicle. 

[Definition; penalty.] The term vehicle herein shall apply 
to any vehicle propelled by its own power or drawn by horses or oxen. 
Any person or persons driving any vehicle, horse-drawn or otherwise, 
on any public road, who shall fail, in meeting or passing, to give the 
required road as herein stated, shall be subject to a fine in a court 
having jurisdiction thereof, in any sum not less than one dollar, nor 
more than ten dollars, and costs of prosecution. (R. S. Sec. 3490. 
Am. 103 v. 556). 

Sec. 7246 (G. C.) [Publication of traffic rules and regula- 
tions; special rules; enforcement.] The state highway com- 
missioner within sixty days after the taking effect of this act, shall 
prepare and publish a set of traffic rules and regulations governing 
the use of, and traffic on, all state roads. All rules and regulations 
that are to apply generally throughout the state, including those 
applicable to roads constructed of the various kinds of road material, 
shall become effective thirty days after publication. Special rules 
and regulations or orders, applying only to specified sections of 
state roads, shall become effective as soon as posted at each end, and 
at all road crossings on such specified section. For the purpose of 
carrying into effect the provisions of this section, it shall be the duty 
of the state highway commissioner, the county commissioners, the 
county highway superintendent, the township highway superinten- 
dent, township trustees, and all patrolmen or deputies employed 
on any highways within the state, to prosecute any violation of this 
section. It shall be unlawful for any person or persons, firm or cor- 
poration to enter upon, or travel over said state roads, except in 
accordance with the traffic rules and regulations promulgated by 
the state highway commissioner. 

Sec. 7477 (G. C.) [Weight of load and tire width pre- 
scribed.] No person, firm or corporation, in a county having 
macadamized, graveled or stone roads shall transport over such roads, 
in a vehicle having a tire of less than three inches in width, a burden, 
including weight of vehicle, of more than thirty-four hundred pounds. 

[Board of directors and duties; penalty.] The county com- 
missioners shall constitute a board of directors for their respective 
counties, with power to prescribe the increased gross weight in excess 
of thirty-four hundred pounds that may be carried, including weight 



TRAFFIC RULES AND REGULATIONS 599 

of vehicles, in vehicles having a width of tire three inches or upwards, 
and cause such regulations to be recorded in their journal. Any 
person violating this section or any regulation duly prescribed by the 
board of county commissioners, made in pursuance thereof, shall be 
fined not less than five dollars nor more than fifty dollars. 

[Enforcement of traffic regulations.] The township trustees 
of any township and the county commissioners of any county, shall 
cause to be prosecuted all persons violating this section or any regu- 
lations prescribed by the board of county commissioners made in 
pursuance of the authority conferred in this section. The county 
commissioners within their respective counties, may appoint a suit- 
able person or persons to enforce such section and regulations. The 
person or persons so appointed shall receive for each conviction by 
them secured under this section, such portion of the fine or penalty 
as the commissioners deem just and proper. 

Sec. 7478 (G. C.) [Publication of traffic rules in coun- 
ties.] The state highway commissioner shall furnish the county 
highway superintendent with a copy of the rules and regulations pro- 
mulgated by said state highway commissioner, and applicable to his 
county. The county highway superintendent shall cause the rules 
and regulations so furnished to him by said highway commissioner 
to be published, at least once each week, for two successive weeks, 
in a newspaper published and of general circulation in said county, 
if there be any such paper published in said county, but if there be 
no newspaper published in said county then in a newspaper having 
general circulation in said county. When such regulations are pub- 
lished in the manner aforesaid, it shall be deemed a sufficient pub- 
lication under the provision of this act. 

Sec. 12603 (G- C.) [Operating motor vehicle unreasonably 
and improperly; penalty.] Whoever operates a motor vehicle 
or motorcycle on the public roads or highways at a speed greater 
than is reasonable or proper, having regard for width, traffic, use and 
the general and usual rules of such road or highway, or so as to en- 
danger the property, life or limb of any person, shall be fined not 
more than twenty-five dollars* and for a second offense shall be fined 
not less than twenty-five dollars nor more than fifty dollars. (99 
v. 541, 543, Sees. 14, 25. Am. 103 v. 161). 

Sec. 12604 (G. C.) [Violation of speed limit.] Whoever 
operates a motorcycle or motor vehicle at a greater speed than eight 
miles an hour in the business and closely built-up portions of a 
municipality or more than fifteen miles an hour in other portions 
thereof or more than twenty miles an hour outside of a municipality, 
shall be fined not more than twenty-five dollars, and for a second 
offense shall be fined not less than twenty-five dollars nor more than 
fifty dollars. (99 v. 541, 543, Sec. 15, 25). 

Sec. 12605 (G. C.) [Failure to stop motor vehicle when 
signalled.] Whoever, operating a motor vehicle, fails to slow down 
and stop it when signalled so to do upon meeting or overtaking a 
horsedrawn vehicle or person on horseback and to remain stationary 
until such vehicle or person has passed, provided such signal to stop 
is given in good faith, under circumstances of necessity, and only 



600 TRAFFIC RULES AND REGULATIONS 

as often and for such length of time as required for such vehicles 
or person to pass, whether approaching from the front or rear, shall 
be fined not more than twenty-five dollars, and for a second offense 
shall be fined not less than twenty-five dollars nor more than fifty 
dollars. (99 v. 541, 543. Sees. 16, 25). 

Sec. 12606 (G. C.) [Failure to stop motor vehicle in case 
of accident.] Whoever, operating a motor vehicle on a public road 
or highway, in case of an accident to a person or property thereon 
due to the operation of such motor vehicle, fails to stop upon the 
request of the person injured or a person present, give his name and 
address, and, if not the owner thereof, the name and address of such 
owner, shall be fined not more than twenty-five dollars, and for a 
second offense shall be fined not less than twenty-five dollars nor more 
than fifty dollars. (90 v. 541, 543, Sees. 16, 25). 

Sec. 12607 (G. C.) [Third or subsequent offense.] For a 
third or subsequent offense, a person convicted of a violation of any 
provision of the next four preceding sections, shall be fined not less 
than fifty dollars nor more than one hundred dollars or imprisoned 
not more than thirty days, but if such subsequent offense occurred 
within one year after any former offense, he shall be imprisoned not 
less than ten days nor more than thirty days. (99 v. 543, Sec. 25.) 

Sec. 1 2614 (G. C.) [Penalty for failing to provide motor 
vehicle with bell, brakes, and lights.] Whoever operates or 
drives a motor vehicle upon the public roads and highways without 
providing it with sufficient brakes to control it at all times and a suit- 
able and adequate bell or other device for signalling, or fails during the 
period from thirty minutes after sunset to thirty minutes before 
sunrise to display a red light on the rear thereof and three white 
lights, two on the front and one on the rear thereof, the rays of which 
rear white light shall shine upon and illuminate each and every part 
of the distinctive number borne upon such motor vehicle, the light 
of which front lamps to be visible at least two hundred feet in the 
direction in which such motor vehicle is proceeding, shall be fined 
not more than twenty-five dollars. Provided, that motor vehicles 
of the type commonly called motor cycles shall display one white 
light in front to be visible at least two hundred feet in the direction 
in which such motor vehicle is proceeding, and one rear combination 
red and white lights showing red in the direction from which such 
motor vehicle is proceeding, and such rear light to be so placed that 
it will reflect its white light upon and fully and clearly illuminate the 
distinctive license identification mark of such motor vehicle. (99 
v. 540, 543, Sees. 12, 24. Am. 103 v. 766). 

Sec. i 2628-1 (G. C.) [Intoxicated person operating motor 
vehicle upon public highway or street, unlawful.] That it shall 
be a misdemeanor for any person to operate a motor cycle or motor 
vehicle of any kind upon any public highway or street while in a state 
of intoxication, and upon conviction he shall be subject to punish- 
ment by a fine not less than twenty-five dollars, nor more than one 
hundred dollars, or imprisonment in the county jail for not more 
than six months, or both. (99 v. 544, Sec. 32. Am. 103 v. 133). 

Sec. 13421-9 (G. C.) [Driving over closed highway ; penalty.] 



TRAFFIC RULES AND REGULATIONS 601 

Whoever drives over, upon, along or across a public highway, or 
any part thereof, which has been closed, while in the process of con- 
struction, reconstruction or repair by order of the state highway 
commissioner, county highway superintendent, county commis- 
sioners, township trustees or other official or employe having au- 
thority to close such highway, shall be fined not more than fifty 
dollars, nor less than five dollars. 

Sec. 1342 i-i i (G. C.) [Placing obstruction in highway; 
penalty.] Whoever unlawfully places any obstruction in, or upon 
a public highway, shall be fined not more than fifty dollars, nor less 
than five. dollars. 

Sec. 1342 i-i 2 (G. C.) [Driving traction engine with destruc- 
tive tires; penalty.] • Whoever drives over the improved highways 
of the state, or any political subdivision thereof, a traction engine 
with tires of wheels equipped with lugs, spikes, chains or other pro- 
jections seriously destructive to such highways, or by any other 
means damages such highways, shall be fined for each offence 
not less than ten dollars nor more than two hundred dollars. 

Sec. 13421-14 (G. C.) [Digging, excavating, piling earth or 
building fence on highways; penalty.] Whoever digs up, removes, 
excavates or places any earth or mud upon any portion of any public 
highway or builds a fence upon the same without legal authority or 
permission so to do, shall be fined not more than two hundred dollars 
nor less than ten dollars. Each day that such person continues to 
dig up, remove or excavate any portion of the public highway shall 
constitute a separate offence. 

Sec. 1342 1-16 (G. C.) [Placing nails, tacks, glass, etc., upon 
highway ; penalty.] Whoever places upon any part of a public 
highway, lane, road, street or alley, any tacks, bottles, wire, glass, 
nails or other articles, except such substances as may be placed there 
by proper authorities for the repair or construction thereof, which 
may damage or injure any person, vehicle or animal traveling along 
or upon said public highway, shall be fined' not more than two hun- 
dred dollars or imprisoned not more than six months or both. 

Sec. 1342 i-i 7 (G. C.) [Violation of traffic rules; penalty.] 
Whoever enters upon, or travels over any portion of the highways, 
within the state, in violation of the traffic rules and regulations duly 
prescribed by law, or the state highway commissioner, or the county 
highway superintendent of any county, shall be fined not more than 
one hundred dollars, nor less than five dollars, and in addition thereto, 
such person shall be liable for all damage done to such highway. 



602 TRAFFIC RULES AND REGULATIONS 



State of New York 
Highway Commission 

AMENDED RULES AND REGULATIONS FOR STATE 
AND COUNTY HIGHWAYS 

Adopted by the Commissioner of Highways of the State of New York 

Sec. i. No traction engine, road engine, hauling engine, trailer, 
steam roller, automobile truck, motor or other power vehicle shall be 
operated upon or over State or County Highways of this State, the 
face of the wheels of which are fitted with flanges, ribs, clamps, 
cleats, lugs or spikes. This regulation applies to all rings or flanges 
upon guiding or steering wheels on any such vehicle. In case of 
traction engines, road engines or hauling engines which are equipped 
or provided with flanges, ribs, clamps, cleats, rings or lugs, such 
vehicles shall be permitted to pass over such highways provided that 
cleats are fastened upon all the wheels of such vehicles, not less than 
2\ inches wide and not more than i \ inches high, and so placed that 
not less than two cleats of each wheel shall touch the ground at all 
times, and the weight shall be the same on all parts of said cleats. 

The foregoing regulations relating to flanges, ribs, clamps, cleats, 
rings or lugs shall not apply to traction engines used solely for agri- 
cultural purposes, but the following requirements shall apply to such 
traction engines: 

The guide band on the front wheels shall not be less than two 
inches in width, but no flanges, ribs, clamps, cleats, rings or lugs 
shall be required upon the front wheels. The full set of cleats upon 
the rear wheels of the original design as furnished with the engines 
must be used, and no rivet heads or bolt heads shall project, and the 
use of such traction engines for agricultural purposes shall not permit 
the use for hauling purposes, excepting the hauling of threshing and 
other agricultural equipment necessary for threshing and agricultural 
purposes. 

This provision shall in no case relieve the owner of any traction 
engines from liability for damage to roads from defective wheels. 

' The use also of ice picks or mud lugs shall be strictly prohibited 
on State and County Highways. 

Sec. 2. No traction engine, trailer, steam roller, automobile 
truck, motor or other power vehicle shall be operated upon or over 
the State or County Highways of this State, nor shall any object be 
moved over or upon any such highways upon wheels, rollers or 
otherwise, in excess of a total weight of fourteen tons, including the 
vehicle, object or contrivance and load, without first obtaining the 
permission of the State Commission of Highways as hereinafter 
provided. No' weight in excess of nine tons shall be carried on any 
one axle of any such vehicle. 

Sec. 3. The tire of each wheel of a traction engine, road engine, 
hauling engine, trailer, steam roller, automobile truck, motor or 
other power vehicle (except traction engines, road engines, and haul- 
ing engines) shall be smooth, and the weight of such vehicle, including 



TRAFFIC RULES AND REGULATIONS 603 

load, shall not exceed 800 lbs. upon' any inch in width of the tire, 
wheel, roller or other object, and any weight in excess of 800 lbs. 
upon an inch of tire is pibrohited unless permission is obtained from 
the State Commission of Highways as hereinafter provided. 

Sec. 4. No motor or other power vehicle shall be operated upon 
any State or County Highway of a greater width than ninety inches, 
except traction engines which may have a width of one hundred ten 
inches. 

Sec. 5.. No traction engine, road engine, hauling engine, trailer, 
steam roller, automobile truck, motor, or other power vehicle, carry- 
ing a weight in excess of four tons, including the vehicle, shall be 
operated upon any State or County Highway of this State at a speed 
greater than fifteen miles an hour; and no such vehicle carrying a 
weight in excess of six tons, including the vehicle, shall be operated 
upon any such highway at a speed greater than six miles an hour 
when such vehicle is equipped with iron or steel tires, nor greater 
than twelve miles an hour when the vehicle is equipped with tires of 
hard rubber or other similar substance. 

Sec. 6. The State Commission of Highways of the State of New 
York, upon proper application in writing, may grant permission for 
the moving of heavy vehicles, loads, objects, or structures in excess 
of a total weight of fourteen tons over its State and County High- 
ways upon proper application in writing being made therefor, and 
under such restrictions as said Commission may prescribe. 

Sec. 7. The owner, driver, operator or mover of any vehicle over 
any State or County Highway shall be responsible for all damage 
which said highway may sustain as a result of a violation of any of 
the provisions of the foregoing Rules and Regulations, and the 
amount thereof may be recovered in an action of tort by the State 
Commission of Highways or by any County Superintendent of 
Highways of any county or by any Town Superintendent of High- 
ways in any town in which said violation occurs. 

Sec. 8. These amended regulations to take effect February 24, 
1914. 



" Section 24 of Chapter 25 of the Consolidated Laws, entitled 
'The Highway Law,' provides that any disobedience of any of the 
foregoing rules and regulations shall be punishable by a fine of not 
less than $10, and not more than $100, to be prosecuted by the 
Town, County or District Superintendent, and paid to the County 
Treasurer to the credit of the fund for the maintenance of such 
highways in the town where such fine is collected." 



INDEX 



A 

Adjustment of instruments 164 

Alignment 18, 144, 206 

Annual charges 108 

Amiesite 82, 285, 441 

Arch Culverts 48, 305 

Areas, formulae 462 

of cross-sections 226 

right of way 261, 262 

Asphalt, Rock 82, 283 

Asphalt Binder (Bituminous Ma- 
terial A) 383-385 

Asphalt Block 85, 290, 449 

Asphalt pavement, 

Concrete foundation for . .327, 427 
Topeka Mix (Mixing Method 

type II) 81. 101, 351, 437 

Asphalt, Sheet, weight of . 352 

Asphaltic Concrete _ (see Bitumi- 
nous Macadam mixing method). 
Asphalts (see Bitumens) 
Automobiles 18, 62, 591,602 

B 

Banked curves 31 

Beam Bridges 43, 44-47 

Beams, bending moments 586 

Beams, steel, properties of 59 

Bench marks 146 

Bitulithic Pavements 439 

Bitumens . . . 130, 377, 382 

Bituminous Binder, Cost of appli- 
cation 281 

Bituminous Macadam, bottom 

course. .65,425 
Contrac- 

tor'splant..3ii 
Costs in 

detail.. 266-312 
crown .... 19, 80 

life_ 3, 107 

mainte- 
nance. .97, 105 
mixing 

methods. . 
81, 101, 351, 437 
penetration 
method. . 

78, 348, 433 
specifica- 
tions. .433,437 
typical 
section. . 
23, 29, 30, 31 

(605 



Bituminous materials 130, 377, 382 

surfacings 

76, 77, 99, 332, 432 
amounts required 

264, 265 

Blasting small boulders 278 

Bonds, Highway 2 

Bottom course, broken stone 65 

construction of . . . 346 
economic design. 73 

gravel 67, 69 

macadam roads. .65, 425 

stone fill 71, 281 

sub-base .... 24, 68, 281 

Boulders, cost of sledging 278 

Brick, properties 129 

tests 390 

Brick cube pavement 92, 284 

Brick pavements 83 

construction .354, 451 

crown 19, 85 

detail costs.;. . . 327 

edging 

24, 83, 328, 355, 417 
estimate of cost 331 
expansion joints. 83, 

84, 329, 330, 452 
foundation .... 

84, 327, 356, 427 
grout 143, 329, 

330,357,375,453 

life of 3, 107 

maintenance. . . 

102, 107 
mortar bed .... 83 
sand cushion. . . 83, 

328. 356. 375, 452 
specifications. . . 451 
typical sections 

24, 31, 83 

Bridge rail and parapets 112 

Bridges, approximate weight of 

plate girder 259, 260 

small span 39 

Burkli-Ziegler formula for run off . 36 

C 

Calcium chloride . . . 76, 334 

Cast-iron, specifications 398, 419 

weight 584 

Cast-iron pipe, culverts ... 3.3, 38, 58, 358 
specifications. . .398, 407 
weights of 54 

) 



6o6 



INDEX 



Catch basins. 116, 406 

Cement, for grouting 330 

specifications 372 

tests and requirements 141, 373 

weight 584 

Center of gravity 588 

Circles, areas and circumferences. . 464 

Clearing and grubbing 401 

Concrete, aggregates 142, 374, 444 

materials, amounts re- 
quired . . . 289, 303, 304, 360 
mixing and placing . .360, 411 

sizes of stone 143 

specifications for ma- 
terial 374 

weight 584 

Concrete culverts, capacities 38 

construction. 350-359 

costs 38, 302-305 

forms. 359, 412 

quantities . . . 304, 361 

standards 

40, 41, 44-51 

Concrete foundations 84, 327, 427 

Concrete Guard Rail no, 306 

Concrete Masonry 410 

Concrete pavement 87 

construction. . 

288, 443 

crown 23, 87 

detail costs. 288-303 
expansion joints 
87. 90, 91, 295, 396 

forms 294 

Hassam type 288, 
350, 442 

life 107 

maintenance . . . 

101, 107 
plant and 

labor .... 289-303 
specifications. . 

_ 442. 443 
typical sec- 
tions 23 

Construction plans 257 

Conversion tables, cu. ft. to cu. yds. 230 
feet to miles. . . 250 
general table. . . 459 

Cosecants, natural 502 

Cosines, logarithmic 539 

( natural 490 

Cost estimates 312 

of miscellaneous minor items 320 

of Roads per mile 3, 108 

of staking out 340 

Costs, comparative: Amiesite 81 

Asphalt Block. 86 
Bituminous 

Macadam. . . 79 
Bituminous 

surfacing. ... 77 
Brick pave- 
ment 84 

Concrete pave- 
ment 87 

Rock Asphalt . . 82 



Costs, comparative: Stone Block 

Pavement. . . 85 
Waterbound 

Macadam . . 74 

Cotangents, logarithmic 539 

natural 479 

Cross-sections, areas . . . . f 226 

notes 146, 209 

templets for 221 

Crowns (see type of pavement) 

parabolic 262 

Crushing stone, cost 274 

proportions of 

sizes 275 

Cubes 91, 92, 284 

cubic feet to 
cubic yards 230 

Culling Brick 332, 356 

Culverts ^ 

capacities 38 

construction 358 

standards 49 

curbs 113, 115, 415 

Curves, banked 31 

functions of i° 170 

length of 170 

methods of running 199 

problems 200-205 

radii of 167 

sharp, avoidance of 18 

tangent length 197 

vertical (see vertical curves) 

D 

Danger signs : . 114, 422 

Deformed bars, areas and weights 57 

specifications 398 

Depth of pavement 64, 74^92, 345 

Depreciation of Contractor's equip- 
ment 309 

Design, economic 263 

reports on 210, 255 

Dicken's formula for Run Off 34 

Distance, measures of 459 

Ditch lining (see gutters) 

Ditches, function of 22 

Drainage 33-60 

notes 149 

Driveway culverts 39 

Double Meridian Distance areas. . 261 

Drop inlet 39. 4°6 

Durax 91 

Dust layers 76, 97-100 

Dustless screenings 280 

E 

Earth, shrinkage of 219 

weight ; 584 

Earth excavation, computation of. 227 

Earth excavation, detail costs 266 

methods. . . . -34 1 . 354 
specification. ... 401 
table of volumes 

228, 238-249 
variation of. . . . i4 _I 7 



INDEX 



607 



Edging 24, 83, 328, 355. 417 

Embankments 64, 342, 403 

shrinkage of earth. 2ig 

Equipment, contractors. . 3°Q 

Estimates of costs, forms for 312 

Excavation (see Earth Excavation) 

Expanded metal 55,-398 

Expansion joints, Brick Pavements 

83, 84, 329, 357, 330, 452 
Concrete Pave- 
ments 

87, 90, 91, 295, 396 



Guard Rail 109, no, 306, 334, 420 

Guide signs 114, 421 

Gutters 115, 307, 417 



H 

Hassam concrete pavement, 288, 350, 442 

Haul, computation of length 320 

Hauling stone, cost 269 

Highway bonds 2 

Horse, tractive power of 6-10 



Field stone, cost of loading 271 

Fillers, bottom course, amount re- 
quired . . 

272, 347 
cost load- 
ing and 
spreading 273 
require- 
ments 129, 426 

Fills, earth 64, 219, 342, 403 

stone 71, 281, 408 

Financing highway improvements 

2, 108 

Foot, decimal equivalents of 460 

Forms, concrete pavement 294 

removal of 359 

specifications 412 

Foundation courses, macadam. . . .61-72 

Foundation soils .61-72, 151, 344 

Functions, Trigonometric, loga- 
rithmic. ..539-583 
natural. . -479 - 5i3 



Geological classification of rocks 

125-127 

Glutrin (sulphite liquor) 77, 445 

Grade crossing eliminations 258 

Grades 4 -1 7 

controlling features 13 

economy of . 13, 221 

effect on hauling 10 

maximum, practice as to. . 5 
asphalt (3|%) 
asphalt block .87, 219 
bituminous ma- 
cadam 80, 219 

brick 85, 219 

concrete 87, 219 

rock asphalt. . . 82 
stone block . .85, 219 
waterbound 

macadam. .75, 219 
woodblock .... 219 

minimum 12 

selection of n, 12 

Grading 341 

Gratings. 116, 117 

Gravel, bottom course 67-69 

specifications 143, 376 

Gravity, center of 588 

Grouting. . . 143, 329, 330, 357, 375 , 453 



Igneous rocks 126 

Inches as decimals of a foot 460 

Interest of plant and payroll 310 

Inertia, moments of 589 

Inspection of construction (see 

Chapter XI) 

Instruments, adjustment of 164 



Kentucky rock asphalt 82, 283 

Kleinpflaster 91 



Land taking surveys 154, 262 

Leaching basins 116, 405 

Level, adjustment of 164 

notes 146, 208 

Levelling, accuracy required 146 

Life of pavements 3, 106-108 

Lignin 77, 445 

Linear measures 459 

Loading stone and filler, costs .... 

268, 271, 273 

Logarithmic functions 539-583 

Logarithms of numbers 514-538 

Lumber 400, 409 

M 

Macadam (see Waterbound and 
Bituminous Macadam) 

Machinery, contractors' 309 

Maintenance 96-108, 337, 338 

Manholes 407 

Maps, preparation of 206-265 

Masonry, concrete 410 

stone 414 

repointing 117 

Mass diagram 251-253 

Materials, strength of 585 

tests 118-143 

report on location 152 

Maximum grades (see Grades, Max- 
imum) 

McClintock cubes 92, 284 

Mesh reinforcement 55, 398 

Metamorphic rocks 127 

Metalling, width of 28, 263 

Moduli of elasticity 585 

Moment of inertia . 589 

Motor truck regulations . . .62, 591, 602 



6o8 



INDEX 



N 

Natural cement 141 

Natural trigonometric function. .479-513 



Oil, table of quantities . . 264 

Oiling (see Bituminous Surfacing) 

Overhaul 251, 404 

Overhead charges 309 

P 

Parabolic crown for pavement .... 262 

Pavements, cost per mile . ._ 3, 108 

economic selection ... 74, 96 

life of 3> 106-108 

maximum grades (see 
Grades, Maximum) 

typical sections 23-32 

thickness. . . .64, 74~Q2, 345 
types (see respective 
headings) 
Amiesite 
Asphalt 
Asphalt Block 
Asphaltic Con- 
crete 
• Bituminous Ma- 
cadam Pene- 
tration 
Bituminous Ma- 
cadam Mixed 
Brick 
Concrete 
Durax 

Kleinpflaster 
McClintock 

Cubes 
Rocmac 
Rock Asphalt 
Stone Block 
Waterbound 
Macadam 

Pavement, width 28, 263 

Paving pitch, expansion joints. .330, 452 

Petroleum 136, 137 

Piles 408 

Pipe, cast-iron, culverts. . .35, 38, 58, 358 
specifications. . .398, 407 

weight 54 

vitrified 3°7» 400, 4°4 

Pipe rail 112, 421 

Pitch expansion joints 330, 452 

Planimeter, use of 226 

Plans, preparation of 206-265 

Plants and payroll 309 

Plate girder bridge weights. . . . 259, 260 

Portland cement 141, 372 

Posts, concrete sign 422 

Profile, plotting of 209 

Puddling, waterbound macadam. . 283 

R 

Radii of curves 167 

Rattler for brick tests 39° 

Reference points 144 



Reinforcement, specifications . . .398, 418 
weights and areas. 55-57 

Relaying old pipe 407 

Repairs (see Maintenance) 

Repointing masonry 117 

Report on design 210, 255 

on materials 152 

on soil 151 

Resurfacing macadam 335 

Retaining walls 111-112 

Rights of way . . 154, 262 

Riprap 117, 409 

Road materials, tests and prop- 
erties. . 1 18-143, 372-382 

Road sections, typical 23-32 

Roads, improved, advantage of . . . 10 

Roadway travelled, width of 20 

Rock, excavation 220, 266, 402-404 

geological classification 125 

properties 122-125, 128 

tests 1 18-128 

Rock asphalt 82, 283 

Rocmac 94 

Rolling, cost of 273 

resistance 7, 10 

Ruling grades (see Grades, Maxi- 
mum) 
Run off 34-37 

S 

Safety measures, banked curves.. . 31 
danger signs . . 114, 422 
grade crossing 
elimination. . . 258 

guard rail 109, no 

shoulder slope ... 19 

shoulder stone . . 29. 90 

sight distance on 

curves. . 18, 208, 225 

Sand, requirements for. . . . 142, 374, 375 

cushion. . . .83, 328, 356, 375, 452 

Scarifying macadam 335, 431 

Screed for concrete pavement 351 

Screenings 128, 272, 280 

Secants, natural 502 

Sedimentary rocks 126 

Shoulder slope 19 

stone 29, 90 

Shrinkage of earth . 219 

Side hill roads, drainage 42 

Sight distances on curves. . . 18, 208, 225 

Signs, guide 114, 421 

danger 114, 422 

Sines, logarithmic 540 

natural 490 

Slag 377 

Slope stakes 341 

Soil 61-72, 344 

Soil examination and report 151 

Specifications, typical 372-458 

Sprinkling 76 

Square roots, table of 464 

yards, table of 263 

Squares, table 464 

Stadia reduction tables 156 

Staking out 339 

Steel 398, 419, 584 



INDEX 



609 



Steel bars, areas and weights 56 

beams., properties 59 

Stone, amounts required for road.. 252 
costs of handling and haul- 
ing. 268-273 

crushing, cost 274 

depths 64, 74-9 2 , 345 

proportions of crusher out- 
put 274 

ratio loose to compacted 

depths 272 

sizes for road work (see 
Pavement T} , pes) 

Stone specifications 376 

tests 1 18-128 

Stone block pavement 

85, 91, 102, 396, 455 
foundation. . 

85, 327, 427 

Stone fills 71, 281, 408 

Stone masonry 414 

Stoneway, width of 28, 263 

Strength of materials 584-587 

Sub-base 64, 345, 423 

bottom course 24, 68, 281 

Sub-grade preparation .65, 344, 354, 403 

Sulphite liquor 77, 445 

Surface measures 459 

Surveys 144-166 

Surveys accuracy required 145 

equipment of party 144 

rights of way 154 

speed 146, 149, 151, 154 



Tangents, logarithmic 539-583 

natural 479-489 

Tar 131, 132-135 

Tar (Bituminous Material T). . .387-389 
Tar surfacing (see Bituminous Sur- 
facing) 

Telford base 69, 423 

Temperature units 459 

Template for concrete pavement . . 351 
Tests of materials .... 1 18-143, 372-382 

Tile, porous. . . . : 400 

vitrified 307, 400, 404 

Timber 400, 409 

Tire, allowable load 62-63 

effect of, on tractive power. . 7, 9 

Toe walls 113 

Top course, economic selection ... 74, 96 
Topeka mix (Mixing Method II) 

81, 101, 351, 437 

Topography notes 150, 208 

Traction engines 4, 62, 591, 602 

Tractive power 6-10 

Traffic, classification of roads as to 74 

regulations 62, 591, 602 

report on 151 

Transit, adjustment 165 

points 144 

Traverse computation 155 

Triangles, solution of 477 

Trigonometric formulae 477 



Trigonometric functions, loga- 
rithmic 530-583 

natural 

479—503 

Trucks, automobile 62, 271 

allowable load- 
ing... 62, 591, 602 

U 

Underdrains 42, 52, 405 

Unloading stone, cost 268 

V 

Velocities of flow 33, 58 

Vertical curves 222, 223, 225 

Vitrified pipe 307, 400, 404 

Voids, determination of 89 

Volume formulae 462 

measures 459 

W 

Wagon, allowable loads on. . . 62. 591, 602 

Water, amount for concrete 304 

puddling 284 

weight 584 

Waterbound macadam 23, 74, 348 

Waterbound macadam, bottom 

course 65-70 

Waterbound macadam, compara- 
tive cost 74 

Waterbound macadam, construc- 
tion 348 

Waterbound macadam, contractor's 

plant 310 

Waterbound macadam, costs in de* 

tail 266-312 

Waterbound macadam, crown . . .19, 75 
Waterbound macadam, life of . . . .3, 106 
Waterbound macadam, mainte- 
nance 97, 106 

Waterbound macadam, resurfac- 
ing . . 335 

Waterbound macadam, specifica- 
tions 428 

Waterbound macadam, typical 

sections. 23-28 

Weights, cast-iron pipe 54 

expanded metal 55 

materials 584 

steel bars 56, 57 

stone 252 

units 459 

Wheel, effect of size on tractive 

power 8 

Width of pavement 20, 263 

Wood block 219, 446 

W^ork, speed of 3°8 

Working stresses 585 

W T rought-iron specifications. . . .398, 419 

Y 

Yearly charges 108 



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